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 GramSchmidt
Orthogonal
matrices and GramSchmidt
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
Wavelets
