Résumé
Linear Algebra with Applications is a flexible blend of theory, important computational techniques, and interesting applications. Instructors can select the topics that give the course their desired perspective. The text provides a solid foundation in the mathematics of linear algebra, while introducing some of the important computational aspects of the field, such as algorithms. The presentation of interesting applications has been one of the most compelling features of this book provides students a well balanced coverage of standard linear algebra topics that apply mathematics by examining real-life applications, making for a enlightening learning experience.
Features- New to this Edition! Introduction to Elimination Methods: An improved introduction of the Gauss-Jordan method is given.
- New to this Edition! Chapter on Vector Space Rn contains an introduction to dot product, angle, magnitude, distance, and an early introduction to linear transformations with applications in computer graphics and fractals.
- New to this Edition! Eigenvalues and Eigenvectors: used in discussing long term trends of phenomena and the diagonalization of matrices are discussed.
- New to this Edition! MATLAB and Graphing Calculator: Collected into manuals at the end of the book, positioned for easy reference.
- The concepts of linear combinations of vectors, linear dependence, and dimension are introduced within the context of general vector spaces.
- The best collection of applications of any linear algebra text, range from theoretical applications, such as, differential equations to practical applications, such as, archaeology and demography.
Contents
Chapter 1 Systems of Linear Equations- Matrices and Systems of Linear Equations
- Gauss-Jordan Elimination
- Curve Fitting, Electrical Networks, and Traffic Flow
- Chapter 1 Review Exercises
- Addition, Scalar Multiplication, and Multiplication of Matrices
- Properties of Matrix Operations
- Symmetric Matrices and Seriation in Archaeology
- The Inverse of a Matrix and Cryptography
- The Leontief Input-Output Model in Economics
- Markov Chains, Population Movements, and Genetics
- A Communication Model and Group Relationships in Sociology
- Chapter 2 Review Exercises
- Introduction to Determinants
- Properties of Determinants
- Numerical Evaluation of a Determinant
- Determinants, Matrix Inverses, and Systems of Linear Equations
- Chapter 3 Review Exercises
- Introduction to Vectors
- Dot Product, Norm, Angle, and Distance
- Introduction to Linear Transformations
- Matrix Transformations, Computer Graphics, and Fractals
- Chapter 4 Review Exercises
- Vector Spaces
- Subspaces
- Linear Combinations of Vectors
- Linear Dependence and Independence
- Bases and Dimension
- Rank of a Matrix
- Orthonormal Vectors and Projections in Rn
- Chapter 5 Review Exercises
- Eigenvalues, Eigenvectors, and Eigenspaces
- Demography and Weather Prediction
- Diagonalization of Matrices
- Quadratic Forms, Difference Equations, and Normal Modes
- Chapter 6 Review Exercises
- Linear Transformations, Kernel, and Range
- Transformations and Systems of Linear Equations
- Coordinate Vectors
- Matrix Representations of Linear Transformations
- Chapter 7 Review Exercises
- Inner Product Spaces
- Non-Euclidean Geometry and Special Relativity
- Approximation of Functions and Coding Theory
- Least=Squares Curves
- Chapter 8 Review Exercises
- Gaussian Elimination
- The Method of LU Decomposition
- Practical Difficulties in Solving Systems of Equations
- Iterative Methods for Solving Systems of Linear Equations
- Eigenvalues by Iteration and Connectivity of Networks
- Chapter 9 Review Exercises
- A Geometrical Introduction to Linear Programming
- The Simplex Method
- Geometrical Explanation of the Simplex Method
- Chapter 10 Review Exercises
- A Cross Product
- B Equations of Lines in Three-Space
- C Graphing Calculator Manual
- D MATLAB Manual
L'auteur - Gareth Williams
Gareth Williams earned a B.S. and a Ph.D. in applied mathematics from the University of Wales, and did graduate work at Kings College University of London. He was formerly on the faculties of the University of Florida and the University of Denver, and now teaches math at Stetson University. He has been an exchange professor at Paedagogische Hochschule, in Freiburg, Germany and has spent sabbaticals at the University of Wales. His mathematical interests include linear algebra, relativity, mathematical modeling, and the computer in mathematics education. Other publications include "The Microcomputer in Linear Algebra", "Fine Topologies for Minkowski Space", "Mathematics in Archaeology", and books on Finite Mathematics, Calculus, and College Algebra. He is the developer of the linear algebra software, "The Linear Algebra Toolbox", for MATLAB, and Mathematica notebooks. Williams is a member of Mathematics Association of America, the American Mathematical Society, and The International Linear Algebra Society. For relaxation Dr. Williams plays golf and tennis and likes to travel.
Autres livres de Gareth Williams
Caractéristiques techniques
| PAPIER | |
| Éditeur(s) | Jones and Bartlett Computer Science |
| Auteur(s) | Gareth Williams |
| Parution | 01/01/2001 |
| Édition | 4eme édition |
| Nb. de pages | 666 |
| Format | 19,5 x 24 |
| Couverture | Relié |
| Poids | 1308g |
| Intérieur | 2 couleurs |
| EAN13 | 9780763714512 |
| ISBN13 | 978-0-7637-1451-2 |
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