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Linear Algebra : A Modern Introduction, 3rd

 
지은이 : Poole
출판사 : Cengage
판수 : Third edition
페이지수 : 768
ISBN : 9780538735445
예상출고일 : 입금확인후 2일 이내
주문수량 :
도서가격 : 품절
     

 
David Poole's innovative book prepares students to make the transition from the computational aspects of the course to the theoretical by emphasizing vectors and geometric intuition from the start. Designed for a one- or two-semester introductory course and written in simple, "mathematical English" the book presents interesting examples before abstraction. This immediately follows up theoretical discussion with further examples and a variety of applications drawn from a number of disciplines, which reinforces the practical utility of the math, and helps students from a variety of backgrounds and learning styles stay connected to the concepts they are learning. Poole's approach helps students succeed in this course by learning vectors and vector geometry first in order to visualize and understand the meaning of the calculations that they will encounter and develop mathematical maturity for thinking abstractly.

1. VECTORS.
1.0 Introduction: The Racetrack Game.
1.1 The Geometry and Algebra of Vectors.
1.2 Length and Angle: The Dot Product.
  Exploration: Vectors and Geometry.
1.3 Lines and Planes.
  Exploration: The Cross Product.
1.4 Applications:
  Force Vectors;
  Code Vectors.
 Vignette: The Codabar System.
2. SYSTEMS OF LINEAR EQUATIONS.
2.0 Introduction: Triviality.
2.1 Introduction to Systems of Linear Equations.
2.2 Direct Methods for Solving Linear Systems.
  Exploration: Lies My Computer Told Me.
  Exploration: Partial Pivoting.
  Exploration: Counting Operations: An Introduction to the Analysis of Algorithms.
2.3 Spanning Sets and Linear Independence.
2.4 Applications:
  Allocation of Resources;
  Balancing Chemical Equations;
  Network Analysis;
  Electrical Networks;
  Linear Economic Models;
  Finite Linear Games.
 Vignette: The Global Positioning System.
2.5 Iterative Methods for Solving Linear Systems.
3. MATRICES.
3.0 Introduction: Matrices in Action.
3.1 Matrix Operations.
3.2 Matrix Algebra.
3.3 The Inverse of a Matrix.
3.4 The LU Factorization.
3.5 Subspaces, Basis, Dimension, and Rank.
3.6 Introduction to Linear Transformations.
  Vignette: Robotics.
3.7 Applications:
  Markov Chains;
  Linear Economic Models;
  Population Growth;
  Graphs and Digraphs;
  Error-Correcting Codes.
4. EIGENVALUES AND EIGENVECTORS.
4.0 Introduction: A Dynamical System on Graphs.
4.1 Introduction to Eigenvalues and Eigenvectors.
4.2 Determinants.
  Vignette: Lewis Carroll's Condensation Method.
  Exploration: Geometric Applications of Determinants.
4.3 Eigenvalues and Eigenvectors of n x n Matrices.
4.4 Similarity and Diagonalization.
4.5 Iterative Methods for Computing Eigenvalues.
4.6 Applications and the Perron-Frobenius Theorem:
  Markov Chains;
  Population Growth;
  The Perron-Frobenius Theorem;
  Linear Recurrence Relations;
  Systems of Linear Differential Equations;
  Discrete Linear Dynamical Systems.
 Vignette: Ranking Sports Teams and Searching the Internet.
5. ORTHOGONALITY.
5.0 Introduction: Shadows on a Wall.
5.1 Orthogonality in Rn.
5.2 Orthogonal Complements and Orthogonal Projections.
5.3 The Gram-Schmidt Process and the QR Factorization.
  Exploration: The Modified QR Factorization.
  Exploration: Approximating Eigenvalues with the QR Algorithm.
5.4 Orthogonal Diagonalization of Symmetric Matrices.
5.5 Applications:
  Dual Codes;
  Quadratic Forms;
  Graphing Quadratic Equations.
6. VECTOR SPACES.
6.0 Introduction: Fibonacci in (Vector) Space.
6.1 Vector Spaces and Subspaces.
6.2 Linear Independence, Basis, and Dimension.
  Exploration: Magic Squares.
6.3 Change of Basis.
6.4 Linear Transformations.
6.5 The Kernel and Range of a Linear Transformation.
6.6 The Matrix of a Linear Transformation.
  Exploration: Tilings, Lattices and the Crystallographic Restriction.
6.7 Applications:
  Homogeneous Linear Differential Equations;
  Linear Codes.
7. DISTANCE AND APPROXIMATION.
7.0 Introduction: Taxicab Geometry.
7.1 Inner Product Spaces.
 Exploration: Vectors and Matrices with Complex Entries.
 Exploration: Geometric Inequalities and Optimization Problems.
7.2 Norms and Distance Functions.
7.3 Least Squares Approximation.
7.4 The Singular Value Decomposition.
  Vignette: Digital Image Compression.
7.5 Applications:
  Approximation of Functions;
  Error-Correcting Codes.
Appendix A: Mathematical Notation and Methods of Proof.
Appendix B: Mathematical Induction.
Appendix C: Complex Numbers. Appendix D: Polynomials.
Appendix D: Polynomials
Appendix E: Technology Bytes Online Only
Answers to Selected Odd-Numbered Exercises
Index

"Having been away from academics for a while, I thought I could use a bit of a referesher in some of the basics. Having learned Linear Algebra using Hugh Campbell's text, I was in for quite a surprise when I began using both Poole's and Lay's texts as refreshers. Both treat the theory of matrices the same. However, Poole introduces the notions of vector spaces early on with clear explanations. The one failing of this text is the treatment of determinants as an afterthought. Rather than have its own chapter, as in Lay, this is a subsection treated more as a curiosity. The development and power of determinants is downplayed all around, but especially in Poole. Overall, however, it is a very good beginners text on a very powerful math subject."


"The true test of a math book is whether or not you keep it around for future reference, and this has been on my bookshelf for the last two years.

Unlike some other math books (and, heaven forbid, higher level physics books) that I have had the dubious pleasure of slogging through during my time at a math and science college, you actually know where the problems are coming from in this LinAl book. They provide copious examples, examples upon examples, and the problems in each chapter are drawn from them, mostly verbatim, with a few numbers changed. A few might find this tedious, but I was so goddam happy to finally know where to find the information that would help me learn the material and finish my homework that I didn't care.

Pros: Lots of examples, LinAl is taught competently, if not excitingly.

Cons: Price. This book was assigned the year it was published, so no used copies existed. I think the college system and the book publishing industry are in cahoots."


"Being a Mathematics major in college it's no surprise that I was required to take the course that uses this textbook. Throughout the class, the professor rarely made mention of the book except to give us homework problems to work through on our own. If you ever had a question, the textbook was not the source you wanted to rely on. The way they organize the examples doesn't truly make sense; it's more of a maze of numbers and decimals. Most will buy this book because it's required for their class, but if using this book as a personal reference there are better sources than this. Only reason I did well in the class was because the professor took his time to explain a lot of things the book barely glanced over, or just threw at you without mention of an explanation.

Overall, if you're forced to use this book then talk to your professor. Don't hope that this book will be able to fill in any blanks that the professor may have missed. You will find them, but it'll take you at least 20-30 minutes to identify precisely what they are referring to. Be careful with this book, it has too much information crammed into too few chapters and/or sub-sections. It's one of its biggest shortcomings."
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