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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)

Lecture 25 - Laplace Transform Solutions to PDEs

Go to the Course Home or watch other lectures:

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