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Introduction to Real Analysis

ISBN-10: 0130457868
ISBN-13: 9780130457868
Edition: 2003
List price: $128.00
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Description: Using an extremely clear and informal approach, this book introduces readers to a rigorous understanding of mathematical analysis and presents challenging math concepts as clearly as possible. The real number system. Differential calculus of  More...

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Book details

List price: $128.00
Copyright year: 2003
Publisher: Prentice Hall PTR
Publication date: 12/4/2002
Binding: Hardcover
Pages: 574
Size: 7.25" wide x 9.25" long x 1.25" tall
Weight: 2.134
Language: English

Using an extremely clear and informal approach, this book introduces readers to a rigorous understanding of mathematical analysis and presents challenging math concepts as clearly as possible. The real number system. Differential calculus of functions of one variable. Riemann integral functions of one variable. Integral calculus of real-valued functions. Metric Spaces. For those who want to gain an understanding of mathematical analysis and challenging mathematical concepts.

Linear Equations and Matrices
Systems of Linear Equations
Matrices
Matrix Multiplication
Algebraic Properties of Matrix Operations
Special Types of Matrices and Partitioned Matrices
Matrix Transformations
Computer Graphics
Correlation Coefficient (Optional)
Solving Linear Systems
Echelon Form of a Matrix
Elementary Matrices: Finding A-1
Equivalent Matrices
LU-Factorization (Optional)
Real Vector Spaces
Vectors in the Plane and in 3-space
Vector Spaces
Subspaces
Span and Linear Independence
Basis and Dimension
Homogeneous Systems
Coordinates and Isomorphisms
Rank of a Matrix
Inner Product Spaces
Standard Inner Product on R2 and R3
Cross Product in R3 (Optional)
Inner Product Spaces
Gram-Schmidt Process
Orthogonal Complements
Least Squares (Optional)
Linear Transformations and Matrices
Definition and Examples
Kernel and Range of a Linear Transformation
Matrix of a Linear Transformation
Vector Space of Matrices and Vector Space of Linear Transformations (Optional)
Similarity
Inroduction to Homogeneous Coordinates (Optional)
Determinants
Definition
Properties of Determinants
Cofactor Expansion
Inverse of a Matrix
Other Applications of Determinants
Determinants from a Computational Point of View
Eigenvalues and Eigenvectors
Eigenvalues and Eigenvectors
Diagonalization and Similar Matrices
Stable Age Distribution in a Population; Markov Processes (Optional)
Diagonalization of Symmetric Matrices
Spectral Decomposition and Singular Value Decomposition (Optional)
Real Quadratic Forms
Conic Sections
Quadric Surfaces
Dominant Eigenvalue and Principal Component Analysis (Optional)
Differential Equations (Optional)
Differential Equations
Dynamical Systems
MATLAB for Linear Algebra
Input and Output in MATLAB
Matrix Operations in MATLAB
Matrix Powers and Some Special Matrices
Elementary Row Operations in MATLAB
Matrix Inverses in MATLAB
Vectors in MATLAB
Applications of Linear Combinations in MATLAB
Linear Transformations in MATLAB
MATLAB Command Summary
MATLAB Exercises
Preliminaries
Sets
Functions
Complex Numbers
Complex Numbers
Complex Numbers in Linear Algebra
Introduction to Proofs
Answers to Odd-Numbered Exercises
Index

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