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Add eSign Presentation Computer. Check out by far the most consumer-warm and friendly knowledge of airSlate SignNow. Handle your complete document finalizing and sharing program electronically. Change from portable, pieces of paper-based and erroneous workflows to automated, computerized and flawless. You can actually produce, produce and indication any papers on any system anyplace. Be sure that your crucial organization circumstances don't slide overboard.
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FAQs
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What is the most asked question on Quora (by the number of questions merged into it)?
As someone who writes mostly technology-related answers, I see the following question so much it makes me want to tear my hair out:“Can iCloud Activation Lock be Bypassed?”For those who don’t know, Apple devices that have an iCloud account active on them with Find My iPhone enabled will lock the device to that Apple ID even if it is restored to factory defaults. This is designed to prevent thievery, since stolen devices (typically iPhones) are useless without the Apple ID password they are locked with to unlock it. It is incredibly common for people to sell devices without removing the lock beforehand (likely because they don’t know it exists, or how to remove it) or because it is stolen. Either way, the lock cannot be bypassed without that password… but that doesn’t stop everyone and their mother from asking if it can be done as if the rules somehow don’t apply to them.Instead of viewing the answers on an existing question, or even asking new people to answer that existing question, they make a new one. Every. Single. Time. Quora is absolutely flooded with these questions, and I get A2A requests for them more than anything else.
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Will China become an innovator?
Yes. Start with the following chart.Innovation is neatly correlated with per capita GDP. That is because for innovation to thrive, you need low borrowing costs, a stable and moderately advanced economy where the risk adjusted returns of doing conventional things are low, consumer sophistication to generate demand for better goods and a conducive business environment. You just need to take a walk down Nanshan's kejiyuan to see how strong China's innovation system is as a subset of it's conventional investment led economy. Consumer sophistication has pushed China's electronics manufacturers to evolve from shanzhai to innovative brands. Chinese firms are investing heavily in R&D. Huawei, Midea, Haier etc compete internationally not on cost but on product quality. The chart also shows you that China is punching way above its weight when it comes to its performance in innovation relative to per capita GDP, that it is already a better innovator than other countries were at a similar level of economic development. Another way to look at innovation in China is to not consider it monolithic. McKinsey identified four key archetypes of innovation and assessed China's performance in each of them. *Revenue share of Chinese companies relative to China's proportion of global GDP. A score more than one shows that the respective cluster of firms have a global share of more than 14 percent. It is clear that Chinese firms have perform really well in efficiency driven and consumer focused innovation. In engineering based innovation, Chinese firms perform well in sectors where government mandated technology transfer helped them in rapid catch up with established players. China lags signNowly in science based innovation. It is perfectly reasonable to make the case that with proper investments and capital accumulation, China will emerge as an innovator in the leagues of say Japan or South Korea in the coming decades. I suggest you read McKinsey Global Institute's China Effect on Global Innovation to read more on innovation in China.The middle income trap is really just a theory based on the growth trajectory of Latin American countries. If you look in disaggregate terms, a lot of areas in China are high income economies. Beijing, Tianjin, Shanghai, Zhejiang and Shenzhen's GDP per capita is more than $22,000. Per capita GDP of Nanshan, Shenzhen's high technology district $49,000, ahead of Hong Kong and several OECD countries. There is no reason to believe that China as a whole will be become stuck in the middle income trap.
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What digital tool, as a real estate agent, do you most use?
As an agent, we have access to the MLS, which the public only has limited access to. In my area the public can see exactly what Zillow can which is active listings. Our board does not disclose the sales price of closed prices, which makes services like Zillow pretty much worthless in my area. (Zillow may be useful in some areas, perhaps many, just not where I work).That said, my favorite and most useful tool, which is also available to the public, is the GIS (Government Information Service). Type in to Google: (Your county)(Your state) GIS [ie: Marion County Indiana GIS ] . While it isn’t available in every county of the country, you will find it in most major areas. It will give you access to the tax assessor records and often times the sales history of the property. The tax records will give you the details of site size, improvements, assessed values and depending on the county may or may not give you the annual taxes.Since real estate agents in some areas count the basement area when they list the size of the property, the GIS will allow me to figure out what is really there if I’m new to the area. For what I am looking for, there is a signNow difference between a stated 3,600 square foot house by the agent and 1,800 square foot above ground over a 1,800 square foot basement. - Lenders only count the above ground square footage as living area when making a loan.Hope this helps.
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What is the best real estate technology?
A survey conducted by Coldwell Banker and CNET found that eighty-one percent of prospective home buyers were drawn to homes equipped with the latest in-home technology. Among those, thirty-five percent of people who preferred what is known as smart homes over traditional residences believed that such features solidified the property as “move-in ready.”Technology is also changing the field of home selling. Here are five ways that apps and other online features are making the life of a real estate agent easier.1. Broadcasting with Periscope and TwitterWhat better way to send out a massive blast than on Twitter? The social media site lets you keep it short but sweet as you tell followers that the home of their dreams has an upcoming open house session. You can also post pictures on Twitter that give potential buyers a better perspective of what they will see during their in-person tour of the property. Take the virtual showing a step further by using Periscope to share live footage of yourself walking through the house online. In past times, a substantial amount of money was necessary to promote property by way of commercials. Twitter and Periscope bring the perk to you for free so long as you have a smartphone or tablet when going live and taking pictures.2. Tracking with Glympse and WazeRunning twenty minutes behind used to be a deal breaker pre-Digital era. Not only did you inconvenience the client but you also provided a guess that was often inaccurate and led to more time wasted at the property. Traffic apps in the twenty-first century have made such estimating unnecessary.Waze is one app that provides navigation tips based on real-time traffic information. You can better coordinate appointments so that clients are not left waiting for several minutes and provide clearer updates when you are running late. Glympse also tracks traffic in real-time but takes things a step further by offering a link by which clients can track your whereabouts. Text or email the URL to prospective buyers and let them follow along as you make your way to the location.3. Meet Online with Reflector 2 and Join.meReal estate agents should consider investing in Reflector 2 instead of bringing their USB stick along to nail that next listing presentation. The app serves as a sort of projector by allowing you to cast all activity on your smartphone and tablet on a larger screen. The Reflector 2 works with nearly any device and does not require additional purchase outside of the app itself.Free Screen Sharing, Online Meetings & Web Conferencing is another app that has made buying a selling a home more convenient. Agents can hold brief meetings with clients without requiring them to come into the office. Sharing your computer screen is the best way to convey pertinent information to new homeowners. The recording and playback feature is particularly useful when you need to recall a client’s home preferences. They will be impressed with your attention to detail in finding a house with a built-in barbecue pit. You will know that such meticulousness is because of Free Screen Sharing, Online Meetings & Web Conferencing.4. Add Transparency and Rapidity with an Automated Mortgage Loan ProcessThe traditional method of the home loan process involved hours spent trying to secure financing. Leaving one paycheck stub or bank statement at home often meant holding off on the process until the client was able to furnish proof of such documentation. There was no transparency in the process, which meant that customers were entirely reliant on the expertise of the real estate agent.Technological advances have revolutionized the mortgage loan process. Automated processing now establishes criteria by which applicants are judged that makes applying simpler. Some financial institutions can pre-approve hopefuls in ten minutes. Individuals who go through the entire process may see their loans finalized in ten days instead of the average four-week period. Digital tools provide real-time updates so that even those who are not approved can move on to the next bank quickly instead of waiting for a rejection letter to arrive by way of snail mail.5. Agree from Home with E-signaturesIn past times, the thrill of closing quickly became inconvenient for buyers upon hearing that all approved owners would need to stop by the real estate agent’s office to sign final documents. Some individuals were forced to take a sick day from work just to make their mark on the paper. Such heartache is why the masses are thrilled to learn that e-signatures have the same weight as traditional marks on legal documents. A real estate agent can email paperwork that his clients can sign at their leisure and return electronically. It is even possible to solidify documents on a smartphone in some instances, which makes the home loan process that much more convenient.
