Look Inside Look Inside Cover: Linear Algebra with Applications, 2nd Edition by Jeffrey Holt
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Linear Algebra with Applications

Second Edition ©2017 Jeffrey Holt

Now available with Achieve, Holt's Linear Algebra with Applications, Second Edition, blends computational and conceptual topics to prepare students for the rigors of conceptual thinking in an abstract setting. The early treatment of conceptual topics in the context of Euclidean space gives...

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Look Inside Look Inside Cover: Linear Algebra with Applications, 2nd Edition by Jeffrey Holt

Now available with Achieve, Holt's Linear Algebra with Applications, Second Edition, blends computational and conceptual topics to prepare students for the rigors of conceptual thinking in an abstract setting. The early treatment of conceptual topics in the context of Euclidean space gives students more time, and a familiar setting, in which to absorb them. This organization also makes it possible to treat eigenvalues and eigenvectors earlier than in most texts. Abstract vector spaces are introduced later, once students have developed a solid conceptual foundation.

Concepts and topics are frequently accompanied by applications to provide context and motivation. Because many students learn by example, Linear Algebra with Applications provides a large number of representative examples, over and above those used to introduce topics. Select exercises can be assigned online in Macmillan's Achieve platform, which provides a flexible, customizable courseware that enhances the trusted content of the text.

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New to This Edition

Achieve is the culmination of years of development work put toward creating the most powerful online learning tool for calculus students. It houses all of our renowned assessments, multimedia assets, e-books, and instructor resources in a powerful new platform.

Achieve supports educators and students throughout the full range of instruction, including assets suitable for pre-class preparation, in-class active learning, and post-class study and assessment. The pairing of a powerful new platform with outstanding content provides an unrivalled learning experience.

Highlights in Achieve include:

  • Homework: Achieve's proprietary grading algorithm combines our homegrown parser and the computer algebra system, SymPy, to accept every valid equivalent answer and to trigger warnings for answers entered in an incorrect format. Detailed feedback and fully worked solutions provide in-question guidance for students as they solve. Homework is easy to format for students by using our intuitive Math Palette, and it is easy to edit for instructors using Macmillan's built-in question editor.
  • LearningCurve adaptive quizzing, which offers individualized question sets and feedback for each student based on their correct and incorrect responses and links directly to the ebook.
  • Easy integration and gradebook sync with iClicker classroom engagement solutions that promote in-class activities and participation through instantaneous student response.
  • Simple integration with your campus LMS and availability through Inclusive Access programs.
  • Instructor resources, including the test bank, lecture slides, and Maple, MATLAB, and Mathematica Manuals.

Features of this Edition Include:

• Early Integration of Computational and Conceptual Topics helps students absorb and digest conceptual topics early, then provides opportunities to apply them when working with eigenvalues and eigenvectors.
• Focusing on Applications provides an understanding of why a topic is of interest and motivates students to engage with the instruction.
• Extensive Exercise Sets cover a wide range of types (from computational to conceptual to proofs) and difficulty levels.
• Additional Representative Examples reinforce students’ learning by going beyond the initial examples used to introduce or explain a topic.
• Integration of Computer Algebra Systems assist students with Mathematica, Maple, and MatLab.
• Coverage of Numerical Methods throughout the text shows students how solving linear algebra problems would work in the real world and make students aware of how real numbers would be used.

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Table of Contents

Preface
1. Systems of Linear Equations
1.1 Lines and Linear Equations
1.2 Linear Systems and Matrices
1.3 Applications of Linear Systems
1.4 Numerical Solutions
2. Euclidean Space
2.1 Vectors
2.2 Span
2.3 Linear Independence
3. Matrices
3.1 Linear Transformations
3.2 Matrix Algebra
3.3 Inverses
3.4 LU Factorization
3.5 Markov Chains
4. Subspaces
4.1 Introduction to Subspaces
4.2 Basis and Dimension
4.3 Row and Column Spaces
4.4 Change of Basis
5. Determinants
 5.1 The Determinant Function
5.2 Properties of the Determinant
5.3 Applications of the Determinant
6. Eigenvalues and Eigenvectors
6.1 Eigenvalues and Eigenvectors
6.2 Diagonalization
6.3 Complex Eigenvalues and Eigenvectors
6.4 Systems of Differential Equations
6.5 Approximation Methods
7. Vector Spaces
7.1 Vector Spaces and Subspaces
7.2 Span and Linear Independence
7.3 Basis and Dimension
8. Orthogonality
8.1 Dot Products and Orthogonal Sets
8.2 Projection and the Gram-Schmidt Process
8.3 Diagonalizing Symmetric Matrices and QR Factorization
8.4 The Singular Value Decomposition
8.5 Least Squares Regression
9. Linear Transformations
9.1 Definition and Properties
9.2 Isomorphisms
9.3 The Matrix of a Linear Transformation
9.4 Similarity
10. Inner Product Spaces
10.1 Inner Products
10.2 The Gram-Schmidt Process Revisited
10.3 Applications of Inner Products
11. Additional Topics and Applications
11.1 Quadratic Forms
11.2 Positive Definite Matrices
11.3 Constrained Optimization
11.4 Complex Vector Spaces
11.5 Hermitian Matrices
Glossary
Answers to Selected Exercises
Index
Headshot of Jeffrey Holt

Jeffrey Holt

Jeff Holt has a B.A. from Humboldt State University and a Ph.D. from the University of Texas. He has been teaching mathematics for over 20 years, the last eleven at the University of Virginia. He currently has a joint appointment in the Department of Mathematics and the Department of Statistics at UVA.
 
During his career, Holt has won several awards for teaching. He has had NSF grants to support student math and science scholarships, the implementation of a computer-based homework system, and the development of an innovative undergraduate number theory course which later was turned into the text, Discovering Number Theory, coauthored with John Jones. In his spare time he enjoys lowering the value of his house with do-it-yourself home-improvement projects.

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Test Bank for Linear Algebra with Applications

Jeffrey Holt | Second Edition | ©2017 | ISBN:9781319057701

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