Mathematics

For sophomore-level or junior/senior-level first courses in Linear Algebra; assumes a Calculus prerequisite.

 

This thorough and accessible text – from one of the leading figures in the use of technology in linear algebra – gives students a challenging and broad understanding of the subject.  The author infuses key concepts with their modern practical applications to offer students examples of how mathematics is used in the real world. Each chapter contains integrated worked examples and chapter tests.  The book stresses the important role geometry and visualization play in understanding linear algebra.  This edition will continue to be packaged with the ancillary ATLAST computer exercise guide, as well as new MATLAB and Maple guides, which are also free in the package.

• Extensive Application of linear algebra concepts to a variety of real world situations – Applications can be used to motivate new material and to show relevance of the material covered.

– Students can easily see what an important tool linear algebra is for solving applied problems.

– See sections 1.3, 5.1, 6.3, and 6.5.

 

• Computer exercises – The most extensive set of chapter-ending computer exercises of any linear algebra text on the market.

– Help students to visualize and discover linear algebra and allow them to explore more realistic applications that are too computationally intensive to work out by hand.

– Provides students with experience in performing matrix computations.

– See the MATLAB section in chapter 6.

 

• Worked out examples make the textbook seem less abstract and more user friendly.

– Enhance student understanding of new concepts.

– See section 1.3 which includes 16 worked out examples illustrating every new concept introduced in that section.

 

• Chapter tests – The most extensive set of chapter-ending computer exercises of any linear algebra text on the market.

– Reinforce course material in the chapter.

– Serves as a wake-up call for students to focus on what material they have yet to master so they can improve their weaknesses.

– See the two chapter tests at the end of chapter 1.

• New and expanded applications – Interesting and current examples including the application of linear transformations to an airplane, eigenvectors determining the orientation of a space shuttle, and how Google^© makes use of linear algebra to rank and order search results.

– Students understand how theories and fundamental linear algebra concepts can help solve modern day problems.

 

• Additional chapter tests and new exercises – A second chapter test with 10 to 12 workout problems has been added to each chapter along with the addition of many new exercises to the exercise sections of the book.

– Aids student self-study and preparation for exams.

 

• Additional new figures

– The addition of seven new figures enhance student visualization of the subject.

 

• MATLAB updates

– The MATLAB appendix has been updated and expanded.  All MATLAB exercises in the book have been checked for compatibility with MATLAB 7.0 (the latest version of MATLAB).  Two MATLAB exercises have been replaced with new exercises.

• A series of MATLAB and Maple guides are FREE when shrink-wrapped with the text.

1. Matrices and Systems of Equations.

Systems of Linear Equations. Row Echelon Form. Matrix Algebra. Elementary Matrices. Partitioned Matrices. Matlab Exercises. Chapter Test.

 

2. Determinants.

The Determinant of a Matrix. Properties of Determinants. Cramer's Rule. Matlab Exercises. Chapter Test.

 

3. Vector Spaces.

Definition and Examples. Subspaces. Linear Independence. Basis and Dimension. Change of Basis. Row Space and Column Space. Matlab Exercises. Chapter Test.

 

4. Linear Transformations.

Definition and Examples. Matrix Representations of Linear Transformations. Similarity. Matlab Exercises. Chapter Test.

 

5. Orthogonality.

The Scalar Product in Rn. Orthogonal Subspaces. Least Squares Problems. Inner Product Spaces. Orthonormal Sets. The Gram-Schmidt Orthogonalization Process. Orthogonal Polynomials. Matlab Exercises. Chapter Test.

 

6. Eigenvalues.

Eigenvalues and Eigenvectors. Systems of Linear Differential Equations. Diagonalization. Hermitian Matrices. The Singular Value Decomposition. Quadratic Forms. Positive Definite Matrices. Nonnegative Matrices. Matlab Exercises. Chapter Test.

 

7. Numerical Linear Algebra.

Floating-Point Numbers. Gaussian Elimination. Pivoting Strategies. Matrix Norms and Condition Numbers. Orthogonal Transformations. The Eigenvalue Problem. Least Squares Problems. Matlab Exercises. Chapter Test.

 

8. Iterative Methods. On the website, as pdfs.

 

9. Jordan Canonical Form. On the website, as pdfs.

 

Appendix: MATLAB.

 

Bibliography.

 

Answers to Selected Exercises.

 

Index.

Introductory Linear Algebra  (Mathematics)

• 
  Linear Algebra with Applications, 8/E
  Leon
  ©2010 | Prentice Hall | Cloth; 552 pp | Instock
  ISBN-10: 0136009298 | ISBN-13: 9780136009290
  Brief Description | Buy from myPearsonStore

  

  This book is for sophomore-level or junior/senior-level first courses in linear algebra and assumes calculus as a prerequisite.

   

  This thorough and accessible text, from one of the leading figures in the use of technology in linear algebra, gives students a challenging and broad understanding of the subject. The author infuses key concepts with their modern practical applications to offer students examples of how mathematics is used in the real world. Each chapter contains integrated worked examples and chapter tests. The book stresses the important roles geometry and visualization play in understanding linear algebra.

