proj-calc-part1 - Numerical Calculus Project Part 1...

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Numerical Calculus Project Part 1: Differentiation Context: Your next project will be all about numerical calculus. This project will be split into three parts. The first two will be preliminary tasks where you will become familiar with numerical differentiation and integration and write and test drive methods to compute numerical derivatives and integrals. The final part of the project will use the functions from the first two parts and bring them together with an interface and analysis. This is the first part. This part of the project requires you to use skills up to Exam 2, but nothing beyond Exam 2. Theory Recall from calculus the concept of the derivative. In this project, we'll be using the computer to help us compute the derivatives of functions at various points. As you hopefully learned in calculus, we can investigate mathematics via the rule of three -- analytically, graphically, and numerically. Taking derivatives analytically often involves those "shortcuts" you know and love, i.e. "multiply by the old power and drop the power by one" and many more. Investigating derivatives graphically involves looking at the slope of the secant line to the curve at the point in question. We're going to focus on the numerical approach here. This is the approach we can explain to a computer to help us approximate the value of the derivative at a point. In some cases, we can get exact answers, but in many cases we cannot. However, in some cases, we can easily and quickly find derivatives analytically, but in other cases, it is quicker to find a numerical approximation.
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