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Linear Algebra and Its Applications ,4th  무료배송

 
지은이 : Lay, David C.
출판사 : Pearson
페이지수 : 576
ISBN : 0321623355
예상출고일 : 입금확인후 2일 이내
주문수량 :
도서가격 : 품절
     

 
Linear algebra is relatively easy for students during the early stages of the course, when the material is presented in a familiar, concrete setting. But when abstract concepts are introduced, students often hit a brick wall. Instructors seem to agree that certain concepts (such as linear independence, spanning, subspace, vector space, and linear transformations), are not easily understood, and require time to assimilate. Since they are fundamental to the study of linear algebra, students' understanding of these concepts is vital to their mastery of the subject. David Lay introduces these concepts early in a familiar, concrete Rn setting, develops them gradually, and returns to them again and again throughout the text so that when discussed in the abstract, these concepts are more accessible.
David C. Lay holds a B.A. from Aurora University (Illinois), and an M.A. and Ph.D. from the University of California at Los Angeles. Lay has been an educator and research mathematician since 1966, mostly at the University of Maryland, College Park. He has also served as a visiting professor at the University of Amsterdam, the Free University in Amsterdam, and the University of Kaiserslautern, Germany. He has over 30 research articles published in functional analysis and linear algebra. As a founding member of the NSF-sponsored Linear Algebra Curriculum Study Group, Lay has been a leader in the current movement to modernize the linear algebra curriculum. Lay is also co-author of several mathematics texts, including Introduction to Functional Analysis, with Angus E. Taylor, Calculus and Its Applications, with L.J. Goldstein and D.I. Schneider, and Linear Algebra Gems-Assets for Undergraduate Mathematics, with D. Carlson, C.R. Johnson, and A.D. Porter. Professor Lay has received four university awards for teaching excellence, including, in 1996, the title of Distinguished Scholar-Teacher of the University of Maryland. In 1994, he was given one of the Mathematical Association of America's Awards for Distinguished College or University Teaching of Mathematics. He has been elected by the university students to membership in Alpha Lambda Delta National Scholastic Honor Society and Golden Key National Honor Society. In 1989, Aurora University conferred on him the Outstanding Alumnus award. Lay is a member of the American Mathematical Society, the Canadian Mathematical Society, the International Linear Algebra Society, the Mathematical Association of America, Sigma Xi, and the Society for Industrial and Applied Mathematics. Since 1992, he has served several terms on the national board of the Association of Christians in the Mathematical Sciences.

1. Linear Equations in Linear Algebra
Introductory Example: Linear Models in Economics and Engineering
1.1 Systems of Linear Equations
1.2 Row Reduction and Echelon Forms
1.3 Vector Equations
1.4 The Matrix Equation Ax = b
1.5 Solution Sets of Linear Systems
1.6 Applications of Linear Systems
1.7 Linear Independence
1.8 Introduction to Linear Transformations
1.9 The Matrix of a Linear Transformation
1.10 Linear Models in Business, Science, and Engineering
Supplementary Exercises
2. Matrix Algebra
Introductory Example: Computer Models in Aircraft Design
2.1 Matrix Operations
2.2 The Inverse of a Matrix
2.3 Characterizations of Invertible Matrices
2.4 Partitioned Matrices
2.5 Matrix Factorizations
2.6 The Leontief Input뾑utput Model
2.7 Applications to Computer Graphics
2.8 Subspaces of Rn
2.9 Dimension and Rank
Supplementary Exercises
3. Determinants
Introductory Example: Random Paths and Distortion
3.1 Introduction to Determinants
3.2 Properties of Determinants
3.3 Cramer뭩 Rule, Volume, and Linear Transformations
Supplementary Exercises
4. Vector Spaces
Introductory Example: Space Flight and Control Systems
4.1 Vector Spaces and Subspaces
4.2 Null Spaces, Column Spaces, and Linear Transformations
4.3 Linearly Independent Sets; Bases
4.4 Coordinate Systems
4.5 The Dimension of a Vector Space
4.6 Rank
4.7 Change of Basis
4.8 Applications to Difference Equations
4.9 Applications to Markov Chains
Supplementary Exercises
5. Eigenvalues and Eigenvectors
Introductory Example: Dynamical Systems and Spotted Owls
5.1 Eigenvectors and Eigenvalues
5.2 The Characteristic Equation
5.3 Diagonalization
5.4 Eigenvectors and Linear Transformations
5.5 Complex Eigenvalues
5.6 Discrete Dynamical Systems
5.7 Applications to Differential Equations
5.8 Iterative Estimates for Eigenvalues
Supplementary Exercises
6. Orthogonality and Least Squares
Introductory Example: Readjusting the North American Datum
6.1 Inner Product, Length, and Orthogonality
6.2 Orthogonal Sets
6.3 Orthogonal Projections
6.4 The Gram뾖chmidt Process
6.5 Least-Squares Problems
6.6 Applications to Linear Models
6.7 Inner Product Spaces
6.8 Applications of Inner Product Spaces
Supplementary Exercises
7. Symmetric Matrices and Quadratic Forms
Introductory Example: Multichannel Image Processing
7.1 Diagonalization of Symmetric Matrices
7.2 Quadratic Forms
7.3 Constrained Optimization
7.4 The Singular Value Decomposition
7.5 Applications to Image Processing and Statistics
Supplementary Exercises
8. The Geometry of Vector Spaces
Introductory Example: The Platonic Solids
8.1 Affine Combinations
8.2 Affine Independence
8.3 Convex Combinations
8.4 Hyperplanes
8.5 Polytopes
8.6 Curves and Surfaces
9. Optimization (Online Only)
Introductory Example: The Berlin Airlift
9.1 Matrix Games
9.2 Linear Programming뺾eometric Method
9.3 Linear Programming뻊implex Method
9.4 Duality
10. Finite-State Markov Chains (Online Only)
Introductory Example: Google and Markov Chains
10.1 Introduction and Examples
10.2 The Steady-State Vector and Google's PageRank
10.3 Finite-State Markov Chains
10.4 Classification of States and Periodicity
10.5 The Fundamental Matrix
10.6 Markov Chains and Baseball Statistics
Appendices
A. Uniqueness of the Reduced Echelon Form
B. Complex Numbers

