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ME 564: Mechanical Engineering Analysis

ME 564: Mechanical Engineering Analysis (Fall 2014, University of Washington). Instructor: Professor Steven Brunton. Ordinary differential equations. Numerical calculus and ODEs. Linear algebra and vector calculus.

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 27 - Potential Flow, Stream Functions, and Examples

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Part 1: Ordinary Differential Equations

Lecture 01 - Overview of Engineering Mathematics

Lecture 02 - Review of Calculus and First Order Linear ODEs

Lecture 03 - Taylor Series and Solutions to First and Second Order Linear ODEs

Lecture 04 - Second Order Harmonic Oscillator, Characteristic Equation, ode45 in Matlab

Lecture 05 - Higher Order ODEs, Characteristic Equation, Matrix Systems of First Order ODEs

Lecture 06 - Matrix Systems of First Order Equations using Eigenvectors and Eigenvalues

Lecture 07 - Eigenvalues, Eigenvectors, and Dynamical Systems

Lecture 08 - 2x2 Systems of ODEs (with Eigenvalues and Eigenvectors), Phase Portraits

Lecture 09 - Linearization of Nonlinear ODEs, 2x2 Systems of ODEs, Phase Portraits

Lecture 10 - Examples of Nonlinear Systems: Particle in a Potential Well

Lecture 11 - Degenerate Systems of Equations and Non-normal Energy Growth

Lecture 12 - ODEs with External Forcing (Inhomogeneous ODEs)

Lecture 13 - ODEs with External Forcing (Inhomogeneous ODEs) and the Convolution Integral

Part 2: Numerical Calculus and ODEs

Lecture 14 - Numerical Differentiation using Finite Difference

Lecture 15 - Numerical Differentiation and Numerical Integration

Lecture 16 - Numerical Integration and Numerical Solutions to ODEs

Lecture 17 - Numerical Solutions to ODEs (Forward and Backward Euler)

Lecture 18 - Runge-Kutta Integration of ODEs and the Lorenz Equation

Lecture 19 - Vectorized Integration and the Lorenz Equation

Lecture 20 - Chaos in ODEs (Lorenz and Double Pendulum)

Part 3: Linear Algebra and Vector Calculus

Lecture 21 - Linear Algebra in 2D and 3D: Inner Product, Norm of a Vector, Cross Product

Lecture 22 - Divergence, Gradient, and Curl

Lecture 23 - Gauss' Divergence Theorem

Lecture 24 - Directional Derivative, Continuity Equation, and Examples of Vector Fields

Lecture 25 - Stokes' Theorem and Conservative Vector Fields

Lecture 26 - Potential Flow and Laplace's Equation

Lecture 27 - Potential Flow, Stream Functions, and Examples

Lecture 28 - ODE for Particle Trajectories in a Time-varying Vector Field