## First Course in Applied Mathematics, A, 1/e

Ronald B. Guenther, Oregon State University
Manfred Konig, University of Munich

Coming March, 2000 by Prentice Hall Engineering/Science/Mathematics

Cloth
ISBN 0-13-519976-X

mailings
on this subject.

Engineering Math-Mathematics

Engineering Mathematics-Mechanical Engineering

For courses in Engineering Mathematics and for all entering graduate students in applied fields needing a math review. Unique in both content and approach, this is the first text at this level to give a unified treatment of mathematical analysis and its applications to physical and modeling problems. It covers both modern and classical topics and features a wide range of significant applications.

A unified presentation—Analysis is used as a unifying tool for a wide range of topics and physical and geometrical applications.
A large number of applications form an integral part of the development—Roughly half of the book is devoted to applications of the results obtained to physical and mathematical or geometric problems. Classical mechanics are treated from a mathematical standpoint and the physical laws provide the mechanism for relating physical reality to a mathematical structure.
Development of analysis and linear algebra—Focuses as much on the math used in the applications as on the applications themselves.
Unique coverage of more modern and recent topics—e.g., wavelets, some chaotic differential equations, and tomagraphy.
Treatment of classical topics—e.g., special functions, classical mechanics, continuum mechanics, vibrations, Fourier series and integrals, mathematical modeling, etc.

• Form the bread and butter of applied mathematics. Many problems are presented throughout the book that ask students to read something of the lives and work of the individuals who have created modern math as know it.
• Add enrichment to student's study of the material and help them appreciate the nature of math as a changing and growing discipline.

0. Review of Calculus and ODE.
1. Sets, Numbers, Functions, R, C, Rn.
2. Linear Algebra.
3. Limits, Sequences, Series, Uniform Convergence Examples: Fractals.
4. Differentiation (inverse, implicit functions, divergence, gradient).
5. Integration (Riemann, Gauss) and Integral Equations.
6. Classical Mechanics.
7. Ordinary Differential Equations.
8. Approximation and Numerical Methods.
9. Fourier Series and Orthogonal Series, Fast-Fourier Transform and Wavelets.
10. Sturm-Liouville Theory with Special Functions.
11. Integral Transforms.
12. Mathematical Models.
13. Partial Differential Equations.
14. Function Theory.
15. Probability Theory and Statistical Mechanics.
16. Image Processing.