The goal of these notes is to stay as true to the term “crash course” as possible, by providing a “no nonsense” introduction to essential mathematical concepts in physics. My hope is that someone who is familiar with undergrad-level math will find great use in these.
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Mathematics For Physics
- Differential Equations (1): Conceptual Introduction & Terminology
- Differential Equations (2): First Order Linear Separable DEs
- Differential Equations (3): First Order Linear DEs-Integrating Factor & A General Solution
- Differential Equations (4): First Order Exact DEs
- Differential Equations (4b): Exactifying First Order DEs
- Partial Differential Equations (1): Introduction (Coming Soon)
- Fourier Series (1): Basic Facts
- Fourier Series (2): Finding The Fourier Series
- Fourier Series (3): Examples (Coming Soon)
- Fourier Transforms (1): Fourier Transform From Fourier Series
- Fourier Transforms (2): Finding The Transform & An Example
- Function Spaces (0): A New Notation For Vectors
- Function Spaces (1): Functions As Vectors
- Function Spaces (2): What Does It Mean?
- Introduction To Completeness
- Eigenfunctions & Differential Operators
- Hermitian Operators (1)
- Hermitian Operators (2) Example: Infinite Square Well & Orthogonality
- Hermitian Operators (3): Completeness