ME 564 - Mechanical Engineering Analysis


Key Links

Video Lectures
Video Lectures (Previous Years)
Homework Dropbox
Midterm, [Solution] (15% of total grade): The midterm will be posted online on Wednesday October 24 at 10:30am and will be due on Friday October 26 at 5:00pm. This is a 4-hour take-home exam. The 4 hours you use for the exam do not need to be consecutive. For example, you can work on the exam for 2 hours on Wednesay and another 2 hours on Thursday. You are allowed to used course notes (online pdfs and your own handwritten notes), online ME564 lecture videos, and your own homework solutions on the exam. All other resources are prohibited, including: the internet, other books, discussing the exam with other people.
Final (25% of total grade): The final will be handed out after class on Wednesday December 5 and will be due at 5pm on Friday December 7. The exam is cumulative. This is a 4-hour take-home exam with the same rules as the midterm.
Homework (60% of total grade): Please turn in via the Dropbox by 5pm on Friday. Please include "ME564 HW1 Submission" or "ME564 HW1 Submission, EDGE" in the email subject.
MATLAB: Student Edition (recommended if you do not have access)
ICL: Matlab laboratory & login access (Communications Bldg B022 and B027)
Textbook : No textbooks are required. We will mainly use course notes (.pdfs below). However, these two books are good references:


Steve Brunton, MEB 305
Office Hours: Wednesday, 10:30-11:15am

Kazuki Maeda, MEB 204
Office Hours: Tuesday 1:30-2:15pm

Teaching Assistants

Gaurav Mahamuni

Brek Meuris

Zhitao Yu

Office Hours: Tuesday 1:00-2:30pm, Wednesday 1-2:30pm, Thursday 10am-4pm, ME 236
Online Skype Office Hours (Edge): Thursday 6:30-7:30pm (username:live:zhitaoyu1)

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 Matlab, and all examples in class will be in Matlab.


Part 1 - Ordinary Differential Equations

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

(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)

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

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

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

(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)

(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)

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

(Lecture 16) Numerical integration and numerical solutions to ODEs (notes, misc. notes, L15_NumericalIntegration.m, L16_SpringMassDamper.m)

(Lecture 17) Numerical solutions to ODEs (Forward and Backward Euler) (notes, L16_SpringMassDamper.m, L17_pend.m, L17_simpend.m)

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

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

(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, and cross product (notes)

(Lecture 22) Div, Grad, and Curl (notes)

(Lecture 23) Gauss's Divergence Theorem (notes)

(Lecture 24) Directional derivative, continuity equation, and examples of vector fields (notes)

(Lecture 25) Stokes' theorem and conservative vector fields (notes)

(Lecture 26) Potential flow and Laplace's equation (notes)

(Lecture 27) Potential flow, stream functions, and examples (notes)

(Lecture 28) Example of ODE for particle trajectories in a time-varying vector field: The double gyre (doublegyreVEC.m, integrateDG.m, rk4singlestep.m).