# 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

Intro Quiz [.pdf] 20 Jan
Vector Calculus
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]

ODEs
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
Eigenvector/values

Basic Problem Set  4 [.pdf] Due 22 Mar
Matrix Operation and Intro Linear Algebra Workshop [.pdf] (updated 08 Mar 3.40pm)

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]

PDEs
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)