Introduction to Linear Algebra for Science and Engineering (2e)

Norman/Wolczuk’s An Introduction to Linear Algebra for Science and Engineering has been widely respected for its unique approach, which helps students understand and apply theory and concepts by combining theory with computations and slowly bringing students to the difficult abstract concepts. This approach includes an early treatment of vector spaces and complex topics in a simpler, geometric context. An Introduction to Linear Algebra for Science and Engineering promotes advanced thinking and understanding by encouraging students to make connections between previously learned and new concepts and demonstrates the importance of each topic through applications.

The highly anticipated second edition of this book will retain the student-friendly writing of the first edition while enhancing pedagogical features by including new mid-section exercises, new and expanded examples and end-of-chapter problems, and improved motivation behind each theorem. The second edition features a fresh two-colour design and a companion website for students that will include additional applications, resources, practice quizzes, and the first edition’s “Essay on Linearity and Superposition in Physics.”

NEW! MyMathLab is now available for this text. The course features assignable homework exercises plus the complete eBook, in addition to tutorial and assessment tools that make it easy to manage your course online.

Visit our showcase website to learn more about this text.

Chapter 1:                    Euclidean Vector Spaces

Chapter 2:                    Systems of Linear Equations

Chapter 3:                    Matrices, Linear Mappings, Inverses

Chapter 4:                    Vector Spaces

Chapter 5:                    Determinants

Chapter 6:                    Eigenvectors and Diagonalization

Chapter 7:                    Orthonormal Bases

Chapter 8:                    Symmetric Matrices and Quadratic Forms

Chapter 9:                    Complex Vector Spaces

• Early introduction of basic theory and important concepts.  The second edition introduces all the concepts of subspaces, linear independence, spanning, and bases in Chapter 1 and revisits them in Chapter 2 and 3 before using them in abstract vector spaces. By introducing the theory slowly, students don’t have to cope with it all at once when they get to the general concept of a vector space in Chapter 4. They are familiar with the concepts so the abstraction is a natural extension.
• Expanded Geometric approach. Building on the first edition’s strong emphasis on geometry, the second edition introduces more advanced concepts such as Spanning and Linear Independence through geometry early in order to aid in visualizing the concepts. This allows for a better understanding of the concepts before they are turned into abstract concepts.
• New mid-section exercises. These short, computational questions allow students to use and check their understanding of a concept before moving on. Solutions are provided in the back of the book.
• New interior design. The second edition has a new two-colour interior design that enhances readability. Definitions, algorithms, theorems, and examples are called out in the margins for easy reference.
• New art program. New illustrations clearly illustrate concepts, examples, and applications.
• Proven, class tested approach. Norman/Wolczuk’s approach has been class tested at the University of Waterloo for eight semesters. Students who study with the text experience higher retention of the material after the course ends, allowing for more challenging work to be covered in following courses.
• Flexible Order of Topics.
• Chapter 5: Determinants and Chapter 6: Eigenvectors and Diagonalization are self contained chapters that can be moved earlier, before Chapter 4: Vector Spaces.
• Standardized notation. The second edition includes standardized notation for vectors in R^n (arrow-hat) and column vectors.
• Additional Examples. Additional worked out examples have been added. Students benefit from have a good number of well selected examples to learn from.
• End of Section Problems. End of Section problems have been reorganized and additional exercises have been added.
• New Chapter 9: Complex Vector Spaces. Discussion of complex numbers and complex vector spaces has been collected into a single chapter.
• Companion Website. The CW will have practice quizzes, additional applications, and the "Essay on Linearity and Superposition in Physics” from the first edition. The self-quizzing in Multiple Choice and True/False format will help students gauge their conceptual understanding of key concepts
• MyMathLab course featuring open-ended, algorithmically generated exercises.

• Student-friendly language. This text is written in a conversational, effortless tone, creating a truly student-friendly text.
  