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Is AI an existential threat to humanity?
Worrying about AI evil superintelligence today is like worrying about overpopulation on the planet Mars. We haven't even landed on the planet yet! AI has made tremendous progress, and I'm wildly optimistic about building a better society that is embedded up and down with machine intelligence. But AI today is still very limited. Almost all the economic and social value of deep learning is still through supervised learning, which is limited by the amount of suitably formatted (i.e., labeled) data. Even though AI is helping hundreds of millions of people already, and is well poised to help hundreds of millions more, I don't see any realistic path to AI threatening humanity. Looking ahead, there're many other types of AI beyond supervised learning that I find exciting, such as unsupervised learning (where we have a lot more data available, because the data does not need to be labeled). There's a lot of excitement about these other forms of learning in my group and others. All of us hope for a technological breakthrough, but none of us can predict when there will be one. I think fears of "evil killer AI" is already causing policy makers and leaders to misallocate resources to address a phantom. There are other problems that AI will cause, most notably job displacement. Even though AI will help us build a better society in the next decade, we as AI creators should also take responsibility to solve the problems we'll cause in the meantime. I hope MOOCs (Coursera) will be part of the solution, but we will need more than just education.
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What's the best Affiliate Network?
Here are some of the top 2018 Afiliate Marketing Programs:1. TerraleadsIt is the world’s first CPA Hub and a direct advertiser of nutra offers represented in the following categories: beauty, diet, health, and adult. TerraLeads works by a COD model and provides the highest approval rates thanks to the local call-centers with native speakers on-board.2. ClickbankClickbank is huge. And it’s been in the game for over 17 years. ClickBank’s focus is digital information products. As one of the largest online retailers, ClickBank has a vast library of over 6 million unique products in order to signNow 200 million customers around the world.3. RakutenRakuten ranks among the top three e-commerce companies in the world with over 90,000 products from 38,500 shop owners and more than 18 million customers. Among its numerous online properties, its flagship B2B2C (business-to-business-to-consumer) model e-commerce site Rakuten Ichiba is the largest e-commerce site in Japan and among the world’s largest by sales.4. Amazon AssociatesAmazon needs no intorduction. Amazon is an American electronic commerce and cloud computing company with headquarters in Seattle, Washington. It is the largest Internet-based retailer in the United States. It’s affiliate network, called Amazon Associates, allows you to tap into over a million products to advertise to your customers.5. ShareaSaleShareASale has been in business for 15 years, exclusively as an affiliate marketing network. Their technology receives accolades for speed, efficiency, and accuracy – and their reputation as a fair and honest business is well known within the industry.6. eBayMany marketers don’t even know that eBay has an affiliate network. eBay has now been online for over 20 years. The ebay Partner Network provides first class tools, tracking, and reporting.7. AvangateAvangate is a player in digital commerce that you may not be familiar with. Avangate, backed by a cloud platform, focuses on online commerce, subscription billing, and global payments for Software, SaaS and Online Services companies. More than 4000 digital businesses in over 180 countries trust Avangate including Absolute Software, Bitdefender, Brocade, FICO, HP Software, Kaspersky Lab, Telestream, Spyrix and CleverControl.8. FlexoffersFlexOffersAffiliate Programs is a premiere affiliate network that builds mutually profitable relationships between strategic, skilled, and trustworthy online publishers and a robust portfolio of 5,000+ popular advertisers spanning all verticals. With over 10+ years of experience in the affiliate marketing industry, they offer unparalleled customer service, an array of optimized data delivery tools, and fast and dependable payments– proving that flexibility is the key to affiliate success. FlexOffers Affiliate Programs was recently ranked the eighth overall affiliate network in the Revenue+Performance Top 20 Affiliate (CPS) Network 2015 Blue Book survey.9. AvantlinkAvantlink is the industry-leading technology platform for affiliate referrals. Avantlink works hard to remain on the cutting edge with constant upgrades and updates to the their platform, rapid implementation of new tools and technology, and an unyielding emphasis on quality over quantity.10. RevenueWireRevenueWire is a global ecommerce platform specifically designed for companies that sell digital products online (just like Clickbank). Combined with industry-leading services like AffiliateWire, their ecommerce platform is a player in more than 120 countries.11. TradedoublerTradedoubler was founded in 1999 by two young Swedish entrepreneurs. They have offices in the UK and multiple countries throughout Europe, including Sweden, Germany, France, Poland and Spain. Their focus has always been to provide smarter results for both clients and affiliates through technology. In 18 years, they’ve amassed an army of 180,000 active publishers, connecting them to over 2,000 merchants in Europe and the UK. Many of these merchants are household names.Here are some of the bes Web Hosting Affiliate Programs that I really recommend:1. WP EngineWP Engine offer best in class WordPress Managed Hosting; I personally recommend WP Engine if you are a serious blogger as they have super fast hosting optimised just for WordPress. They offer an excellent $200 per sign up for new customers you refer.2. DreamhostDreamhost have been around for a long time and provide a variety of web hosting services from dedicated web hosting, VPS Hosting, managed WordPress hosting and shared hosting. Right now Dreamhost offer $97 