Engineering Programming 11 - Calculus
Channel: Keith Doc
Date: 2022-10-04

This video is covers how to do calculus (derivatives and integrals) in Matlab. It's intended audience is those interested in the STEM field who have little to no experience with programming and want to figure out how to apply it to STEM.

0:00 Intro
1:25 Review - fit data to curve then diff/int that equation
3:23 Constructing a symbolic from a polynomial
5:38 Reivew - Differentiating an equation
7:10 Review of the derivative so we can derive the numerical derivative
9:09 Approximating the numerical derivative
10:00 Equations for forward, backwards, and center difference
11:08 Final equations - Forward, Backward, and Center difference methods to calculate derivative
11:58 Limitations of the difference methods
13:38 Preferred method of calculating the derivative from differences
14:50 Going to Matlab
15:54 Matlab - calculating forward difference at a specific point
16:35 Matlab - calculating center difference at a specific point
17:06 Matlab - calculating backward difference at a specific point
17:47 Matlab - the lines for the slopes to view the differences graphically
19:19 The forward difference at n is the same as the backward difference at n+1
20:12 Matlab - calculating the forward, backward, and center difference at every point
23:24 Matlab - Visualizing the derivative
26:06 Limitation of numerical derivatives
26:50 Matlab - Making a function to calculate the numerical derivative
31:37 Matlab - builtin function gradient to calculate difference
32:30 Plotting the gradient results with my forward difference and the data
34:49 How we could make a function that does the same as gradient
35:41 Comparing the two methods of finding the derivative of some data
39:40 Integrals
39:52 Review of the Integral so we can define the numerical integral
44:20 Matlab - calculating the integrals at a single point
45:53 Matlab - computing the integral at every point
49:16 Matlab - builtin function for numerical integration trapz
51:50 Compare Matlab numerical vs built-in trapz
52:43 Comparison of results with the symbolic, numerical, and builtin trapz methods
55:00 Changing the input data to see how that affects the integral
56:44 Noting how noise is filtered out with integration
57:47 Review