• Balances theory and computations. An Introduction to Linear Algebra for Science and Engineering introduces students to the theory and computational aspects of linear algebra simultaneously. This ensures that students realize that linear algebra is not just computations. It allows important concepts to be developed and extended slowly and it encourages the use of computational problems to understand the theory rather than the memorization of algorithms.
  
• Strong emphasis on geometry. Students are usually familiar with the geometrical interpretation of vectors from high school math and physics. Concepts that are introduced early are done so using geometry to explain and motivate.
  
• Applications support theory. This text distributes applications of linear algebra throughout text where relevant (rather than gathering them in a separate section.) Applications are included where the relevant theory is developed keeping the focus on the theory. Applications include:
  • Minimum distance from a point to a plane (Section 1.4)
  • Area and Volume (Section 1.5, Section 5.4)
  • Electrical Circuits (Section 2.4, Section 9.2)
  • Planar Trusses (Section 2.4)
  • Linear Programming (Section 2.4)
  • Magic Squares (Chapter 4 Review)
  • Markov Processes (Section 6.3)
  • Differential Equations (Section 6.4)
  • Curve of Best Fit (Section 7.3)
  • Overdetermined Systems (Section 7.3)
  • Graphing Quadratic Forms (Section 8.3)
  • Small Deformations (Section 8.4)
  • The Inertia Tensor (Section 8.4)
    
• The problem set at the end of each section includes four types of questions
  • A: practice problems intended to provide a variety and number of standard computational problems, with some theoretical problems, necessary for students to master the techniques of the course. Answers to A-type problems are provided at the back of the text.
  • B: homework problems similar to A problems but without answers in the back of the text.
  • C: problems that require the use of a suitable computer program and help student familiarise themselves with using computer software to solve linear algebra problems. These problems remind students that linear algebra uses real numbers as well as integers and simple fractions. C-type problems are platform-neutral; they can be used with any linear algebra software.
  • D: problems that require students to work with general cases, write simple arguments or invent examples, all of which are important aspects of mastering mathematics ideas that all students should attempt.
    
• End-of-chapter Chapter Review. Contains Suggestions for Review, Chapter Quiz, Further Exercises, and aids students in reviewing material presented in each chapter.
  
• Student Resources include:
  • Student Solutions Manual, prepared by Dan Wolczuk, contains full solutions to the Practice Problems and Chapter Quizzes.
  • Companion Website includes practice quizzes, additional applications, and the First Edition's "Essay on Linearity and Superposition in Physics."
    
• Instructor's Resource CD-ROM includes the following valuable teaching tools:
  • Instructor’s Solutions Manual containing answers for all problems in the text: Practice Problems, Homework Problems, Computer Problems, Conceptual Problems, Chapter Quizzes, and Further Problems.
  • Instructor's Resource Manual featuring additional Problems and teaching notes.
  • A Test Bank with a large selection of questions for every chapter of the text.
  • Customizable Beamer presentations for each chapter.
  • Image Library.

Daniel Norman, born 1938.  B.A. (University of Toronto), M.A.(Queen's University at Kingston), Ph.D. (University of London, King's College). His Ph.D. thesis was in General Relativity.  Appointed to the Department of Mathematics at Queen's in 1965, he remained interested in applied mathematics. He taught undergraduate courses at all levels, mostly calculus, linear algebra and differential equations, to engineering students.  After teaching introductory linear algebra for several years, he was frustrated with texts then available for those students so he began writing Introduction to Linear Algebra for engineering students in 1989.  Versions of it were used in the large first year engineering class from 1991 until its publication as a book in 1995 and it continued to be used until he retired from the Department of Mathematics and Statistics at Queen's, as an Associate Professor, in 2001.

Dan Wolczuk has been lecturing at the University of Waterloo since 2004.  Since he teaches nine courses a year, mostly first and second year linear algebra and calculus courses, he has spent considerable effort researching how to teach these courses more effectively. Dan is very passionate about teaching and spends much of his spare time teaching mathematics to gifted elementary and high school students.