Table of Contents
Chapter 1 Finite Differences
Introduction
Sequences — The Simplest Functions
Chapter 2 Local Linear Description
Introduction
Tangent Lines: Convenient Linear Approximations
The Fundamental Linear Approximation
Continuity and Calculating Derivatives
Rules for Computing Derivatives
Chapter 3 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
Chapter 4 Recovering Global Information, Integration
Introduction
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
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
Chapter 6 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
Chapter 7 Infinite Series
Introduction
Preliminaries
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
Introduction
Local Behavior of Function of n
Variables
Chapter 9 Coordinate Systems — Linear Algebra
Introduction
Tangent Hyperplane Coordinate Systems
Solution of Systems of Linear Equations
Chapter 10 Matrices 327
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
Chapter 11 Orthogonal Complements
Introduction
General Solution Structure
Homogeneous Solution
Particular and General Solution of Ax = y
Selected Applications
Impulse Response
Chapter 12 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
Chapter 13 Preferred Coordinate Systems
Introduction
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
Introduction
Fourier Series
Fourier Integrals and Laplace Transforms
Generating Functions and Extensions
Chapter 15 Generalized Functions
Introduction
Overview
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
Epilogue
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
Bibliography
Glossary
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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