Revised Study Guide Pages

Page 56
Page 94

Instructor's Solutions Manual, 7/E
Leon
©2006 | Prentice Hall | Paper; 180 pp | Instock
ISBN-10: 0131936255 | ISBN-13: 9780131936256
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Student Study Guide, 7/E
Leon
©2006 | Prentice Hall | Paper; 148 pp | Instock
ISBN-10: 0131936239 | ISBN-13: 9780131936232
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Addison-Wesley's Algebra Review
Addison-Wesley
©2004 | Prentice Hall | Paper | Out of Stock
ISBN-10: 0321247086 | ISBN-13: 9780321247087

Addison-Wesley's Basic Math Review
Addison-Wesley
©2004 | Prentice Hall | Paper | Instock
ISBN-10: 0321247078 | ISBN-13: 9780321247070

Algebra Review Study Card, 2/E
D'Ippolito & Generazzo
©2006 | Prentice Hall | Study Card; 6 pp | Instock
ISBN-10: 0321394739 | ISBN-13: 9780321394736
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Allied Health Study Card, 2/E
Forshier
©2006 | Prentice Hall | Study Card | Instock
ISBN-10: 0321394747 | ISBN-13: 9780321394743
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Basic Math Review Card, 2/E
Addison-Wesley
©2006 | Prentice Hall | Study Card; 6 pp | Instock
ISBN-10: 0321394763 | ISBN-13: 9780321394767
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Concept Videos: Algebra
Addison-Wesley
©2008 | Prentice Hall | Multiple Media Package | Instock
ISBN-10: 0321517199 | ISBN-13: 9780321517197

Concept Videos: Basic Math & Prealgebra
Addison-Wesley
©2008 | Prentice Hall | Multiple Media Package | Instock
ISBN-10: 032151758X | ISBN-13: 9780321517586

Discovering Algebra: Examples with Keystrokes on the TI-83/TI-82 and TI-85/TI-86, A Laboratory Approach
Pirich & Bigliani
©1997 | Prentice Hall | Paper; 195 pp | Instock
ISBN-10: 0136492037 | ISBN-13: 9780136492030
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Finite Mathematics Study Card
Addison-Wesley
©2006 | Prentice Hall | Study Card | Instock
ISBN-10: 0321374398 | ISBN-13: 9780321374394
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Flash Review Series: Algebra
Becker
©2004 | Prentice Hall | Paper | Instock
ISBN-10: 0321143094 | ISBN-13: 9780321143099
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Graphing Calculator Reference Card, 3/E
Ripley
©2006 | Prentice Hall | Study Card; 6 pp | Instock
ISBN-10: 0321394755 | ISBN-13: 9780321394750
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Graphing Calculator Tutorial CD
Addison-Wesley
©2006 | Prentice Hall | CD-ROM Only | Instock
ISBN-10: 0321357744 | ISBN-13: 9780321357748
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Interwrite Personal Response System
EduCue, Addison-Wesley & Benjamin Cummings
©2004 | Prentice Hall | Electronic Supplement | Instock
ISBN-10: 0321267354 | ISBN-13: 9780321267351

Math for Allied Health Study/Reference Card
Forshier
©2006 | Prentice Hall | Study Card; 0 pp | Out of Stock
ISBN-10: 0321336542 | ISBN-13: 9780321336545

Mathematics Spanish Glossary, 2/E
Lara & Peeples
©2000 | Prentice Hall | Paper; 48 pp | Instock
ISBN-10: 0201728966 | ISBN-13: 9780201728965
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Overcoming Math Anxiety, 2/E
Davidson & Levitov
©2000 | Prentice Hall | Paper | Instock
ISBN-10: 0321069188 | ISBN-13: 9780321069184
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Pearson TI Rebate Coupon $15, 2/E
Pearson
©2009 | Prentice Hall | Paper | Instock
ISBN-10: 0321566041 | ISBN-13: 9780321566041

Prealgebra Review Workbook
Wheel
©2006 | Prentice Hall | Paper; 300 pp | Instock
ISBN-10: 0321473329 | ISBN-13: 9780321473325
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Review of Algebra, A
Howard
©2002 | Prentice Hall | Paper; 224 pp | Instock
ISBN-10: 0201773473 | ISBN-13: 9780201773477
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Saleable Technology Bundle, 2/E
Pearson
©2009 | Prentice Hall | Multiple Media Package | Estimated Availability : 09/01/2008
ISBN-10: 0321561880 | ISBN-13: 9780321561886

Spanish Basic Math Study Card
Leonarte
©2007 | Prentice Hall | Study Card | Instock
ISBN-10: 0321438582 | ISBN-13: 9780321438584
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Stand-alone Access Code Tutor Center
Addison-Wesley
©2008 | Prentice Hall | Access Code Card | Instock
ISBN-10: 0201721708 | ISBN-13: 9780201721706
URL:  http://www.aw-bc.com/tutorcenter
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For Introductory Linear Algebra

Understanding Linear Algebra Using MATLAB
Kleinfeld & Kleinfeld
©2001 | Prentice Hall | Paper; 210 pp | Instock
ISBN-10: 0130609455 | ISBN-13: 9780130609458

Visualizing Linear Algebra Using Maple
Keith
©2001 | Prentice Hall | Paper; 250 pp | Out of Stock
ISBN-10: 0130418161 | ISBN-13: 9780130418166

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