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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