Single Variable Calculus

Video Lectures for Single-variable Calculus

Over 50 short videos by Selwyn Hollis (University of Houston) on basic calculus topics - the first 5 have the titles: Limits and Graphs (11 minutes), Calculation of Limits (17 minutes), Trigonometric Limits (17 minutes), Continuity (19.5 minutes), The Derivative (18.5 minutes). View using Apple's QuickTime 7 player or stream to an iPhone or iPod Touch. These are not videoed lectures taken in a lecture room but a very effective mix of graphics (equations, graphs etc) with audio.

Calculus Lecture Notes

These notes by S. Tryphonas and P. Hill (University of Toronto, Scarborough) are in fact problem sets, old tests and exams - hundreds of them and some with solutions.

Calculus

Textbook by Gilbert Strang, made available by MIT OpenCourseWare and covering single and multivariable calculus in depth - and rich with applications. There are also answers to odd-numbered problems, a table of integrals, an instructor's manual and a student study guide with model problems with complete solutions, extra drill problems, read-through questions from the text with the blanks filled in and solutions to selected even-numbered problems in each section. The book (more than 600 pages) can be downloaded as a single PDF file but individual chapters are also available.

Chapter headings are: Introduction to Calculus, Derivatives, Applications of the Derivative, The Chain Rule, Integrals, Exponentials and Logarithms, Techniques of Integration, Applications of the Integral, Polar Coordinates and Complex Numbers, Infinite Series, Vectors and Matrices, Motion along a Curve, Partial Derivatives, Multiple Integrals, Vector Calculus, Mathematics after Calculus

Multivariable Calculus

Vector Calculus

A text on elementary multivariable calculus by Michael Corral (Schoolcraft College, Michigan), designed for students who have completed courses in single-variable calculus. It covers basic vector algebra (lines, planes and surfaces), vector-valued functions, functions of 2 or 3 variables, partial derivatives, optimization, multiple integrals and line and surface integrals. There is also a discussion of numerical methods and a section dealing with applications to probability. Over 400 exercises are included with solutions to some.

Wolfram MathWorld

Calculus and Analysis: Calculus, Functional Analysis, Norms, Calculus of Variations, Functions, Operator Theory, Catastrophe Theory, General Analysis, Polynomials, Complex Analysis, Generalized Functions, Roots, Differential Equations, Harmonic Analysis, Series, Differential Forms, Inequalities, Singularities, Differential Geometry, Integral Transforms, Special Functions, Dynamical Systems, Manifolds, Fixed Points, Measure Theory

Interactive Real Analysis

An online, interactive textbook for Real Analysis or Advanced Calculus in one real variable by Bert G. Wachsmuth (Seton Hall University). Topics include sets, sequences, series, continuity, differentiability, integrability (Riemann and Lebesgue), topology and power series and Java applets illustrate or experiment with concepts introduced in the text. View the structure of the hypertext book and its main dependencies from the site overview.

A Problem Text in Advanced Calculus, A Companion to Real Analysis

John M. Erdman (Portland State University, Oregon) offers 2 online textbooks. A Problem Text " ..... is intended for students of mathematics and others who have completed (or nearly completed) a standard introductory calculus sequence and who wish to understand where all those rules and formulas come from."

Companion to Real Analysis was "..... written for a year long course in real analysis for seniors and first year graduate students".

Complex Analysis

An 11 chapter online introductory text by George Cain (Georgia Institute of Technology). Chapter headings are: Complex Numbers; Complex Functions; Elementary Functions; Integration; Cauchy's Theorem; More Integration; Harmonic Functions; Series, Taylor and Laurent Series; Poles, Residues and All That; Argument Principle.

Differential Equations

Undetermined coefficients and variation of parameters; Sinusoidal and exponential signals: oscillations, damping, resonance; Complex numbers and exponentials; Fourier series, periodic solutions; Delta functions, convolution, and Laplace transform methods; Matrix and first order linear systems: eigenvalues and eigenvectors; and Non-linear autonomous systems: critical point analysis and phase plane diagrams."