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Advanced Topics in Calculus

by John Hubbard and Barbara Burke Hubbard

The three volumes of Advanced Topics in Calculus are a continuation of Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach, but they can be used independently by any student with sufficient background in linear algebra, multivariable calculus, and differential forms.

Volume 1: Inner Products, Fourier Analysis, Wavelets, and Orthogonal Polynomials

Volume 2: Differential Equations, Eigenvalues...

Volume 3: Differential Forms and Electromagnetism

Volume 1

Topics covered:

Fields and Vector Spaces

Change of Basis

 Real Inner products and Schwarz

Orthonormal bases and Gram-Schmidt

Orthogonal matrices and Gram-Schmidt

Complex Inner Products

Fourier Series

Convergence of Fourier Series

Windows and Signal Processing

Fast Fourier Transform

Orthogonal Polynomials and Gaussian Integration

Fourier Transforms

Signal Processing and the Heisenberg Uncertainty Principle

Signal Processing and the Sampling Theorem