Please note that the unabridged version of the text may not be used by Caltech students in ACM 95/100.

You can download the text in the following formats by saving the link to your computer. The PDF versions are better for viewing on your computer; they are hyperlinked. Get the postscript version if you are going to print the text.

- PDF, (Portable Document Format), suitable for viewing on the computer. This version has a page layout with smaller margins, larger fonts and a lower aspect ratio. 9.7 megabytes.
- PDF This version is in letter format. 8.9 megabytes.
- zipped postscript. 5.8 megabytes.

- zip archive 8.3 megabytes.
- gzip'ed tarball 7.7 megabytes.

Some of the exercises in the text are solved in Mathematica notebooks. These exercises are labeled with the name of the notebook. Below is a list of these notebooks. You can download files to your computer and open them in Mathematica. You can also download all the notebooks in a tarball. (I have also written a set of tutorial Mathematica notebooks that I have used in teaching a Mathematica class.)

- Calculus
- Differential Calculus
- Definition of Differentiation, definition.nb
- Rules of Differentiation, rules.nb
- Implicit Differentiation, implicit.nb
- Maxima and Minima, maxima.nb
- Mean Value Theorems, taylor.nb
- L'Hospital's Rule, lhospitals.nb

- Integral Calculus
- Fundamental Integration Formulas, fundamental.nb
- Integration by Parts, parts.nb
- Partial Fractions, partial.nb
- Definite Integrals, definite.nb
- Improper Integrals, improper.nb
- Taylor Series, taylor.nb

- Differential Calculus
- Functions of a Complex Variable
- Series and Convergence
- Series of Constants, constants.nb

- Series and Convergence
- Ordinary Differential Equations
- First Order Differential Equations
- First Order Systems of Differentials Equations
- First Order Systems, systems.nb

- Techniques for Linear Differential Equations
- Constant Coefficient Equations, constant.nb
- Euler Equations, euler.nb

- Inhomogeneous Differential Equations
- Undetermined Coefficients, undetermined.nb
- Variation of Parameters, variation.nb

- Series Solutions of Differential Equations
- Series Solutions, series.nb

- The Laplace Transform
- Laplace Transform, laplace.nb

- Algebra
- Sets and Functions - Very preliminary.
- Vectors - Finished. An elementary treatment.

- Calculus
- Differential Calculus - Short, but done.
- Integral Calculus - Short, but done.
- Vector Calculus - Very preliminary.

- Functions of a Complex Variable
- Complex Numbers - Done.
- Functions of a Complex Variable - Done.
- Analytic Functions - Done.
- Analytic Continuation - Disorganized.
- Contour Integration and Cauchy's Formula - Done.
- Cauchy's Integral Formula - Done.
- Series and Convergence - Done.
- The Residue Theorem - Done.

- Ordinary Differential Equations
- First Order Differential Equations - Done.
- First Order Systems of Differentials Equations - Preliminary.
- Theory of Linear Ordinary Differential Equations - Done.
- Techniques for Linear Differential Equations - Done.
- Techniques for Nonlinear Differential Equations - Preliminary.
- Transformations and Canonical Forms - Preliminary.
- The Dirac Delta Function - Preliminary.
- Inhomogeneous Differential Equations - Done.
- Difference Equations - Preliminary.
- Series Solutions of Differential Equations - Done.
- Asymptotic Expansions - Preliminary.
- Hilbert Spaces - Very Preliminary.
- Self Adjoint Linear Operators - Very Preliminary.
- Self Adjoint Boundary Value Problems - Very Preliminary.
- Fourier Series - Done.
- Regular Sturm-Liouville Problems - Done.
- Integrals and Convergence - Preliminary.
- The Laplace Transform - Done.
- The Fourier Transform - Done.
- The Gamma Function - Preliminary.
- Bessel Functions - Preliminary.

- Partial Differential Equations - All the chapters are very preliminary.
- Calculus of Variations - No text, just some exercises and solutions.
- Nonlinear Differential Equations - No text, just some exercises and solutions.

http://www.its.caltech.edu/~sean/, sean@caltech.edu / Last Modified: August 22, 2005