Math Methods (Engn/Phys 225), winter 2021

Syllabus and Course Calendar

Syllabus and Course Policies [.pdf]

Daily Schedule [last updated 31 Mar 2021]

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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]
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) 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]
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)