Unabridged Version of Sean's Applied Math Book
Download. Latest Build: January 24, 2004
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.
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.)
- Calculus
- Differential Calculus
- Integral Calculus
- Functions of a Complex Variable
- Ordinary Differential Equations
- First Order Differential Equations
- Exact Differential Equations,
exact.nb
- The First Order, Linear Differential Equation,
linear.nb
- First Order Systems of Differentials Equations
- Techniques for Linear Differential Equations
- Inhomogeneous Differential Equations
- Series Solutions of Differential Equations
- The Laplace Transform
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.