commission for new customers.3. CloudwaysCloudways takes care of the management of open-source tools for hosting websites, like Magento, WordPress, Drupal, and Joomla. They offer a $100 referral fee for each new customer you provide – their most popular cloud hosting packages range from $10 to $30 per month.4. BluehostBlueHost are another well known popular web hosting brand and one which I have featured on this website for the past few years, you can read my BlueHost Review to see why. They offer $65 commission for new customers which can go above $120 per signup if you can provide high volumes of new customers to them.5. Inmotion HostingInMotion Hosting is a web hosting company that focus mainly on business users. Its technical support staff are based within the US, and they offer a 90-day money-back guarantee to offer clients complete peace of mind. InMotion Hosting keeps its plans simple by providing Linux-only web hosting.6. FlywheelThousands of designers and developers are super fans of Flywheel WordPress hosting. Flywheel offers blazing fast site speeds, friendly and efficient customer service, industry-leading management tools, and inspiring design. With commissions of up to $500 per sale – they offer one of the best payouts in the web hosting affiliate space.Finance Affiliate Programs:1. Regal AssetsGold Investing is one of the most lucrative niches on the Internet right now, and Regal Assets has the best offer for serious affiliates. While other gold investing affiliate programs only pay you a small flat-rate for each lead, Regal Assets gives you a flat-rate + a piece of the total investment amount.Commission Structure Details$30-$100 per lead (any qualified lead with name, email & phone number)$30-$100 per call (any inbound call lasting 10 minutes or longer)3% of total investment amount (if your lead invests $50,000 in precious metals with Regal Assets, you will get a $1,500 commission)2. Colmex ProColmex Pro is the leading European Regulated CFD Broker. Offering Tier 2 CFD’s, as well as Live Equities, Indices, Commodities, Futures, and Forex, Colmex Pro offers nearly every investment vehicle available on the US Stock Market to international day traders. Coupled with their partner’s educational packages and trade room access Colmex Pro offers investors the best opportunity to grow and learn how to day trade successfully. CPA up to $1000.Health & Fitness Affiliate Programs:1. SellHealthIt’s free to join the SellHealth affiliate program, though you do have to apply and be accepted before you can start promoting their products. Once you’re accepted, you’ll have access to a number of tools, graphics, banners and more that you can use to promote SellHealth products. The sales are actually made at company-owned Websites, which look professional and handle all of the selling. Commissions vary, but the base rate is 30% of all sales and upsells, and SellHealth says you can earn up to $350 per sale.2. Market HealthThe Market Health Affiliate Program allows you to market and promote the world’s leading health and beauty offers online. We offer the highest paying affiliate program and best tracking software in our industry. If you have a web site and are interested in making money off the explosive sales in the health and beauty industry, then Health and Beauty Affiliate Program is perfect for you. Offers include products in the health, beauty, supplement, weight loss, and skin care industries.3. MoreNicheWith possibly the most transparent affiliate network online, we give affiliates access to stats no other program dare, including earning data, conversion stats, demographic information and seasonality trends. With ethics and consumer protection being high on the agenda, you can rest assured when working with MoreNiche you are working with an honest, trustworthy and transparent company.Internet Marketing Affiliate Programs:1. SendibleSendible is a great social media management tool which allows online marketers to schedule posts and manage multiple social accounts all at once. They offer 30% on all sign ups for the first 12 months which means you could earn up to a whopping $716 per sign up.2. ShopifyShopify is a very popular site building platform for people interested in building eCommerce stores. It has been around for the past few years and seen signNow growth in its user base over this time. You can earn a staggering 200% per sale for every new customer you refer to them, which means that there is up to $2400 per new customer on offer.3. SEMRushSEMRush is a popular tool for SEO’s and bloggers providing insight into how well websites perform in Google. You can earn 40% commission on all new customer sign ups. Commissions are recurring, so you will get 40% of what your referral pays them every month until they stop paying for their subscription.4. URL ProfilerURL Profiler is a website and content auditing tool launched in 2014. They offer 25% lifetime commissions. For example, if a server license is purchased for $29.95 via your affiliate link, you will earn $7.49 for every month that they remain a customer (so, a 12 month subscription would yield $89.88 total commission).
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What must be my strategy to score full marks in the GATE mathematics (also suggest best book for practicing prev. year’s questio
Mathematics is a very scoring subject. And it is very important for those who just want to pass or to get below 2000 or top 100. Who want to miss easy 10+ marks??? Some of the problems students face related to mathematics are: * Students have studied it in the first year and have completely forgotten * Mathematics is widely regarded as one of the toughest subjects * Students think they can’t learn that subject since it is beyond them So overcome your fears and see that it is very easy provided, you study well. Did I tell you, my most favorite subject is mathematics. I learnt mathematics by practice only! When I see a new topic, I too feel blank inside my head. Then I realize that all I need to do is to understand the concepts by practicing then I feel comfortable in doing those concepts. I will try to explain important topics here and give some tips to prepare mathematics. Finally I will give some timetable to study it so that you finish