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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.

"…good mixture of mathematical and standard items…a unified approach…emphasis to increase understanding and provide a natural approach to problem formulation and solution."

--H.-Ch. Reichel, Buchbesprechungen

"…good collection of problems; chapter exercises; very useful appendix."

-D.E. Bentil, CHOICE, January 2000

FINITE DIFFERENCES

Introduction

Sequences-The Simplest Functions

LOCAL LINEAR DESCRIPTION

Introduction

Tangent Lines: Convenient Linear Approximations

The Fundamental Linear Approximation

Continuity and Calculating Derivatives

Rules for Computing Derivatives

GRAPHING AND SOLUTION OF EQUATIONS

Introduction

An Intuitive Approach to Graphing

Using the Mean Value Theorem

Solving g(x) = 0: Bisection and Newton's Method

RECOVERING GLOBAL INFORMATION - INTEGRATION

Introduction

Integration: Calculating ƒ from Dƒ

Some Elementary Aspects of Integration

Overview of Proper Integral Development

The Lebesgue Integral

Elementary Numerical Integration

Integration via Antidifferentiation

The Fundamental Theorem of Calculus

ELEMENTARY TRANSCENDENTAL FUNCTIONS

Introduction

The Logarithm and Exponential Functions

Precise Development of ln and exp

Formulas as Functions

Applications of exp

Trigonometric Functions, Intuitive Development

Precise Development of sin, cos: Overview

First Applications of sin, cos

TAYLOR'S THEOREM

Introduction

Simplest Version of Taylor's Theorem

Applications of Taylor's Theorem

The Connection Between exp, cos, and sin

Properties of Complex Numbers

Applications of Complex Exponentials

INFINITE SERIES

Introduction

Preliminaries

Tests for Convergence, Error Estimates

Uniform Convergence and Its Applications

Power Series Solutions of Differential Equations

Operations on Infinite Series

MULTIVARIABLE DIFFERENTIAL CALCULUS

Introduction

Local Behavior of Function of n Variables

COORDINATE SYSTEMS - LINEAR ALGEBRA

Introduction

Tangent Hyperplane Coordinate Systems

Solution of Systems of Linear Equation

MATRICES

Introduction

Matrices as Functions, Matrix Operations

Rudimentary Matrix Inversion

Change of Coordinates and Rotations by Matrices

Matrix Infinite Series - Theory

The Matrix Geometric Series

Taylor's Theorem in n Dimensions

Maxima and Minima in Several Variables

Newton's Method in n Dimensions

Direct Minimization by Steepest Descent

ORTHOGONAL COMPLEMENTS

Introduction

General Solution Structure

Homogeneous Solution

Particular Solution of Ax = y

Selected Applications

Impulse Response

MULTIVARIABLE INTEGRALS

Introduction

Multiple Integrals

Iterated Integrals

General Multiple Integral Evaluation

Multiple Integral Change of Variables

Some Differentiation Rules in n Dimensions

Line and Surface Integrals

Complex Function Theory in Brief

PREFERRED COORDINATE SYSTEMS

Introduction

Choice of Coordinate System to Study Matrix

Some Immediate Eigenvector Applications

Numerical Determination of Eigenvalues

Eigenvalues of Symmetric Matrices

FOURIER AND OTHER TRANSFORMS

Introduction

Fourier Series

Fourier Integrals and Laplace Transforms

Generating Functions and Extensions

GENERALIZED FUNCTIONS

Introduction

Overview

A Circuit Problem and Its Differential Operator L

Green's Function for L

Generalized Functions: Definition, Some Properties

LX = Y,Existence and Uniqueness Theorems

Solution of the Original Circuit Equations

Green's Function for P(D); Solution to P(D)X =d

Notational Change

Generalized Eigenfunction Expansions; Series

Continuous Linear Functionals

Further Extensions

Epilogue

APPENDICES

The Real Numbers

Inverse Functions

Riemann Integration

Curves and Arc Length

MLAB Dofiles

Newton's Method Computations

Evaluation of volume AnxnIun ***n should be a subscript of the subscript u***

Determinant Column and Row Expansions

Cauchy Integral Theorem Details

BIBLIOGRAPHY

GLOSSARY

LIST OF DEFINITIONS

INDEX

- MAT000000
- MATHEMATICS / General
- MAT007000
- MATHEMATICS / Differential Equations
- TEC009070
- TECHNOLOGY & ENGINEERING / Mechanical