Engineering Mathematics for Mechanical Engineers II

Course Description

This is the second part of Prof. Steve Brunton's course on Mechanical Engineering Mathematics. It will provide an in-depth overview of powerful mathematical techniques for the analysis of engineering systems. In addition to developing core analytical capabilities, students will gain proficiency with various computational approaches used to solve these problems. Applications will be emphasized, including fluid mechanics, elasticity and vibrations, weather and climate systems, epidemiology, space mission design, and applications in control.

In this course, we will develop many powerful analytic tools. Equally important is the ability to implement these tools on a computer. The instructor and TAs use Matlab, and all examples in class will be in Matlab.

Engineering Mathematics for Mechanical Engineers II
From Lecture 22: Laplace Transform and ODEs
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Video Lectures & Study Materials

Visit the official course website for more study materials:

# Lecture Play Lecture
1 Complex numbers and functions Play Video
2 Roots of unity, branch cuts, analytic functions, and the Cauchy-Riemann conditions Play Video
3 Integration in the complex plane (Cauchy-Goursat Integral Theorem) Play Video
4 Cauchy Integral Formula Play Video
5 ML Bounds and examples of complex integration Play Video
6 Inverse Laplace Transform and the Bromwich Integral Play Video
7 Canonical Linear PDEs: Wave equation, Heat equation, and Laplace's equation Play Video
8 Heat Equation: derivation and equilibrium solution in 1D (i.e., Laplace's equation) Play Video
9 Heat Equation in 2D and 3D. 2D Laplace Equation (on rectangle) Play Video
10 Analytic Solution to Laplace's Equation in 2D (on rectangle) Play Video
11 Numerical Solution to Laplace's Equation in Matlab. Intro to Fourier Series Play Video
12 Fourier Series Play Video
13 Infinite Dimensional Function Spaces and Fourier Series Play Video
14 Fourier Transforms Play Video
15 Properties of Fourier Transforms and Examples Play Video
16 Discrete Fourier Transforms (DFT) Play Video
17 Bonus: DFT in Matlab Play Video
18 Fast Fourier Transforms (FFT) and Audio Play Video
19 FFT and Image Compression Play Video
20 Fourier Transform to Solve PDEs: 1D Heat Equation on Infinite Domain Play Video
21 Numerical Solutions to PDEs Using FFT Play Video
22 The Laplace Transform Play Video
23 Laplace Transform and ODEs Play Video
24 Laplace Transform and ODEs with Forcing and Transfer Functions Play Video
25 Convolution integrals, impulse and step responses Play Video
26 Laplace transform solutions to PDEs Play Video
27 Solving PDEs in Matlab using FFT Play Video
28 SVD Part 1 Play Video
29 SVD Part 2 Play Video
30 SVD Part 3 Play Video


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