Engineering Mathematics for Mechanical Engineers I

Course Description

This course by Prof. Steve Brunton 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.

In this course, we will develop many powerful analytic tools. Equally important is the ability to implement these tools on a computer. The instructor and TAs use Matlab, and all examples in class will be in Matlab.

Engineering Mathematics for Mechanical Engineers I
From Lecture 6: Matrix systems of first order equations using eigenvectors and eigenvalues
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Video Lectures & Study Materials

Visit the official course website for more study materials:

# Lecture Play Lecture
1 Overview of engineering mathematics Play Video
2 Review of calculus and first order linear ODEs Play Video
3 Taylor series and solutions to first and second order linear ODEs Play Video
4 Second order harmonic oscillator, characteristic equation, ode45 in Matlab Play Video
5 Higher-order ODEs, characteristic equation, matrix systems of first order ODEs Play Video
6 Matrix systems of first order equations using eigenvectors and eigenvalues Play Video
7 Eigenvalues, eigenvectors, and dynamical systems Play Video
8 2x2 systems of ODEs (with eigenvalues and eigenvectors), phase portraits Play Video
9 Linearization of nonlinear ODEs, 2x2 systems, phase portraits Play Video
10 Examples of nonlinear systems: particle in a potential well Play Video
11 Degenerate systems of equations and non-normal energy growth Play Video
12 ODEs with external forcing (inhomogeneous ODEs) Play Video
13 ODEs with external forcing (inhomogeneous ODEs) and the convolution integral Play Video
14 Numerical differentiation using finite difference Play Video
15 Numerical differentiation and numerical integration Play Video
16 Numerical integration and numerical solutions to ODEs Play Video
17 Numerical solutions to ODEs (Forward and Backward Euler) Play Video
18 Runge-Kutta integration of ODEs and the Lorenz equation Play Video
19 Vectorized integration and the Lorenz equation Play Video
20 Chaos in ODEs (Lorenz and the double pendulum) Play Video
21 Linear algebra in 2D and 3D: inner product, norm of a vector, and cross product Play Video
22 Div, Grad, and Curl Play Video
23 Gauss's Divergence Theorem Play Video
24 Directional derivative, continuity equation, and examples of vector fields Play Video
25 Stokes' theorem and conservative vector fields Play Video
26 Potential flow and Laplace's equation Play Video
27 Potential flow, stream functions, and examples Play Video
28 ODE for particle trajectories in a time-varying vector field Play Video


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