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Basic Matrix Algebra with Algorithms and Applications: Chapman Hall/CRC Mathematics Series

Autor Robert A. Liebler
en Limba Engleză Paperback – 13 dec 2002
Clear prose, tight organization, and a wealth of examples and computational techniques make Basic Matrix Algebra with Algorithms and Applications an outstanding introduction to linear algebra. The author designed this treatment specifically for freshman majors in mathematical subjects and upper-level students in natural resources, the social sciences, business, or any discipline that eventually requires an understanding of linear models.

With extreme pedagogical clarity that avoids abstraction wherever possible, the author emphasizes minimal polynomials and their computation using a Krylov algorithm. The presentation is highly visual and relies heavily on work with a graphing calculator to allow readers to focus on concepts and techniques rather than on tedious arithmetic. Supporting materials, including test preparation Maple worksheets, are available for download from the Internet.

This unassuming but insightful and remarkably original treatment is organized into bite-sized, clearly stated objectives. It goes well beyond the LACSG recommendations for a first course while still implementing their philosophy and core material. Classroom tested with great success, it prepares readers well for the more advanced studies their fields ultimately will require.
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Specificații

ISBN-13: 9781584883333
ISBN-10: 1584883332
Pagini: 260
Ilustrații: 80 b/w images and 250 equations
Dimensiuni: 156 x 234 x 14 mm
Greutate: 0.49 kg
Ediția:New.
Editura: CRC Press
Colecția Chapman and Hall/CRC
Seria Chapman Hall/CRC Mathematics Series


Public țintă

Undergraduate

Cuprins

SYSTEMS OF LINEAR EQUATIONS AND THEIR SOLUTION: Recognizing Linear Systems and Solutions. Matrices, Equivalence and Row Operations. Echelon Forms and Gaussian Elimination. Free Variables and General Solutions. The Vector Form of the General Solution. Geometric Vectors and Linear Functions. Polynomial Interpolation. MATRIX NUMBER SYSTEMS: Complex Numbers. Matrix Multiplication. Auxiliary Matrices and Matrix Inverses . Symmetric Projectors, Resolving Vectors . Least Squares Approximation. Changing Plane Coordinates. The Fast Fourier Transform and the Euclidean Algorithm. DIAGONALIZABLE MATRICES: Eigenvectors and Eigenvalues. The Minimal Polynomial Algorithm. Linear Recurrence Relations. Properties of the Minimal Polynomial. The Sequence {Ak}. Discrete Dynamical Systems. Matrix Compression with Components
DETERMINANTS: Area and Composition of Linear Functions. Computing Determinants. Fundamental Properties of Determinants . Further Applications. APPENDIX. SELECTED PRACTICE PROBLEM ANSWERS. INDEX.

Recenzii

"In brief, I think the book is wonderful! … It's pedagogically excellent … The examples are very thoughtfully chosen, anticipating possible misunderstandings and illuminating both the main idea and some subtleties … The emphasis on recursion is unusual and valuable … It's rich in topics not often, if at all, treated effectively in texts at this level … Again, I think this book is terrific …"
-Harriet Pollatsek, Professor of Mathematics and
Julia and Sarah Ann Adams Professor of Science,
Mount Holyoke College, South Hadley, Massachusetts, USA

Descriere

Classroom tested with great success, this text builds the foundation in matrix algebra needed by freshman students in mathematics, physics, and computer science and by upper-level business and social science students. The author presents the material with outstanding pedagogical clarity, many figures and diagrams, and interrelated examples. The presentation relies heavily on the use of a graphing calculator, includes section summaries, and provides exercises in each chapter. Organized into bite-sized objectives, this relatively gentle treatment prepares readers well for the advanced studies their fields will require. Supporting material, including Maple worksheets, are available for download from the Internet.