Mathematical Analysis for Modeling is intended for those who want to understand the substance of mathematics, rather than just having familiarity with its techniques. It provides a thorough understanding of how mathematics is developed for and applies to solving scientific and engineering problems. The authors stress the construction of mathematical descriptions of scientific and engineering situations, rather than rote memorizations of proofs and formulas. Emphasis is placed on algorithms as solutions to problems and on insight rather than formal derivations.
Finite Differences. Local Linear Description. Graphing and Solution of Equations. Recovering Global Information, Integration. Elementary Transcendental Functions. Taylor's Theorem. Infinite Series. Multivariable Differential Calculus. Coordinate Systems - Linear Algebra. Matrices. Orthogonal Complements. Multivariable Integrals. Preferred Coordinate Systems. Fourier and Other Transforms. Generalized Functions. Appendices. Index.