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


Go to the Course Home or watch other lectures:

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