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Introduction to Linear Algebra with Applications 1st Edition by Jim DeFranza, Daniel Gagliardi ISBN 1478627778 9781478627777

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Introduction to Linear Algebra with Applications 1st Edition Jim Defranza Digital Instant Download

Author(s): Jim DeFranza, Daniel Gagliardi
ISBN(s): 9781478627777, 1478627778
Edition: 1
File Details: PDF, 16.41 MB
Year: 2015
Language: english
SKU: EB-5507054 Category: Tags: ,

Introduction to Linear Algebra with Applications 1st Edition by Jim DeFranza, Daniel Gagliardi – Ebook PDF Instant Download/Delivery: 1478627778, 9781478627777
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ISBN 10: 1478627778 
ISBN 13: 9781478627777
Author: Jim DeFranza, Daniel Gagliardi

Over the last few decades, linear algebra has become more relevant than ever. Applications have increased not only in quantity but also in diversity, with linear systems being used to solve problems in chemistry, engineering, economics, nutrition, urban planning, and more. DeFranza and Gagliardi introduce students to the topic in a clear, engaging, and easy-to-follow manner. Topics are developed fully before moving on to the next through a series of natural connections. The result is a solid introduction to linear algebra for undergraduates’ first course.

Introduction to Linear Algebra with Applications 1st Table of contents:

Chapter 1: Systems of Linear Equations and Matrices
1.1 Systems of Linear Equations
The Elimination Method
Exercise Set 1.1
1.2 Matrices and Elementary Row Operations
Solving Linear Systems with Augmented Matrices
Echelon Form of a Matrix
Exercise Set 1.2
1.3 Matrix Algebra
Matrix Multiplication
Transpose of a Matrix
Exercise Set 1.3
1.4 The Inverse of a Square Matrix
Exercise Set 1.4
1.5 Matrix Equations
Exercise Set 1.5
1.6 Determinants
Properties of Determinants
Cramer’s Rule
Exercise Set 1.6
1.7 Elementary Matrices and LU Factorization
Elementary Matrices
The Inverse of an ElementaryMatrix
LU Factorization
Solving a Linear System Using LU Factorization
PLU Factorization
Exercise Set 1.7
1.8 Applications of Systems of Linear Equations
Balancing Chemical Equations
Network Flow
Nutrition
Economic Input-Output Models
Exercise Set 1.8
Review Exercises for Chapter 1
Chapter 1: Chapter Test
Chapter 2: Linear Combinations and Linear Independence
2.1 Vectors in R superscript n
Exercise Set 2.1
2.2 Linear Combinations
Vector Form of a Linear System
Matrix Multiplication
Exercise Set 2.2
2.3 Linear Independence
Linear Systems
Linear Independence and Determinants
Exercise Set 2.3
Review Exercises for Chapter 2
Chapter 2: Chapter Test
Chapter 3: Vector Spaces
3.1 Definition of a Vector Space
Exercise Set 3.1
3.2 Subspaces
Span of a Set of Vectors
The Null Space and Column Space of aMatrix
Exercise Set 3.2
3.3 Basis and Dimension
Dimension
Finding a Basis
Exercise Set 3.3
3.4 Coordinates and Change of Basis
Change of Basis
Inverse of a Transition Matrix
Exercise Set 3.4
3.5 Application: Differential Equations
The Exponential Model
Second-Order Differential Equations with Constant Coefficients
Fundamental Sets of Solutions
Exercise Set 3.5
Review Exercises for Chapter 3
Chapter 3: Chapter Test
Chapter 4: Linear Transformations
4.1 Linear Transformations
Operations with Linear Transformations
Exercise Set 4.1
4.2 The Null Space and Range
Matrices
Linear Systems
Exercise Set 4.2
4.3 Isomorphisms
Exercise Set 4.3
4.4 Matrix Representation of a Linear Transformation
Exercise Set 4.4
4.5 Similarity
Exercise Set 4.5
4.6 Application: Computer Graphics
Graphics Operations in R superscript 2
Projection
Exercise Set 4.6
Review Exercises for Chapter 4
Chapter 4: Chapter Test
Chapter 5: Eigenvalues and Eigenvectors
5.1 Eigenvalues and Eigenvectors
Geometric Interpretation of Eigenvalues and Eigenvectors
Eigenspaces
Eigenvalues and Eigenvectors of Linear Operators
Exercise Set 5.1
5.2 Diagonalization
Diagonalizable Linear Operators
Exercise Set 5.2
5.3 Application: Systems of Linear Differential Equations
Uncoupled Systems
The Phase Plane
Diagonalization
Exercise Set 5.3
5.4 Application: Markov Chains
State Vectors and Transition Matrices
Diagonalizing the Transition Matrix
Steady-State Vector
Exercise Set 5.4
Review Exercises for Chapter 5
Chapter 5: Chapter Test
Chapter 6: Inner Product Spaces
6.1 The Dot Product on R superscript n
The Angle between Two Vectors
Exercise Set 6.1
6.2 Inner Product Spaces
Orthogonal Sets
Exercise Set 6.2
6.3 Orthonormal Bases
Orthogonal Projections
Gram-Schmidt Process
A Geometric Interpretation of the Gram-Schmidt Process
Exercise Set 6.3
6.4 Orthogonal Complements
Matrices
Linear Systems
Exercise Set 6.4
6.5 Application: Least Squares Approximation
Least Squares Solutions
Linear Regression
Fourier Polynomials
Exercise Set 6.5
6.6 Diagonalization of Symmetric Matrices
Orthogonal Diagonalization
Exercise Set 6.6
6.7 Application: Quadratic Forms
Rotation of Axes
Quadric Surfaces
Exercise Set 6.7
6.8 Application: Singular Value Decomposition
Singular Values of an m × n Matrix
Singular Value Decomposition (SVD)
The Four Fundamental Subspaces
Data Compression
Exercise Set 6.8
Review Exercises for Chapter 6
Chapter 6: Chapter Test
Appendix A: Preliminaries
A.1 Algebra of Sets
Operations on Sets
Exercise Set A.1
A.2 Functions
Inverse Functions
Composition of Functions
Exercise Set A.2
A.3 Techniques of Proof
Direct Argument
Contrapositive Argument
Contradiction Argument
Quantifiers
Exercise Set A.3
A.4 Mathematical Induction
Binomial Coefficients and the Binomial Theorem
Exercise Set A.4
Answers to Odd-Numbered Exercises

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