Lecture Notes for PHYS:4761 Mathematical Methods of Physics I
Below are links to the scanned PDF versions of the lecture notes handed out in class:
- Lecture #1: Infinite Series, Series of Functions, Binomial Theorem
- Lecture #2: Series Expansion of Functions, Vectors, Complex Functions
- Lecture #3: Derivatives, Integrals, and the Delta Function
- Lecture #4: Determinants
- Lecture #5: Matrices
- Lecture #6: Vector Analysis: Basics and Transformations
- Lecture #7: Vector Differentiation and Integration
- Lecture #8: Integral Theorems and Potential Theory
- Lecture #9: Curvilinear Coordinates
- Lecture #10: Tensor Analysis
- Lecture #11: Jacobians and Differential Forms
- Lecture #12: Vectors in Function Spaces
- Lecture #13: Gram-Schmidt Orthogonalization and Operators
- Lecture #14: Transformations, Invariants, and Matrix Eignevalue Problems
- Lecture #15: Hermitian and Normal Matrix Eigenvalue Problems
- Lecture #16: Ordinary Differential Equations
- Lecture #17: Second-Order Linear ODEs
- Lecture #18: Homogeneous and Inhomogeneous ODEs, Sturm-Liouville Theory
- Lecture #19: Variation Method and Partial Differential Equations
- Lecture #20: Separation of Variables
- Lecture #21: Laplace, Poisson, Wave, and Diffusion Equations
- Lecture #22: Green's Functions
- Lecture #23: Multidimensional Green's Functions and Probability
- Lecture #24: Random Variables and Binomial and Poisson Distributions
- Lecture #25: Normal Distribution, Transformations, and Statistics