that subject. Before we start, see the GATE syllabus here: * A [ http://www.gate.iitg.ac.in/Syllabi/AE_Aerospace-Engineering.pdf ]E [ http://www.gate.iitg.ac.in/Syllabi/AE_Aerospace-Engineering.pdf ], Civil [ http://www.gate.iitg.ac.in/Syllabi/CE_Civil-Engineering.pdf ], Chemical [ http://www.gate.iitg.ac.in/Syllabi/CH_Chemical-Engineering.pdf ], CS [ http://www.gate.iitg.ac.in/Syllabi/CS_Computer-Science-and-Information-Technology.pdf ], ECE [ http://www.gate.iitg.ac.in/Syllabi/EC_Electronics-and-Communications_Engineering.pdf ], EE [ http://www.gate.iitg.ac.in/Syllabi/EE_Electrical-Engineering.pdf ], ME [ http://www.gate.iitg.ac.in/Syllabi/ME_Mechanical-Engineering.pdf ], Petroleum [ http://www.gate.iitg.ac.in/Syllabi/PE_Petroleum_Engineering.pdf ], Instrumentation [ http://www.gate.iitg.ac.in/Syllabi/IN_Instrumentation-Engineering.pdf ] All branches except CS have almost same syllabus. So I will focus on these common topics. You can study from either ACE material or Made Easy material or B. S. Gravel or any good textbook along with previous year papers. Try to spend daily an hour on Mathematics till you become confident in it. * Linear Algebra: Generally the topics asked are related to finding rank, determinant, Eigenvalues and Eigenvectors, Solution of simultaneous equations, Finding inverse and power of matrix. * * Rank: It is the minimum of ( independent rows or columns ) in the given matrix. To find the rank. try to write the given equations in to matrix form and reduce it into row echelon form [ http://stattrek.com/matrix-algebra/echelon-transform.aspx ]. The number of non-zero rows left in the matrix is the rank of the matrix. Ex: Rank of matrix [ https://math.stackexchange.com/questions/2080554/how-to-calculate-matrix-rank ] * Determinant: You can solve these problems in two methods: * * Expand the matrix by finding co-factors and then simplifying it gives the determinant and straightforward. Refer here for complete procedure: The Determinant of a Square Matrix [ https://people.richland.edu/james/lecture/m116/matrices/determinant.html ] * Next approach is very simple and easy. Try to convert the given matrix into row echelon form. Then the determinant is just the product of diagonal terms. Only point you need to keep in mind is, when you interchange two adjacent rows, rank doesn’t change but determinant changes to opposite sign. So if you interchange two rows say [math]i^{th}[/math] and [math]j^{th}[/math]. Then, determinant changes the sign to [math](-1)^{j-i}[/math]. Also another point to remember is not to multiply any row by a constant. Rank doesn’t change but determinant changes. * Solution of simultaneous equations: To solve there questions, try to write the Augmented matrix [math][A|b][/math] from [math]Ax=b[/math]. Find the rank of [math][A|b][/math] and also for A. * * If [math]R(A) = R([A|b]) = n[/math] (no. of rows or columns in the given matrix), then we have unique solution. * If [math]R(A) = R([A|b]) %3C n[/math] (no. of rows or columns in the given matrix), then we have multiple solutions. * If [math]R(A) \neq R([A|b])[/math], then we have no solution. * Eigenvalues and Eigenvectors: Eigenvalues and Eigenvectors are the solutions the equation [math]Ax=\lambda x[/math], [math]\lambda[/math] is the Eigenvalue and [math]x[/math] is the Eigenvector. To solve these types of problems, since we have one equation and two unknowns ([math]\lambda[/math] and [math]x[/math]) so there is no unique solution to given equation. Refer here for a solved example: Eigenvalues and Eigenvectors example [ https://www.scss.tcd.ie/~dahyotr/CS1BA1/SolutionEigen.pdf ] * * To find Eigenvalues, write given equation as [math](A-\lambda I)x=0[/math]. Find the determinant of [math](A-\lambda I)[/math]. [math]\lambda[/math] is Eigenvalues obtained. * Next for each Eigenvalue [math]\lambda[/math] obtained, find the Eigenvector corresponding to it. Since the equation becomes to some [math]Bx=0[/math], we don’t have a unique solution. Assume one of the values in vector as 1. Find the rest of the terms. * Finding inverse and Power of matrix: use Cayley Hamilton theorem to solve these problems. Every matrix satisfies its own characteristic equation [math]|A-\lambda I|=0[/math]. From this find the equation in terms of [math]\lambda[/math]. Replace [math]\lambda[/math] with [math]A[/math] and then we get characteristic equation. From this, we can find any power or inverse easily. Refer here for a solved problem: Cayley Hamilton Theorem Examples [ https://www.math.upenn.edu/~rimmer/math240/8_9powers.pdf ] * Calculus: Some topics to focus are finding maximum and minimum values, Finding Limits, Continuity and Differentiability of functions, Taylor and Maclaurin series, Vector calculus, Finding area and Volumes, * * Maximum and Minimum values: Differentiate the given equation and find [math]f'(x)=0[/math]. Then, find [math]f"(x)[/math] at the same values obtained. Refer this for further clarification: Minimum and Maximum Values [ http://tutorial.math.lamar.edu/Classes/CalcI/MinMaxValues.aspx ] * * [math]f"(x)%3C0[/math], then value is local maxima * [math]f"(x)%3E0[/math], then value is local minima * [math]f"(x)=0[/math], then nothing can be said * Also check with the boundaries too. They could be maximum or minimum in the given interval. * Limit, Continuity and Differentiability: Refer this for some solved examples: Continuity and Differentiability [ http://tekoclasses.com/ENGLISH%20PDF%20PACKAGE/28%20CONTINUITY%20&%20DIFFRENTIABILITY%20PART%201%20of%201.pdf ] * * Limits: To find the limit of form, [math]0/0[/math] or [math]\infty/\infty[/math] we need to use L-Hospital rule. [math]0/\infty 0[/math] and [math]\infty/0 \to \pm \infty[/math] and so limit does not exist, if limit is checked from left and right of zero. For [math]0\times \infty[/math] form, write it as [math]0/(1/\infty) = 0/0[/math] form and use L-Hospital rule. A simple approach to solve majority of the trigonometric and logarithmic problems is by expanding the terms in x. And then simplifying gives directly the limit. * Ex. of above limit application: [math]\lim_{x \to 0} \dfrac{\sin{x}-x}{x^3} =\lim_{x \to 0} \dfrac{(x-x^3/6+x^5/120-...)