Elementary Linear Algebra, Applications Version, EMEA Edition

Häftad, Engelska, 2019

Av Howard Anton, Chris Rorres, Anton Kaul, Howard (Drexel University) Anton, Chris (Drexel University) Rorres

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Elementary Linear Algebra: Applications Version, 12th Edition gives an elementary treatment of linear algebra that is suitable for a first course for undergraduate students. The aim is to present the fundamentals of linear algebra in the clearest possible way; pedagogy is the main consideration. Calculus is not a prerequisite, but there are clearly labeled exercises and examples (which can be omitted without loss of continuity) for students who have studied calculus.

Produktinformation

Utgivningsdatum2019-12-05
Mått10 x 10 x 10 mm
Vikt454 g
FormatHäftad
SpråkEngelska
Antal sidor816
Upplaga12
FörlagJohn Wiley & Sons Inc
ISBN9781119666141

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Algebra inom Naturvetenskap och teknik

1 Systems of Linear Equations and Matrices 11.1 Introduction to Systems of Linear Equations 21.2 Gaussian Elimination 111.3 Matrices and Matrix Operations 251.4 Inverses; Algebraic Properties of Matrices 401.5 Elementary Matrices and a Method for Finding A−1 531.6 More on Linear Systems and Invertible Matrices 621.7 Diagonal, Triangular, and Symmetric Matrices 691.8 Introduction to Linear Transformations 761.9 Compositions of Matrix Transformations 901.10 Applications of Linear Systems 98• Network Analysis 98• Electrical Circuits 100• Balancing Chemical Equations 103• Polynomial Interpolation 1051.11 Leontief Input-Output Models 1102 Determinants 1182.1 Determinants by Cofactor Expansion 1182.2 Evaluating Determinants by Row Reduction 1262.3 Properties of Determinants; Cramer’s Rule 1333 Euclidean Vector Spaces 1463.1 Vectors in 2-Space, 3-Space, and n-Space 1463.2 Norm, Dot Product, and Distance in Rn 1583.3 Orthogonality 1723.4 The Geometry of Linear Systems 1833.5 Cross Product 1904 General Vector Spaces 2024.1 Real Vector Spaces 2024.2 Subspaces 2114.3 Spanning Sets 2204.4 Linear Independence 2284.5 Coordinates and Basis 2384.6 Dimension 2484.7 Change of Basis 2564.8 Row Space, Column Space, and Null Space 2634.9 Rank, Nullity, and the Fundamental Matrix Spaces 2765 Eigenvalues and Eigenvectors 2915.1 Eigenvalues and Eigenvectors 2915.2 Diagonalization 3015.3 Complex Vector Spaces 3115.4 Differential Equations 3235.5 Dynamical Systems and Markov Chains 3296 Inner Product Spaces 3416.1 Inner Products 3416.2 Angle and Orthogonality in Inner Product Spaces 3526.3 Gram–Schmidt Process; QR-Decomposition 3616.4 Best Approximation; Least Squares 3766.5 Mathematical Modeling Using Least Squares 3856.6 Function Approximation; Fourier Series 3927 Diagonalization and Quadratic Forms 3997.1 Orthogonal Matrices 3997.2 Orthogonal Diagonalization 4087.3 Quadratic Forms 4167.4 Optimization Using Quadratic Forms 4297.5 Hermitian, Unitary, and Normal Matrices 4368 General Linear Transformations 4468.1 General Linear Transformations 4468.2 Compositions and Inverse Transformations 4598.3 Isomorphism 4718.4 Matrices for General Linear Transformations 4778.5 Similarity 4878.6 Geometry of Matrix Operators 4939 Numerical Methods 5099.1 LU-Decompositions 5099.2 The Power Method 5199.3 Comparison of Procedures for Solving Linear Systems 5289.4 Singular Value Decomposition 5329.5 Data Compression Using Singular Value Decomposition 54010 Applications of Linear Algebra 54510.1 Constructing Curves and Surfaces Through Specified Points 54610.2 The Earliest Applications of Linear Algebra 55110.3 Cubic Spline Interpolation 55810.4 Markov Chains 56810.5 Graph Theory 57710.6 Games of Strategy 58710.7 Forest Management 59510.8 Computer Graphics 60210.9 Equilibrium Temperature Distributions 61010.10 Computed Tomography 61910.11 Fractals 62910.12 Chaos 64510.13 Cryptography 65810.14 Genetics 66910.15 Age-Specific Population Growth 67810.16 Harvesting of Animal Populations 68710.17 A Least Squares Model for Human Hearing 69510.18 Warps and Morphs 70110.19 Internet Search Engines 71010.20 Facial Recognition 716Supplemental Online Topics• Linear Programming - A Geometric Approach• Linear Programming - Basic Concepts• Linear Programming - The Simplex Method• Vectors in Plane Geometry• Equilibrium of Rigid Bodies• The Assignment Problem• The Determinant Function• Leontief Economic ModelsAppendix A Working with Proofs A1Appendix B Complex Numbers A5Answers to Exercises A13Index I1