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
Copyright 2000, 750 pp.
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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 presentationAnalysis 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 developmentRoughly 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 algebraFocuses
as much on the math used in the applications as on the applications
Unique coverage of more modern and recent topicse.g.,
wavelets, some chaotic differential equations, and tomagraphy.
Treatment of classical topicse.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
0. Review of Calculus and ODE.
1. Sets, Numbers, Functions, R, C, Rn.
2. Linear Algebra.
3. Limits, Sequences, Series, Uniform Convergence Examples:
4. Differentiation (inverse, implicit functions, divergence,
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.