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Math Methods (Engn/Phys 225), winter 2021

Syllabus and Course Calendar

Syllabus and Course Policies [.pdf]

Daily Schedule [last updated 31 Mar 2021]

Problem Sets and Resources

Module/Readings/pptx Problem Sets and Due Dates Resources
Intro to Math Methods

  The many applications of math [.pptx]

Intro Quiz [.pdf] 20 Jan  
Vector Calculus
   Directional Derivative and Gradient [.pptx]
   The Curl [.pptx]
   The Divergence [.pptx]
   The Laplacian [.pptx]
Basic Problem Set  1 [.pdf]    Due 05 Feb    PS1 Solutions [.pdf]

Basic Problem Set 2 [.pdf]    Due 15 Feb

Matlab workshop Guide  [.pdf]  [.docx]

Demo code [on box]

Complex Numbers
   Euler’s Identity: Trig and Complex Exponentials [.pptx]   
   Oscillations of real system
  Complex Numbers/Euler’s ID overview and worksheet [.pdf]  and Solutions to worksheet probs [.pdf]
    1st order ODE
    2nd order ODEs (under-, over-, critically-damped systems)
    2nd order ODEs (damped, driven systems)
Basic Problem Set  3 [.pdf]  (last updated 15 Mar 2021)
Intro ODEs worksheet [.pdf]   and ODE intro solutions [.pdf]
Linear Algebra 
    Basic Matrix Operations
Basic Problem Set  4 [.pdf] Due 22 Mar
Matrix Operation and Intro Linear Algebra Workshop [.pdf] (updated 08 Mar 3.40pm)

Math Models in Medicine: Coupled ODEs [.pptx]  
Diabetes Math Model Worksheet [.pdf] (last modified: 16 Mar 2021)  and Solutions [pdf]

Fourier Series and Frequency Spectra
   sin/cos form
   complex exponential form
 Intro to Fourier Series: Math meets music [.pptx]Analyzing real world data with the discrete fourier transform
 Discrete Fourier Transform: Intro theory [.pdf]
Basic Problem Set 5 [.pdf] Due 05 Apr


Fourier Series Coefficients workshop [.pdf]  (26 Mar 2021) and Solution Set [.pdf]

DFT/FFT matlab workshop [.pdf]

  1-D wave equation [pptx]
    1-D diffusion equation 
    2-D wave equation (time permitting)


1-D Wave Equation Worksheet: Separation of Variables Method [pdf]

Challenge Problems and Resources

  1. Challenge Problem Presentations: format and grading rubric [.pdf] 
  2. Challenge Problem 01 [.pdf]  Due 22 Feb
  3. Challenge Problem  02 [.pdf] Presentations 09 Apr 

Exam/Final Problem

(choose exam or final problem above, not both!  Due 14 Apr 2021)

  1. Concept Review [.pdf] 
  2. Sample Exam Problems [.pdf] (exam will be 3 hours total, closed book, expected to take 1 hr to write)
  3. Sample PDEs problem [.pdf] (this will be open everything, and will likely take about 3 hrs to write)