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Course Resources

Lecture notes, summaries, etc.

General
pdf.gif Greek alphabet
html.gif Math anxiety?
Algebra
pdf.gif Newton's binomial and Pascal's triangle
html.gif Multi-index notation
pdf.gif Multinomial formula
pdf.gif Summation formulas
html.gif Permutations
Geometry
html.gif The Star Trek theorem
Linear Algebra
pdf.gif Vector spaces and linear maps
html.gif Vector space
html.gif Basis
html.gif Linear maps and matrices
html.gif Fundamental question of linear algebra
pdf.gif Projection and dot product
pdf.gif Determinant
pdf.gif Linear Algebra Glossary
Calculus
pdf.gif Calculus synopsis
pdf.gif Linear approximation and the rules of differentiation
html.gif Geometric series
Vector Calculus
pdf.gif Calculus in R3 synopsis
html.gif Differentiable functions
pdf.gif Derivative as a linear map
pdf.gif Higher derivatives as multilinear maps
pdf.gif Exterior product and differentiation
pdf.gif Parametric curves and integration
pdf.gif Frenet frame
pdf.gif Fundamental Theorem of Calculus for curve integrals
pdf.gif Path independence and potential
pdf.gif Simplices and boundary
pdf.gif Path, surface, and volume integrals, etc.
pdf.gif Fundamental Theorem of Calculus
pdf.gif Fundamental Theorem of Calculus diagram
pdf.gif Vector interpretations of exterior calculus
pdf.gif Green's identities and harmonic functions
pdf.gif Flows induced by sources, doublets and vortex filaments
Functions of a complex variable
html.gif Introduction to complex numbers
html.gif Fundamental Theorem of Algebra
html.gif Complex differentiable functions
pdf.gif Functions C -> C as plane transformations
pdf.gif Complex Calculus
pdf.gif Normal convergence
pdf.gif Holomorphic functions
pdf.gif Germs and continuation along paths
pdf.gif Stereographic projection, the Riemann sphere, and the chordal metric
pdf.gif Flow past a cylinder and an inclined plate
pdf.gif Taylor series with remainder
pdf.gif Complex iteration and Newton's method
html.gif sinh z
html.gif cos z
html.gif z cos (1/z)
html.gif f(z)=e1/z
html.gif Gamma function
html.gif Weierstrass P-function
html.gif Addition theorems
pdf.gif Complex analysis problems from UC Berkeley prelims
Topology and analysis
pdf.gif Normality of metric spaces and the shrinking lemma
html.gif TRUE/FALSE questions in Real Analysis
pdf.gif The Intermediate Value Theorem
html.gif Interchange theorems
pdf.gif Spaces of complex valued functions
pdf.gif From Laurent to Fourier
pdf.gif Convergence of Fourier series in the mean
pdf.gif Pointwise convergence of Fourier series
pdf.gif Poisson summation formula
pdf.gif Fourier series and transforms
Differential equations
pdf.gif Energy, entropy and uniqueness
pdf.gif Heat equation in 1-d via the Fourier transform
pdf.gif Eigenfunctions and adjoints
pdf.gif Circular membrane
pdf.gif Approximation of elliptic boundary value problems
Abstract algebra
pdf.gif Natural transformations and adjoints
pdf.gif Subobject classifier and the category of actions

Last updated: Jul 19 17:43 / Last fetched: Wed Aug 27 21:21:13 CDT 2008