-x}{x^3}=\frac{-1}{6}[/math] * Continuity: To find whether function is continuous or not, simply find the [math]\lim_{x \to 0^+}[/math] and [math]\lim_{x \to 0^-}[/math] and [math]f(0)[/math] and see that all three values are equal. * Differentiability: Along with continuity, the function need to have a unique limit of differentiated value. [math]f'(x)|_{x=0} = lim_{h \to 0^+} \dfrac{f(x+h)-f(x)}{h}=lim_{h \to 0^-} \dfrac{f(x+h)-f(x)}{h}[/math] * For two variable problems, limit has to be same in any order we apply for continuity and differentaiability. Also if limit doesn’t exist, just solve the problems with one the given order. * Taylor series and Maclaurin Series: To solve problems related to this, find the function first, second and third etc. derivatives at x=a (for Taylor) and x=0 (for Maclaurin. Then get the expansion of the function. Taylor series is the expansion of function along x=a (from: Taylor Series [ http://tutorial.math.lamar.edu/Classes/CalcII/TaylorSeries.aspx ]) Maclaurin series is the expansion of function along x=0 * * Definite and Indefinite integrals: Indefinite integrals are very tricky. Try to solve solutions and check if we get given question. Definite integrals are the toughest. Learn formulas of [math]\int \sqrt{x}[/math], [math]\int_{ 0}^{ \pi/2} \sin^n {x}, \int_{0}^{\pi/2} \cos^n {x}, [/math] * * Solve some problems of definite integrals from here: Computing Definite Integrals [ http://tutorial.math.lamar.edu/Problems/CalcI/ComputingDefiniteIntegrals.aspx ] * Most of the definite problems can be solved by method of substitutions like [math]x=t^2[/math] for [math]\sqrt{x}[/math], [math]x=a\tan{x}[/math] for [math]x^2+a^2[/math] in denominator, [math]x=a\sin{x}[/math] for [math]\sqrt{a^2-x^2}[/math] and so on. Refer here for examples of all models: Substitution Rule for Indefinite Integrals [ http://tutorial.math.lamar.edu/Classes/CalcI/SubstitutionRuleIndefinite.aspx ], More Substitution Rule [ http://tutorial.math.lamar.edu/Classes/CalcI/SubstitutionRuleIndefinitePtII.aspx ] * Area between two curves is [math]\int_{a}^b {f(x)-g(x)} dx[/math] is the area between [math]f(x)[/math] and [math]g(x)[/math] where a and b are the two intersection points of the curve. To find area of the curve and x axis, take [math]g(x)[/math] as zero. Refer here for some solved examples of Area Between Curves [ http://tutorial.math.lamar.edu/Classes/CalcI/AreaBetweenCurves.aspx ] * To calculate volumes, use [math]\int Ady[/math] or [math]\int Adx[/math]. Where, [math]A[/math] represents the area of the typical disc. Refer here for some solved example: Volume of Revolution [ http://www.mathcentre.ac.uk/resources/uploaded/mc-ty-volumes-2009-1.pdf ] * Vector Calculus: The questions asked from this topic are very easy if we know the formulas. Very important operator is Del: [math]\nabla = \dfrac{\partial}{\partial x} \overrightarrow{i}+\dfrac{\partial}{\partial y} \overrightarrow{j}+\dfrac{\partial}{\partial z} \overrightarrow{k}[/math] * * Curl [math]\overrightarrow{F}[/math]is defined as the cross product between [math]\nabla[/math] and [math]\overrightarrow{F}[/math]= [math]\nabla \times \overrightarrow{F}[/math] * * * Divergence or div [math]\overrightarrow{F}[/math] is defined as [math]\nabla. \overrightarrow{F}[/math]. Refer here to solve some problems: Curl and Divergence [ http://tutorial.math.lamar.edu/Classes/CalcIII/CurlDivergence.aspx ] * * * Gradient is defined for a scalar only where as we defined Curl and Divergence to a vector. Gradient is defined as [math]\overrightarrow{\nabla} F=\dfrac{\partial \overrightarrow{F}}{\partial x}\overrightarrow{i} +\dfrac{\partial \overrightarrow{F}}{\partial y}\overrightarrow{j} +\dfrac{\partial \overrightarrow{F}}{\partial z}\overrightarrow{k}[/math]. The rate of change of function is defined by gradient. * To get directional derivative of the function, simply calculate the gradient and calculate [math]\overrightarrow{\nabla} f.\overrightarrow{u}[/math] (where . is dot product and [math]\overrightarrow{u}[/math] is unit vector in the direction of given vector. Refer here for some solved problems: Directional Derivatives [ http://tutorial.math.lamar.edu/Classes/CalcIII/DirectionalDeriv.aspx#Gradient_Defn ]. To calculate the maximum rate of change given function [math]f(x,y,z)[/math], simply compute [math]\overrightarrow{\nabla} f.\dfrac{\overrightarrow{\nabla} f}{|\overrightarrow{\nabla} f|}[/math] * To compute tangent and normal of a function, compute gradient first. Refer here for solved problems: Gradient Vector, Tangent Planes and Normal Lines [ http://tutorial.math.lamar.edu/Classes/CalcIII/GradientVectorTangentPlane.aspx ] Tangent of a function [math]f(x,y,z)[/math] at [math](x_0,y_0,z_0)[/math] is represented by: Similarly normal is represented by * * * If the field is conservative [ http://tutorial.math.lamar.edu/Classes/CalcIII/ConservativeVectorField.aspx ], we can calculate potential which is nothing but the gradient of function. * For line integrals, just take the equation of the path given and integrate along it. Refer here: Line, Surface and Volume Integrals [ https://www.robots.ox.ac.uk/~dwm/Courses/2VA/2VA-N4.pdf (https://www.robots.ox.ac.uk/~dwm/Courses/2VA/2VA-N4.pdf ] * Greens Theorem: Refer here for example: Green's Theorem [ http://tutorial.math.lamar.edu/Classes/CalcIII/GreensTheorem.aspx ]. It converts line integral to area integral. It is defined only for 2D as shown: * * * Stokes Theorem: It is the higher version of Greens Theorem. It converts surface integral to volume integral. Refer here for example: Stokes' Theorem [ http://tutorial.math.lamar.edu/Classes/CalcIII/StokesTheorem.aspx ]. It is defined as: * * * Gauss Divergence Theorem: It converts volume integral to surface integral (or reverse of Stokes theorem). Refer here for example: Gauss Divergence Theorem [ http://tutorial.math.lamar.edu/Classes/CalcIII/DivergenceTheorem.aspx (http://tutorial.math.lamar.edu/Classes/CalcIII/DivergenceTheorem.aspx ] * Transformations: Key points to focus would be finding of transform for given function specially half sine, cosine, unit step function, and Dirac Delta function, and its inverse or convolution and its application to compute the differential equations. * * Fourier Series: * * Fourier Series Tutorial I [ http://www.cse.salford.ac.uk/physics/gsmcdonald/H-Tutorials/Fourier-series-tutorial.pdf (http://www.cse.salford.ac.uk/physics/gsmcdonald/H-Tutorials/Fourier-series-tutorial.pdf ] * Fourier Series Tutorial II [ http://nptel.ac.in/courses/111103021/15.pdf ] * Fourier Series Examples [ https://www.math.psu.edu/tseng/class/Math251/Notes-PDE%20pt2.pdf ] * Laplace Transforms: * * Laplace Transforms Overview I [ http://www.vyssotski.ch/BasicsOfInstrumentation/LaplaceTransform.pdf ] * Laplace Transforms Overview II [ http://www.math.psu.edu/shen_w/250/NotesLaplace.pdf ] * Step Functions [ https://www.math.psu.edu/tseng/class/Math251/Notes-LT2.pdf ] * Initial Value Problems (IVP) [ https://www.math.psu.edu/tseng/class/Math251/Notes-LT1.pdf ] * Dirac Delta Function [ https://www.math.psu.edu/tseng/class/Math251/Notes-LT3.pdf ] * Formulas sheet: Laplace Transforms Formulas [ http://personal.maths.surrey.ac.uk/st/Mark.Holland/Old_ms200/formula_sheet.pdf (http://personal.maths.surrey.ac.uk/st/Mark.Holland/Old_ms200/formula_sheet.pdf ] * Inverse Laplace Transforms [ https://sites.ualberta.ca/~csproat/Homework/MATH%20334/Chapter%20Solutions/Chapter%20Part%202.pdf ] * Dirac Delta function: Function is infinite at a single value and is zero at rest of the values. Applying Fourier and Laplace transforms to it very important. Refer here for its applications [ http://materia.dfa.unipd.it/salasnich/dfl/dfl.pdf ] * z‐Transform: Key points to note are applying z-transforms, inverse z-transforms, finding poles and zeros, and application to compute power series. * * Zeros are locations where numerator of function is zero and Pole is a location where the denominator is zero so function is infinite there. For ex. consider [math]H(z) = \dfrac{z-1}{z+1}[/math]. Zeros are [math]z=1[/math] and poles are [math]z=-1[/math]. * Z-Transforms Complete [ http://www.uobabylon.edu.iq/uobcoleges/ad_downloads/4_7629_305.doc ] * Z-Transforms [ https://wolfweb.unr.edu/~fadali/ee472/Ztransform.pdf ] * Z-Transforms Overview [ http://nptel.ac.in/courses/106106097/pdf/Lecture12_ExampleZTransforms.pdf ] * Properties of Z-Transforms [ http://nptel.ac.in/courses/106106097/11 ] * Power series expansion exists only if region of convergence [math]|R| %3C 1[/math]Power Series and Functions [ http://tutorial.math.lamar.edu/Classes/CalcII/PowerSeriesandFunctions.aspx ] * Ordinary Differential Equations: Some key points to remember is learning different first order types, for second order with particular integral as [math]\sin {x},\cos{x},e^x,x^n,[/math] combination of any of these, application of method of variation of parameters to any general function like [math]\tan {x}, \sec{x}, \log{x}[/math] etc. and application of Euler-Cauchy method for variable coefficients. Solving IVP, BVP. * * Order [ http://www3.ul.ie/cemtl/pdf%20files/bm2/DegreeOrder.pdf ]is the highest order differential equation. Degree [ http://www3.ul.ie/cemtl/pdf%20files/bm2/DegreeOrder.pdf ]is the power of highest order in given differential equation after differential equation is radical free (meaning free from [math]1/3[/math] power etc.) * First Order Linear equations: If only [math]y'[/math] term is present it is first order. Linear if [math]y'[/math] is free linear. Some of the types of standard models available are: * * Linear * Homogeneous * Exact * Variable Separable * Bernoulli's equation * Above types can be found here: Recognizing types of ODE [ http://www.math.hawaii.edu/~lee/calculus/DE.pdf ] and First Order DE's [ http://tutorial.math.lamar.edu/Classes/DE/IntroFirstOrder.aspx ] and Problems I [ https://rutherglen.science.mq.edu.au/wchen/lnfycfolder/fyc15.pdf ] * Second Order Equations with constant coefficients: Standard form is [math]ay"+by'+cy=f(x) = (aD^2+bD+c)y=f(x)[/math]. Where, [math]D=d/dx[/math]. To solve these equations, * * First form an characteristic equation i,e, [math]aD^2+bD+c=0[/math]. Solve for D. Let [math]D=a[/math] be a root, * If roots are unique, solution is [math]y=c_1e^{ax}[/math]. By using superposition combine all the roots. Real & Distinct Roots [ http://tutorial.math.lamar.edu/Classes/DE/RealRoots.aspx ] * If two roots are equal say [math]D=a[/math], then solution is [math]y=(C_0+xC_1)e^{ax}[/math].Differential Equations - Repeated Roots [ http://tutorial.math.lamar.edu/Classes/DE/RepeatedRoots.aspx ] * If roots are complex say [math]D=a\pm ib[/math], then the solution is [math]y=(c_0\sin{bx}+c_1\cos{bx})e^{ax}[/math]. Differential Equations - Complex Roots [ http://tutorial.math.lamar.edu/Classes/DE/ComplexRoots.aspx ] * After finding the roots, we need to particular integral (PI). i,e, solution which is just satisfying the given function. We have [math]F(D)y=f(x)[/math] * If PI is of form [math]e^{ax}[/math], then solution is [math]\dfrac{1}{F(a)} e^{ax}[/math] * If PI is of form [math]\sin {ax}[/math], [math]\cos {ax}[/math] then replace [math]D^2[/math] with [math]-a^2[/math]. * If PI is of [math]x^{ax}[/math], then simply find partial fractions of [math]\dfrac{1}{F(D)}[/math] and then integrate. * If we have some combination of [math]e^{ax},\sin{bx}[/math], then first write [math]\sin{bx}[/math] or [math]\cos{bx}[/math] into exponential form using Euler identity [math]e^{ibx}=\cos{bx}+i\sin{bx}[/math]. Then combine both of the exponential terms and solve. * There is an alternative way to find solution. If PI is of form [math]e^{ax}[/math], the solution is of form [math]Ae^{ax}[/math]. If PI is of form [math]\sin {ax}[/math], or [math]\cos {ax}[/math] the solution is of form [math]A\cos {ax}+B\sin{ax}[/math]. If PI is of form [math]c_0x^2+c_1x+c_2[/math], then solution is of form [math]ax^2+bx+c[/math]. Once we assume the solution, then substitute in the given differential equation and find the coefficients. * Refer here for solved problems: Problems I [ https://rutherglen.science.mq.edu.au/wchen/lnfycfolder/fyc16.pdf ] and Problems II [ http://epsassets.manchester.ac.uk/medialand/maths/helm/19_3.pdf ] * Application of Differential Equations [ http://epsassets.manchester.ac.uk/medialand/maths/helm/19_4.pdf ] * Method of variation of parameters: It is used for any particular integral. Refer here how to solve: Variation of Parameters I [ https://math.berkeley.edu/~ehallman/math1B/variation-sols.pdf ], Solving tan (x) [ http://home.iitk.ac.in/~sghorai/TEACHING/MTH203/ode10.pdf ] * Variable coefficients: If the differential equation is of form [math]c_0x^nD^n+c_1x^{n-1}D^{n-1}+...