ME 564 - Mechanical Engineering Analysis


Key Links

Video Lectures
Homework Dropbox
Homework (100% of total grade): Please turn in via the Dropbox by 5pm on Friday. Please include "ME564 HW1 Submission" in the email subject.
Textbook : No textbooks are required. We will mainly use course notes (.pdfs below). However, this book is a good reference:


Steve Brunton, MEB 305
Office Hours: TBD

Alan Kaptanoglu, MEB 120
Office Hours: Friday 10:30-11:30am

Teaching Assistants

Andrea Exil

Alexander Novokhodko

Minho Song

Office Hours: Tuesday 1:00-2:30pm, Wednesday 1:00-2:30pm, Thursday 10:00am-4:00pm, ME 236
Online Zoom Office Hours: Thursday 6:00-8:00pm

Course Description

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.


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 Python or Matlab, and all examples in class will be in these two languages.

MATLAB: Student Edition (recommended if you do not have access)
ICL: Matlab laboratory & login access (Communications Bldg B022 and B027)

(MATLAB Intro) (Matlab_Introduction.m, ode_test.m)

(Python Intro) (Python_Introduction.ipynb)


Part 1 - Ordinary Differential Equations

(Lecture 01) Class overview, example weather model in MATLAB (notes, L01_weather.m, L01_weather.ipynb)

(Lecture 02) Review of Calculus (derivative, power series, chain rule), First order linear ODEs with examples (notes, EX_LotkaVolterra.m)

(Lecture 03) Taylor series and solutions to first and second order (linear) ODEs (notes, L03_TaylorSeries.m, L03_TaylorSeries.ipynb)

(Lecture 04) Second order harmonic oscillator, characteristic equation, ode45 in Matlab (notes, L04_SpringMassDamper.m, L04_SpringMassDamper.ipynb)

(Lecture 05) Higher-order linear ODEs, characteristic equation, matrix systems of first order equations (notes, L05_ode45.m, L05_ode45.ipynb)

(Lecture 06) Higher-order linear ODEs, characteristic equation, matrix systems of first order equations, diagonalization using eigenvectors and eigenvalues (notes)

(Lecture 07) Eigenvalues, eigenvectors, and dynamical systems (linear systems of ODEs) (notes)

(Lecture 08) Examples of 2x2 systems of ODEs (with eigenvalues and eigenvectors), phase portraits (notes)

(Lecture 09) Linearization of nonlinear ODEs, Examples of 2x2 systems of ODEs (with eigenvalues and eigenvectors), phase portraits (notes)

(Lecture 10) Examples of nonlinear systems: particle in a potential well (notes)

(Lecture 11) Degenerate systems of equations and non-normal energy growth (notes, nonNormal.m, L11_nonNormal.ipynb)

(Lecture 12) ODEs with external forcing (inhomogenous ODEs) (notes)

(Lecture 13) ODEs with external forcing (inhomogenous ODEs) and the convolution integral! (notes)

Part 2 - Numerical Calculus and ODEs

(Lecture 14) Numerical differentiation using finite difference (notes, L14_FiniteDifference.m, L14_FiniteDifference2.m, L14_FiniteDifference.ipynb, L14_FiniteDifference2.ipynb)

(Lecture 15) Numerical differentiation and numerical integration (notes, NumericalIntegration.m, NumericalIntegration.ipynb)

(Lecture 16) Numerical integration and numerical solutions to ODEs (notes, misc. notes, L15_NumericalIntegration.m, L15_NumericalIntegration.ipynb)

(Lecture 17) Numerical solutions to ODEs (Forward and Backward Euler) (notes, L17_pend.m, L17_simpend.m, L17_pend.ipynb, L17_simpend.ipynb)

(Lecture 18) Runge-Kutta integration of ODEs and the Lorenz equation (notes, rk4singlestep.m, lorenz.m, L18_simulateLORENZ.m, L18_simulateLorenzSLOW.m,rk4singlestep.ipynb, lorenz.ipynb, L18_simulateLORENZ.ipynb, L18_simulateLorenzSLOW.ipynb)

(Lecture 19) Vectorized integration and the Lorenz equation (lorenz3D.m, L18_simulateLorenzFAST.m,lorenz3D.ipynb, L18_simulateLorenzFAST.ipynb)

(Lecture 20) Chaos in ODEs (Lorenz and double pendulum)

Part 3 - Complex Analysis

(Lecture 21) Complex numbers and functions (notes)

(Lecture 22) Roots of unity, branch cuts, analytic functions, and the Cauchy-Riemann conditions (notes)

(Lecture 23) Integration in the complex plane (Cauchy-Goursat Integral Theorem) (notes)

(Lecture 24) Cauchy Integral Formula (notes)

(Lecture 25) ML Bounds and examples of complex integration (notes)

(Lecture 26) Inverse Laplace Transform and the Bromwich integral (notes)