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.