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Lectures:
Lecture 00: Introduction
Lecture 01: Calculus; Linear Algebra; Hyperbolic Functions; Cycloid
Lecture 02: Euler's Identity; δ Function; Fourier Transform
Lecture 03: Orthogonal Coordinate System
Lecture 04: Vector Analysis
Lecture 05: Calculus of Variations
Lecture 06: Poisson Equation and Heat Equation
Lecture 07: Analytic Functions
Lecture 08: Laurent Expansion and Residue Theorem
Lecture 09: Γ Function; Analytic Continuation
Lecture 10: Art of Series
Lecture 11: Contour Integration
Lecture 12: Advanced Topics on δ Function and Fourier Transform
Lecture 13: Wavelet Transform
Lecture 14: Laplace Transform
Lecture 15: Stirling Formula;
n
D spherical integral
midterm solutions
Lecture 16: Wave Equation
Lecture 17: Separation of Variables; Green's Function
Lecture 18: Equations with source
Lecture 19: Harmonic Theory; Sturm-Liouville Equation; Bessel Function Introduction
Lecture 20: Bessel Function J
m
(x)
Lecture 21: More about Bessel Function J
m
(x)
Lecture 22: Bessel Function N
m
(x)
Lecture 23: Spherical Harmonic Y
lm
(x)
Lecture 24: Spherical Bessel j
l
(x)
Lecture 25: Legendre Polynomials; More about Y
lm
(x)
Lecture 26: Solving ODEs with Series Expansion
Lecture 27: Leapfrog algorithm (symplectic method)
Lecture 28: Nonlinear ODEs
Lecture 29: Advanced Topics on Green's Function
Lecture 30: Physical Approximations
Lecture 31: Green Function for 1D wave equation
Lecture 32: Green Function for 2D wave equation
Lecture 33: Green Function for 3D wave equation
summary of harmonic functions
the best memories of MMP
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