Unabridged Version of Sean's Applied Math Book (original) (raw)

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.
• PDFThis 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 guidethat describes how to use the source of the text.
• zip archive8.3 megabytes.
• gzip'ed tarball7.7 megabytes.

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 notebooksthat 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
• Functions of a Complex Variable
  • Series and Convergence
    * Series of Constants,constants.nb
• 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
    * 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

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.

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