Engineering Mathematics (UW ME564 and ME565)

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About Course

Engineering Mathematics is designed for students with little math backgrounds to learn Applied Mathematics in the most simple and effective way. The aim of this course is to provide students with the knowledge of not only mathematical theories but also their real-world applications so students understand how and when to use them.

This Engineering Mathematics course is divided into 2 sections. Section 1 (the first 28 lectures) covers the most fundamental math that anyone should learn of ME564. Here you will learn everything about ME564. At the end of section 1, you should have a better understanding of the ME564 classes. Section 2 (29 Lecture ) introduces you to the world of calculus. Here you will learn the fundamental definition of integration and differentiation. You will also learn the most commonly-used rules and properties through simple examples and full knowledge of the ME565 class lecture.

At the end of this course, you should have a good understanding of all the topics covered in this course and be able to use them in real-world applications.

Who this Engineering Mathematics course is for:

  1. Students who wish to learn applied mathematics. That is, how mathematics is used in the practical world.
  2. Students who are going to learn more advanced engineering courses. Most intermediate engineering courses will require the basic math covered in this course.
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What Will You Learn?

  • Ability to distinguish different numbers types and understand power, logarithm, sine, and cosine
  • Understanding the difference between functions and equations and knowing how to plot basic functions and solve equations.
  • Knowing the definition of differentiation and integration from the first principle and how to use some properties and rules to find the derivatives and integration of more complicated functions
  • Ability to do basic complex number arithmetic using both polar and rectangular forms.
  • Understanding sequence and series and knowing how to evaluate a series.
  • Knowing why all of these topics are important in engineering

Course Content

Engineering Mathematics

  • ME564 Lecture 1: Overview of engineering mathematics
    41:16
  • ME564 Lecture 2: Review of calculus and first order linear ODEs
    48:43
  • ME564 Lecture 3: Taylor series and solutions to first and second order linear ODEs
    53:23
  • ME564 Lecture 4: Second order harmonic oscillator, characteristic equation, ode45 in Matlab
    00:00
  • ME564 Lecture 5: Higher-order ODEs, characteristic equation, matrix systems of first order ODEs
    00:00
  • ME564 Lecture 6: Matrix systems of first order equations using eigenvectors and eigenvalues
    00:00
  • ME564 Lecture 7: Eigenvalues, eigenvectors, and dynamical systems
    00:00
  • ME564 Lecture 8: 2×2 systems of ODEs (with eigenvalues and eigenvectors), phase portraits
    00:00
  • ME564 Lecture 9: Linearization of nonlinear ODEs, 2×2 systems, phase portraits
    00:00
  • ME564 Lecture 10: Examples of nonlinear systems: particle in a potential well
    00:00
  • ME564 Lecture 11: Degenerate systems of equations and non-normal energy growth
    00:00
  • ME564 Lecture 12: ODEs with external forcing (inhomogeneous ODEs)
    00:00
  • ME564 Lecture 13: ODEs with external forcing (inhomogeneous ODEs) and the convolution integral
    00:00
  • ME564 Lecture 14: Numerical differentiation using finite difference
    00:00
  • ME564 Lecture 15: Numerical differentiation and numerical integration
    00:00
  • ME564 Lecture 16: Numerical integration and numerical solutions to ODEs
    00:00
  • ME564 Lecture 17: Numerical solutions to ODEs (Forward and Backward Euler)
    00:00
  • ME564 Lecture 18: Runge-Kutta integration of ODEs and the Lorenz equation
    00:00
  • ME564 Lecture 19: Vectorized integration and the Lorenz equation
    00:00
  • ME564 Lecture 20: Chaos in ODEs (Lorenz and the double pendulum)
    00:00
  • ME564 Lecture 21: Linear algebra in 2D and 3D: inner product, norm of a vector, and cross product
    00:00
  • ME564 Lecture 22: Div, Grad, and Curl
    00:00
  • ME564 Lecture 23: Gauss’s Divergence Theorem
    00:00
  • ME564 Lecture 24: Directional derivative, continuity equation, and examples of vector fields
    00:00
  • ME564 Lecture 25: Stokes’ theorem and conservative vector fields
    00:00
  • ME564 Lecture 26: Potential flow and Laplace’s equation
    00:00
  • ME564 Lecture 27: Potential flow, stream functions, and examples
    00:00
  • ME564 Lecture 28: ODE for particle trajectories in a time-varying vector field
    00:00
  • ME565 Lecture 1: Complex numbers and functions
    00:00
  • ME565 Lecture 2: Roots of unity, branch cuts, analytic functions, and the Cauchy-Riemann conditions
    00:00
  • ME565 Lecture 3: Integration in the complex plane (Cauchy-Goursat Integral Theorem)
    00:00
  • ME565 Lecture 4: Cauchy Integral Formula
    00:00
  • ME565 Lecture 5: ML Bounds and examples of complex integration
    00:00
  • ME565 Lecture 6: Inverse Laplace Transform and the Bromwich Integral
    00:00
  • ME565 Lecture 7: Canonical Linear PDEs: Wave equation, Heat equation, and Laplace’s equation
    00:00
  • ME565 Lecture 8: Heat Equation: derivation and equilibrium solution in 1D (i.e., Laplace’s equation)
    00:00
  • ME565 Lecture 9: Heat Equation in 2D and 3D. 2D Laplace Equation (on rectangle)
    00:00
  • ME565 Lecture 10: Analytic Solution to Laplace’s Equation in 2D (on rectangle)
    00:00
  • ME565 Lecture 11: Numerical Solution to Laplace’s Equation in Matlab. Intro to Fourier Series
    00:00
  • ME565 Lecture 12: Fourier Series
    00:00
  • ME565 Lecture 13: Infinite Dimensional Function Spaces and Fourier Series
    00:00
  • ME565 Lecture 14: Fourier Transforms
    00:00
  • ME565 Lecture 15: Properties of Fourier Transforms and Examples
    00:00
  • ME565 Lecture 16: Discrete Fourier Transforms (DFT)
    00:00
  • ME565 Lecture 16 Bonus: DFT in Matlab
    00:00
  • ME565 Lecture 17: Fast Fourier Transforms (FFT) and Audio
    00:00
  • ME565 Lecture 18: FFT and Image Compression
    00:00
  • ME565 Lecture 19: Fourier Transform to Solve PDEs: 1D Heat Equation on Infinite Domain
    00:00
  • ME565 Lecture 20: Numerical Solutions to PDEs Using FFT
    00:00
  • ME565 Lecture 21: The Laplace Transform
    00:00
  • ME565 Lecture 22: Laplace Transform and ODEs
    00:00
  • ME565 Lecture 23: Laplace Transform and ODEs with Forcing and Transfer Functions
    00:00
  • ME565 Lecture 24: Convolution integrals, impulse and step responses
    00:00
  • ME565 Lecture 25: Laplace transform solutions to PDEs
    00:00
  • ME565 Lecture 26: Solving PDEs in Matlab using FFT
    00:00
  • ME 565 Lecture 27: SVD Part 1
    00:00
  • ME565 Lecture 28: SVD Part 2
    00:00
  • ME565 Lecture 29: SVD Part 3
    00:00
  • The Laplace Transform: A Generalized Fourier Transform
    00:00

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