"The book isn't too bad, but two weeks into class and we find out that some of the answers in the back of the book are incorrect. How do print a textbook and not find these errors? Chapter 1:Section 1? Really? The author should be able to do this in his sleep and find these mistakes? They should at least make note of this to those who pay over $100 for this book and are struggling in the first section, not by their lack of effort or understanding, but trying to get a correct answer. If you can't figure out Chapter 1, then you have been set up for failure. Don't get me wrong, I think the book is decent, but I feel that this is an issue that is very important and needs to be dealt with, if it hasn't already."


"Overall it is a mediocre math textbook with classic math textbook layout, theorem-proof-example, but the language it used is quite confusing. I mean, not pedantic that kind of confusing, but rather the interchanging of terminologies makes it hard to follow up. Linear algebra this subject has a huge amount of concepts that tell you the same thing from different perspectives and it requires a lot of work to be done by yourself so that you can absorb the concepts and convert from one to the other. Yet this book uses too often different terminologies, even in the same sentence, to explain a simple example without further explanation. So sometimes you need to look back and forth just to understand what he is talking about, which is frustrating. And most of the points are made between examples, without a clear definition before and after the them, which is kind of messy. The major complaint I have for this book is its lack of explanations. Most of the time it just tells you the exact procedure to solve a problem, like the way to perform LU matrix factorization, but fails to explain how to derive it from the knowledge mentioned before. And this book uses a really implicit way to point out the connection of chapters so sometimes when you look back several chapters you will find everything become clear. In addition, notations used in this book are HORRIBLE!! For instance, chapter 4.8 difference equation, if you study by yourself without your instructor's notes, you will completely get lost in its disastrous way of using notations. I cannot even figure out what is vector, what is sequence and what is scalar. This book adopts nontraditional way to organize the material. Instead of applying the knowledge after fully introducing them, this book first talks about really basic skills and then mixes the most advanced concepts and theorems with real world application and does not tell you how to relate them with previous chapter. Drawback of this approach is it definitely escalates the level of difficulty for students to learn them, but advantage is if you work really hard and once you understand the model, you will master the material. Another complaint I have about this book is it just tell you this is the model and how to solve it but not to mention how to set up the model...So whether this book is good or not, you can make the decision by your own.

Some advice to do better using this book:
1. fully understand all the basic concepts.
2. go through examples carefully and connect them with prior knowledge if you want to know why it is like that.
3. if you don't understand something just refer previous chapters you may find some clues."


"Half-way through the semester and this seems to be a decent book.
You will definitely want to get the study guide too ISBN 0321388836.
The study guide has more "plain English." I asked a professor/friend why they didn't just put that in the book, and he said the regular book is expected to be written in a somewhat academic tone of voice. I guess math professors like that.
Linear algebra isn't too bad, the hardest part is grasping some of the abstract concepts and translating them into something I understand. For this my professor friend and the tutoring center help."
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