# InfoCoBuild

## ME 565: Mechanical Engineering Analysis

ME 565: Mechanical Engineering Analysis (Winter 2015, University of Washington). Instructor: Professor Steven Brunton. Complex analysis. Partial differential equations. Transform methods (Laplace and Fourier transforms).

This course 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. (from washington.edu)

 Complex Numbers and Functions

 Part 1: Complex Analysis Lecture 01 - Complex Numbers and Functions Lecture 02 - Roots of Unity, Branch Cuts, Analytic Functions, and the Cauchy-Riemann Conditions Lecture 03 - Integration in the Complex Plane (Cauchy-Goursat Integral Theorem) Lecture 04 - Cauchy's Integral Formula Lecture 05 - ML Bounds and Examples of Complex Integration Lecture 06 - Inverse Laplace Transform and the Bromwich Integral Part 2: Partial Differential Equations and Transform Methods (Laplace and Fourier) Lecture 07 - Canonical Linear PDEs: Wave Equation, Heat Equation, and Laplace's Equation Lecture 08 - Heat Equation: Derivation and Equilibrium Solution in 1D (i.e., Laplace's Equation) Lecture 09 - Heat Equation in 2D and 3D, 2D Laplace Equation (on Rectangle) Lecture 10 - Analytic Solution to Laplace's Equation in 2D (on Rectangle) Lecture 11 - Numerical Solution to Laplace's Equation in Matlab, Intro to Fourier Series Lecture 12 - Fourier Series Lecture 13 - Infinite Dimensional Function Spaces and Fourier Series Lecture 14 - Fourier Transforms Lecture 15 - Properties of Fourier Transforms and Examples Lecture 16 - Discrete Fourier Transforms (DFT) Lecture 17 - Fast Fourier Transforms (FFT) and Audio Lecture 18 - FFT and Image Compression Lecture 19 - Fourier Transform to Solve PDEs: 1D Heat Equation on Infinite Domain Lecture 20 - Numerical Solutions to PDEs Using FFT Lecture 21 - The Laplace Transform Lecture 22 - Laplace Transform and ODEs Lecture 23 - Laplace Transform and ODEs with Forcing and Transfer Functions Lecture 24 - Convolution Integrals, Impulse and Step Responses Lecture 25 - Laplace Transform Solutions to PDEs Lecture 26 - Solving PDEs in Matlab using FFT Lecture 27 - Singular Value Decomposition (SVD) and Data Science 1 Lecture 28 - Singular Value Decomposition (SVD) and Data Science 2 Lecture 29 - Singular Value Decomposition (SVD) and Data Science 3

 References ME 565 - Mechanical Engineering Analysis (Winter 2015) Instructor: Professor Steven Brunton. Syllabus. Lecture Notes. Homework and Solutions. This course will provide an in-depth overview of powerful mathematical techniques for the analysis of engineering systems.