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Wednesday, October 10, 2012

Mathematical Analysis for Modeling

Table of Contents

Chapter 1  Finite Differences
  Sequences — The Simplest Functions

Chapter 2  Local Linear Description

  Tangent Lines: Convenient Linear Approximations
  The Fundamental Linear Approximation
  Continuity and Calculating Derivatives
  Rules for Computing Derivatives

Chapter 3  Graphing and Solution of  Equations

  An Intuitive Approach to Graphing
  Using the Mean Value Theorem
  Solving g(x) = 0: Bisection  and  Newton’s Method

Chapter 4  Recovering Global Information, Integration

  Integration: Calculating f  from Df

  Some Elementary Aspects of Integration
  Overview of Proper Integral Development
  The Lebesgue Integral
  Elementary Numerical Integration
  Integration via Antidifferentiation
  The Fundamental Theorem of Calculus

Chapter 5  Elementary Transcendental Functions
  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

Chapter 6  Taylor’s  Theorem
  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

Chapter 7  Infinite  Series
  Tests for Convergence,  Error Estimates
  Uniform  Convergence and  Its Applications
  Power Series Solution of Differential Equations
  Operations on Infinite Series

Chapter 8  Multivariable Differential Calculus
  Local Behavior of Function of  n

Chapter 9  Coordinate Systems — Linear Algebra
  Tangent Hyperplane Coordinate Systems
  Solution of Systems of Linear Equations

  Chapter 10  Matrices 327
  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
  Maxima and Minima in Several Variables
  Newton’s  Method in  n
  Direct Minimization by Steepest Descent

Chapter 11  Orthogonal Complements
  General Solution Structure
  Homogeneous Solution
  Particular and General Solution of  Ax = y
   Selected  Applications
  Impulse Response

Chapter 12  Multivariable Integrals
  Multiple Integrals
  Iterated Integrals
  General Multiple Integral Evaluation
  Multiple Integral Change of Variables
  Some Differentiation Rules in   n   

  Line and Surface Integrals
  Complex Function Theory in Brief

Chapter 13  Preferred  Coordinate  Systems
  Choice of Coordinate System to Study Matrix
  Some  Immediate  Eigenvector  Applications
  Numerical Determination of Eigenvalues
  Eigenvalues of Symmetric Matrices

Chapter 14  Fourier and Other Transforms
  Fourier Series
  Fourier Integrals and Laplace Transforms
  Generating Functions and Extensions

Chapter 15  Generalized Functions
  A Circuit Problem and Its Differential Operator   L
   Green’s Function for   L
   Generalized Functions: Definition, Some Properties  L X   =   Y   

Existence and Uniqueness Theorems
  Solution of the Original Circuit Equations
  Green’s Function for  P(D); Solution to   Notational  Change
  Generalized Eigenfunction Expansions, Series
  Continuous Linear Functionals
  Further Extensions

 Appendix 1  The real numbers 
Appendix 2   Inverse Functions 
Appendix 3   Riemann Integration 
Appendix 4  Curves and Arc Length 
Appendix 5   MLAB  Dofiles 
Appendix 6  Newton’s Method Computations 
Appendix 7  Evaluation of volume   
Appendix 8  Determinant Column and Row Expansions 
Appendix 9  Cauchy Integral Theorem Details 

Other core of cs books
Discrete Mathematics, 6th Edition (Instructor's Manual)
Concrete Mathematics - A Foundation for Computer Science
Mathematics - Wikipedia, the free encyclopedia
Fun Mathematics Lessons by Cynthia Lanius

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