Mathematical Analysis for Modeling (Hardcover)

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 ? from D?
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