_  ___      _   _                          _   _           _  
|  \/  |     | | | |                        | | (_)         | |  
| .  . | __ _| |_| |__   ___ _ __ ___   __ _| |_ _  ___ __ _| |  
| |\/| |/ _` | __| '_ \ / _ \ '_ ` _ \ / _` | __| |/ __/ _` | |  
| |  | | (_| | |_| | | |  __/ | | | | | (_| | |_| | (_| (_| | |  
\_|  |_/\__,_|\__|_| |_|\___|_| |_| |_|\__,_|\__|_|\___\__,_|_|  
                                                             
                                                             
       ______ _               _                            
       | ___ \ |             (_)                           
       | |_/ / |__  _   _ ___ _  ___ ___                   
       |  __/| '_ \| | | / __| |/ __/ __|                  
       | |   | | | | |_| \__ \ | (__\__ \                  
       \_|   |_| |_|\__, |___/_|\___|___/                  
                     __/ |                                 
                    |___/                                                                                                                                              

Author: Benjamin L’Huillier (Sejong University)
Date: 2025 Spring

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📄 License

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

📚 Course Content

Note: the lecture notes will be released when they are ready.

I. Mathematical Physics I (Spring)

1. Mathematical Foundations
   1.1 Elements of Logic
   1.2 Type of Reasoning
   1.3. Predicate and Quantifiers

2. Linear Algebra
   2.1 Intro
   2.1 Algebraic Structures
   2.2 Vector Spaces
   2.3 Linear Maps
   2.4 Matrices
   2.5 Determinants
   2.6 Inner Product
   2.7 Triple Product and Cross Product
   2.8 Eigenvalues and Eigenvectors (Notebook)

3. Vector Calculus
   3.1 Geometry in ℝ³: Coordinates (Notebook)
   3.2 Scalar Fields
   3.3 Vector Fields & Vector Operators
   3.4 Vector Calculus Theorems

4. Fourier Analysis
   4.1. Fourier Series (Notebook)
   4.2. Fourier Transform
   4.3. Discrete Fourier Transform
   4.4. $N$-dimensional Fourier Transform

5. Differential Equations 5.4 Distributions & Generalized Functions ([Notebook][Examples/IV_DiffEq/Distributions.ipynb])

II. Mathematical Physics II (Fall)

TBD; moslty Differential Equations

🎨 Examples and Illustrations

📚 References

Books

• Afken, Mathematical Methods for Physicists , Academic Press; 7th edition (2012)
• Boas, Mathematical Methods in the Physical Sciences, Wiley; 3rd edition (2005)
• Riley, Hobson & Bence, Mathematical Methods for Physics and Engineering: A Comprehensive Guide, Cambridge University Press; 3rd edition (2006)
• Wong Introduction to Mathematical Physics: Methods & Concepts, Oxford University Press; 2nd edition (2013)

Videos

• 3Blue1Brown’s excellent Essence of Linear Algebra: excellent for visualisation
• Dr Trevor Bazett's Calculus IV: Vector Calculus

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This README serves as an outline for the spring 2025 offering of Mathematical Physics I.