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Welcome to Mathematical Modeling in Physics

0 - Intro and Syllabus

Syllabus and Overview of PHY 415

1 - Mechanics and ODEs

29 Aug 23 - Activity: What is a Model?
29 Aug 23 - Notes: Simple Harmonic Oscillator
31 Aug 23 - Notes: Frames and Coordinates
31 Aug 23 - Activity: Frames and Coordinates
5 Sept 23 - Notes: Lagrangian Dynamics
5 Sep 23 - Activity: Calculus of Variations and Lagrangian Dynamics
7 Sept 23 - Notes: Numerical Integration in 1D
7 Sep 23 - Activity: Numerical Integration and More Lagrangians
12 Sept 23 - Notes: Dynamical Systems and Phase Space
12 Sep 23 - Activity: The Dynamical Systems Approach and Phase Portraits
14 Sept 23 - Conducting a complete analysis of an ODE
19 Sep 23 - Notes: Heading towards Chaos
19 Sep 23 - The Duffing Oscillator

2 - E&M and PDEs

26 Sept 23 - Notes: Maxwell’s Equations
26 Sept 23 - Notes: Static Fields
26 Sep 23 - Activity: Electrostatic Fields
28 Sep 23 - Activity: Superposition of Fields
3 Oct 23 - Notes: Electric Potential - a scalar field
3 Oct 23 - Activity: PDEs and Separation of Variables
5 Oct 23 - Activity: Solving PDEs in Spherical Coordinates
9 Oct 23 - Notes: Method of Relaxation
10 Oct 23 - Activity: Matching Boundary Conditions and Plotting the Potential
12 Oct 23 - Activity: Method of Relaxation

3 - Waves and Oscillations

16 Oct 23 - Notes: Coupled Oscillations
16 Oct 23 - Notes: Introduction to Waves
17 Oct 23 - Activity: Normal Modes
19 Oct 23 - Activity: Normal Modes of N Coupled Oscillators
25 Oct 23 - Notes: Solutions to The Wave Equation
26 Oct 2023 - Activity: 1-Dimensional Travelling Waves
30 Oct 2023 - Notes: Deconstructing Waves
31 Oct 23 - Activity: Signal Deconstruction
2 Nov 23 - Activity: Automated Signal Deconstruction & Reconstruction
6 Oct 23 - Notes: Fast Fourier Transform
7 Nov 23 - Activity: The Fast Fourier Transform
9 Nov 23 - Activity: Applying The Fast Fourier Transform
13 Nov 23 - Notes: Applications of FFTs
14 & 16 Nov 23 - Using the FFT with Real Data

4 - Randomness and Distributions

20 Nov 23 - Notes: Random Processes
21 Nov 23 - Activity: Introduction to Random Processes
27 Nov 23 - Notes: Counting and Combinatorics
27 Nov 23 - Notes: Monte Carlo Simulations
28 Nov 23 - Activity: Model of Two Bodies in Thermal Contact
30 Nov 23 - Activity: Monte Carlo Integration
4 Dec 23 - Notes: Markov Chain Monte Carlo Modeling
7 Dec 23 - Activity: Modeling

Assignments

Updated Rubric for Worked Problems and Projects
Worked Problem Assignment 1
Worked Problem Assignment 2
Project 1 - Classical Mechanics and ODEs
Worked Problem Assignment 3
Worked Problem Assignment 4
Project 2 - PDEs, Laplace’s Equation, and the Method of Relaxation
Worked Problem Assignment 5
Worked Problem Assignment 6
Project 3 - Waves and Fourier Analysis
Worked Problem Assignment 7
Project 4 - Probabilistic Modeling

Appendices

Works Cited

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By Danny Caballero, Alia Valentine

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