# Unabridged Version of Sean's Applied Math Book

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

• 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.
You can also download the source, (the LaTeX and graphics files). There is a makefile for compiling the sources. Feel free to cut and paste the sources to make documents that suit your needs. I have a users guide that describes how to use the source of the text.

## Mathematica Notebooks

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.)

## Status of the Text

• 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.