+c_n)y=f(x)[/math], we need to assume [math]y=x^r[/math] as solution and substitute in the differential equation and solve for [math]r[/math]. Refer here for solved examples: Differential Equations - Euler Equations [ http://tutorial.math.lamar.edu/Classes/DE/EulerEquations.aspx ] * Partial Differential Equations: variable separable method is widely used in these problems. Some key points are: * * Partial derivatives determination [ https://www.math.psu.edu/tseng/class/Math251/Notes-Partial%20Differentiation.pdf ]is important to solve these problems. * If First order PDE is of form, [math]a\dfrac{\partial z}{\partial x}+b\dfrac{\partial z}{\partial y}=c[/math], The solution is solved by using [math]\dfrac{dx}{a}=\dfrac{dy}{b}=\dfrac{dz}{c}[/math]. Refer this to solve some problems Linear PDE [ http://nptel.ac.in/courses/111103021/7 ] * Refer this to solve non linear first order PDE: Problems I [ http://nptel.ac.in/courses/111103021/8 ] and Problems II [ http://nptel.ac.in/courses/111103021/10 ] * General second order equation is [math]au_{xx}+bu{xy}+cu_{yy}+du_x+eu_y+fu=g(x,y)[/math]. * * If [math]b^2-4ac%3C0[/math], PDE is elliptic. Ex: Laplace equation * If [math]b^2-4ac=0[/math], PDE is parabolic. Ex: Heat equation * If [math]b^2-4ac%3C0[/math], PDE is hyperbolic. Ex: Wave equation * One-Dimensional diffusion equation: [math]\dfrac{\partial u}{\partial t} =\kappa\dfrac{\partial^2 u}{\partial^2 x}[/math]. Where [math]\kappa = \dfrac{K_0}{c\rho}[/math] is called thermal diffusion. Refer here for solved example: 1D Diffusion equation [ https://ocw.mit.edu/courses/mathematics/18-303-linear-partial-differential-equations-fall-2006/lecture-notes/heateqni.pdf ] * Heat equation: [math]\alpha^2 u_{xx}=u_t[/math]. * * We get the solution in variable separable form by assuming of [math]y=X(x)T(t)[/math]. * Substituting the above yields to [math]\alpha^2X"(x)T(t)=X(x)T'(t)[/math] * [math]\Rightarrow \dfrac{X"(x)}{X(x)} =\dfrac{T'(t)}{\alpha^2 T(t) }=C[/math](Constant. Since LHS is a function of x and RHS is a function of t). * Solve the two equations and substitute boundary conditions. * Solved example of Heat equation [ https://www.math.psu.edu/tseng/class/Math251/Notes-PDE%20pt1.pdf ] * Wave equation: [math]\alpha^2 u_{xx}=u_{tt}[/math]. Solve as above and solve by variable separable method. Refer here for solved example: Wave Equation [ https://www.math.psu.edu/tseng/class/Math251/Notes-PDE%20pt4.pdf ] * Numerical Methods: Key topics to focus are solution of algebraic equation by Newton’s method, single step numerical differentiation and Simpson and Trapezoidal methods. * * Simpson’s 1/3 rule: Used to determine area approximately. * * Given by: [math]\int\limits^{b}_{a}f(x)dx = \frac{h}{3}\left [y_{0}+y_n+4\left(\sum_{i = odd}y_{i}\right) + 2\left (\sum_{i=even}y_{i}\right)\right][/math] * Error [math]E= -\frac{b-a}{180}\overline{\Delta^4 y}[/math], where [math]\overline{\Delta^4 y}[/math] is fourth forward difference. * Solved example here: Simpson’s 1/3 Rule Example [ http://nptel.ac.in/courses/122104018/node121.html ] * Trapezoidal rule: * * Given by [math]\int\limits^{b}_{a}f(x)dx = h\left[\frac{y_0+y_n}{2}+\sum_{i=1}^{n-1} y_i\right][/math] * Error [math]E=-\frac{b-a}{12}\overline{\Delta^2 y}[/math] * Solved example here: Trapezoidal Rule Example [ http://nptel.ac.in/courses/122104018/node120.html ] * Simpson’s 3/8 rule: * * Given by: [math]\int\limits^{b}_{a}f(x)dx = \frac{3h}{8} \left[y_{0}+y_n+3\left(\sum_{i = 1,2,4,5,\cdots} y_{i} \right)+2\left(\sum_{i=3,6,\cdots} y_{i}\right)\right][/math] * Error [math]E= -\frac{3(b-a)}{80}h^4\overline{\Delta^4 y}[/math] * Solved example here: Simpson’s 3/8 Rule Example [ http://mathforcollege.com/nm/mws/gen/07int/mws_gen_int_txt_simpson3by8.pdf ] * Euler’s forward method: Refer this for solved example [ http://nptel.ac.in/courses/122104018/node124.html ] * * Given by: [math]y_{i+1} = y_i + h f(x_i, y_i) + \frac{h^2}{2!} f(x_i, y_i) + \cdots[/math] * It is a single step forward method. Error order [math]O(h^2)[/math] * For Euler’s backward method, use [math]y_{i-1}[/math] instead of [math]y_{i+1}[/math] and [math]h[/math] with [math]-h[/math] * Range-Kutta 2nd Order: It has error order 2. Given by [math]y_{k+1} = y_k + \frac{h}{2} \left( f(x_k, y_k) + f(x_k + h, y_k + h f(x_k)) \right)[/math] * Range-Kutta 4th Order: It has error order 4 i.e [math]O(h^5)[/math]. * * Given by [math]y_{k+1} = y_k + \frac{k_1 + 2 k_2 + 2 k_3 + k_4}{6}[/math], where, * [math]k_1 = h f(x_k, y_k)[/math] * [math]k_2 = h f(x_k + \frac{h}{2}, y_k + \frac{k_1}{2})[/math] * [math]k_3 = h f(x_k + \frac{h}{2}, y_k + \frac{k_2}{2})[/math] * [math]k_4 = h f(x_k + h, y_k + k_3)[/math] * Refer here for Newton Interpolating Polynomial [ http://nptel.ac.in/courses/122104019/numerical-analysis/Rathish-kumar/rathish-oct31/fratnode5.html ] and Lagrangian Interpolating Polynomial [ http://nptel.ac.in/courses/122104019/numerical-analysis/Rathish-kumar/rathish-oct31/fratnode4.html ] * Newton-Raphson method: Used for solving roots of algebraic and transcendental equations. Given by [math]x_{i+1}=x_i+\frac{f(x_i)}{f'(x_i)}[/math]. Refer here for solved examples [ https://www.math.ubc.ca/~anstee/math104/104newton-solution.pdf ] * Bisection Method and False Position Method - Linear convergence; Secant Method - 1.618 and Newton’s Raphsons Method - 2 * Probability and Statistics: Key topics to focus are Bayes Theorem, Conditional and Joint probability, Binomial, Poisson, normal and exponential distribution — there mean, variance and standard deviation, Correlation and regression. * * Properties of Probability [ https://onlinecourses.science.psu.edu/stat414/node/7 ]: * * [math]0\leq P(A)\leq 1[/math] * [math]P(A)=1-P(A')[/math] * [math]P(\varnothing)=0 [/math] * [math]P(\cup)=1[/math] * Conditional Probability [ https://onlinecourses.science.psu.edu/stat414/node/10 ]: Given by * * [math]P(A \cap B) = P(A | B) × P(B)[/math] * [math]P(A \cap B) = P(B | A) × P(A)[/math] * Bayes Theorem: [math]P(E_i|A)=\frac{P(E_i)P(E_i|A)}{\sum\limits_{k=0}^{n}P(E_k)P(A|E_k)}[/math], where [math]P(E_i|A)=\frac{P(E_i \cap A)}{P(A)}[/math]. Refer here for solved examples [ https://onlinecourses.science.psu.edu/stat414/node/12 ] * Discrete Distribution [ https://onlinecourses.science.psu.edu/stat414/node/48 ]: * * Binomial Distribution [ https://onlinecourses.science.psu.edu/stat414/node/53 ]: [math]f(x)=\binom{n}{x} p^x (1-p)^{n-x}[/math], denoted by [math]X \sim b(n, p)[/math]. Mean [math]\mu=np[/math], Variance [math]\sigma^2 = np(1-p)[/math] * Geometric Distribution [ https://onlinecourses.science.psu.edu/stat414/node/55 ]: [math]f(x)=P(X=x)=(1-p)^{x−1}p[/math]. Cumulative distribution function is [math]F(x)=P(X\leq x)=1-(1-p)^x[/math]. Mean [math]\mu=E(X)=\frac{1}{p}[/math], Variance [math]\sigma^2=Var(X)=\frac{1-p}{p^2}[/math] * Negative Binomial Distribution [ https://onlinecourses.science.psu.edu/stat414/node/78 ]: [math]f(x)=P(X=x)=\binom{x-1}{r-1}(1-p)^{x-r}p^r[/math], Mean [math]\mu = E(X) = \frac{r}{p}[/math] and Variance [math]\sigma^2=\frac{r(1-p)}{p^2}[/math] * Poisson Distribution [ https://onlinecourses.science.psu.edu/stat414/node/54 ]: [math]f(x)=\frac{e^{-\lambda}\lambda^x}{x!}[/math], Mean [math]\mu=\lambda[/math], Variance [math]\sigma^2=\lambda[/math] * Continuous Distribution [ https://onlinecourses.science.psu.edu/stat414/node/86 ]: * * Exponential Distribution [ https://onlinecourses.science.psu.edu/stat414/node/138 ]: [math]f(x)=\frac{1}{\theta}e^{-x/\theta}[/math], Mean [math]\mu = \theta[/math], Variance [math]\sigma^2=\theta^2[/math] * Normal Distribution [ https://onlinecourses.science.psu.edu/stat414/node/139 ]: [math]f(x)=\frac{1}{\sigma \sqrt{2\pi}}-e^{\frac{-1}{2} (\frac{x-\mu}{\sigma})^2}[/math], Mean [math]\mu[/math] and the variance of X is [math]\sigma^2[/math] * Substituting [math]Z=\dfrac{X-\mu}{\sigma}[/math] converts normal distribution into standard normal distribution. Solve example problems here [ https://onlinecourses.science.psu.edu/stat414/node/150 ] * Hypothesis testing can be studied from here [ https://onlinecourses.science.psu.edu/stat414/node/290 ] and Correlation and Regression from here [ https://academic.macewan.ca/burok/Stat141/notes/regression.pdf ] For specific doubts, comment below. It would be grateful if someone could assist me in creating the PDF (with proper links and formulas)of this file and add a link here so that it would be very helpful to all.
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What moment at the office made you realize, "It's time to start looking for a new job"?
My boss stopped by my office and whispered: “You’re alright.” She wasn’t trying to whisper. She just didn’t have the energy to speak in her normal voice.I had never seen her like this, all tied up in knots and on the verge of tears. Then she went back to her office and closed the door. She stayed in there for a while with our senior engineer, and then she left. I had survived the day’s round of layoffs. Colleagues nearby had been cleaning out their cubicles for the past few hours, then leaving with their boxes of personal stuff.This was not a new thing. We were one of the formerly high-flying minicomputer companies, part of an industry that was clearly in decline. There had been several previous rounds over the previous five years. This round, was different, though. The cuts were deep. People who had been with my boss the whole way, making great contributions to our product, were hit this time. We lost key developers and project leaders, and we were going to have to re-think a lot of things about how we were going to move forward.Our senior engineer got the rest of us together, and he told us what our boss had told him: She had been given the folders the night before. All the names had been chosen for her. She had no input. A committee of about a dozen senior managers, drawn from across the R&D division, had been given all the folders to put on a table and they were told “This table is the parking lot. Everyone’s on the outside. Here are the projects that are going to keep their funding. Pick N people, regardless of their current projects, and invite them back into the building.” We had been brought back in. Our friends who weren’t in the room were gone.We also knew that our project was on the list to go forward, but with reduced scope and some big changes. We were going to get new resources from projects that had been cut, and we were going to explore some new directions in our older product set while simultaneously trying to refocus our next generation product set in order to find a way to get it to market sooner.I went home, and I realized why I still had my job. My job on our team had been integration of our software products with the company’s other software products. Every important product in the company had to integrate with us. We had one other guy doing integration with one particular group as part of his job — he got cut, and I had all the other integration. That meant that I knew people all across R&D. I worked with their teams, got to know their products and their engineers, and helped them work with us. I coordinated with their managers, negotiated when necessary and sold them on the approaches to integration that we were taking, and the benefits it would bring for both product sets.I was good at this, and some of those managers were on that committee. Some of them knew me by name. That’s why I was brought back, while my friends who did their jobs just as well as I did mine ended up in the parking lot. Their jobs just didn’t involve contact with the people who had made the decisions.From then on, I knew that I wasn’t really going to be working to satisfy my boss. I was going to be working to keep my name in the minds of every other manager I dealt with. I was good at that. I was going to be safe for as long as they continued to use that system.That didn’t sit well with me at all. The guy in the cube next to me was every bit as valuable to our product as I was, but he never got to work outside our own team so he was unknown to everyone on that committee of senior managers. I got around. I was known. There was always going to be a manager on the committee who knows me.I decided that night that I would start looking in three months. I would let my friends who had just been laid off get a good head start, but once I saw them starting to get jobs I would start putting my resumes out on the street to see what opportunities I could find.
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