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Bundle: Linear Algebra: A Modern Introduction + Calculus, International Metric Edition : 1st Edition - David Poole

Bundle: Linear Algebra: A Modern Introduction + Calculus, International Metric Edition

1st Edition

Book with Other Items Published: 15th October 2015
ISBN: 9780170276603

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LINEAR ALGEBRA: A MODERN INTRODUCTION

David Poole's innovative Linear Algebra: A Modern Introduction, 4e emphasizes a vectors approach and better prepares students to make the transition from computational to theoretical mathematics. Balancing theory and applications, the book is written in a conversational style and combines a traditional presentation with a focus on student-centered learning. Theoretical, computational, and applied topics are presented in a flexible yet integrated way. Stressing geometric understanding before computational techniques, vectors and vector geometry are introduced early to help students visualize concepts and develop mathematical maturity for abstract thinking. Additionally, the book includes ample applications drawn from a variety of disciplines, which reinforce the fact that linear algebra is a valuable tool for modeling real-life problems.

New to this Edition

  • Writing Projects offer students opportunities to research and write about linear algebra. Projects are designed for individual or group work.

  • Chapter 8: Codes is an online chapter combining all material on codes previously interspersed throughout the text.

  • More than 100 new or revised exercises.


About the Author

David Poole is Professor of Mathematics at Trent University, where he has been a faculty member since 1984. Dr. Poole has won numerous teaching awards: Trent University's Symons Award for Excellence in Teaching (the university's top teaching award), three merit awards for teaching excellence, a 2002 Ontario Confederation of University Faculty Associations Teaching Award (the top university teaching award in the province), a 2003 3M Teaching Fellowship (the top university teaching award in Canada, sponsored by 3M Canada Ltd.), a 2007 Leadership in Faculty Teaching Award from the province of Ontario, and the Canadian Mathematical Society's 2009 Excellence in Teaching Award. From 2002-2007, Dr. Poole was Trent University's Associate Dean (Teaching & Learning). His research interests include discrete mathematics, ring theory, and mathematics education. He received his B.Sc. from Acadia University in 1976 before earning his M.Sc. (1977) and Ph.D. (1984) from McMaster University. When he is not doing mathematics, David Poole enjoys hiking and cooking, and he is an avid film buff.





CALCULUS INTERNATIONAL METRIC EDITION

James Stewart's Calculus, International Metric Version texts are widely renowned for their mathematical precision and accuracy, clarity of exposition, and outstanding examples and problem sets. Millions of students worldwide have explored calculus through Stewart's trademark style, while instructors have turned to his approach time and time again. In the Eighth Edition of CALCULUS, INTERNATIONAL METRIC EDITION, Stewart continues to set the standard for the course while adding carefully revised content. The patient explanations, superb exercises, focus on problem solving, and carefully graded problem sets that have made Stewart's texts best-sellers continue to provide a strong foundation for the Eighth Edition. From the most unprepared student to the most mathematically gifted, Stewart's writing and presentation serve to enhance understanding and build confidence.

New to this Edition
  • The data in examples and exercises have been updated. New examples have been added and the solutions to some of the existing examples have been amplified.

  • Several new application based problems in the book have been added to help the students strengthen the understanding of concepts and make the leap to discovering the impact of Calculus in its various applications.

  • Three new projects have been added: the project, Controlling Red Blood Cell Loss During Surgery describes the ANH procedure, in which blood is extracted from the patient before an operation and is replaced by saline solution. This dilutes the patient’s blood so that fewer red blood cells are lost during bleeding and the extracted blood is returned to the patient after surgery. The project, Planes and Birds: Minimizing Energy asks how birds can minimize power and energy by flapping their wings versus gliding. In the project, The Speedo LZR Racer Suit, it is explained that this suit reduces drag in the water and, as a result, many swimming records were broken. Students are asked why a small decrease in drag can have a big effect on performance.


About the Author

The late James Stewart received his M.S. from Stanford University and his Ph.D. from the University of Toronto. He did research at the University of London and was influenced by the famous mathematician George Polya at Stanford University. Stewart was most recently Professor of Mathematics at McMaster University, and his research field was harmonic analysis. Stewart was the author of a best-selling calculus textbook series published by Cengage Learning, including CALCULUS, CALCULUS: EARLY TRANSCENDENTALS, and CALCULUS: CONCEPTS AND CONTEXTS, as well as a series of precalculus texts.

Linear Algebra: A Modern Introduction


1. VECTORS.

Introduction: The Racetrack Game. The Geometry and Algebra of Vectors. Length and Angle: The Dot Product. Exploration: Vectors and Geometry. Lines and Planes. Exploration: The Cross Product. Writing Project: Origins of the Dot Product and the Cross Product. Applications.

2. SYSTEMS OF LINEAR EQUATIONS.

Introduction: Triviality. Introduction to Systems of Linear Equations. Direct Methods for Solving Linear Systems. Writing Project: A History of Gaussian Elimination. Explorations: Lies My Computer Told Me; Partial Pivoting; Counting Operations: An Introduction to the Analysis of Algorithms. Spanning Sets and Linear Independence. Applications. Vignette: The Global Positioning System. Iterative Methods for Solving Linear Systems.

3. MATRICES.

Introduction: Matrices in Action. Matrix Operations. Matrix Algebra. The Inverse of a Matrix. The LU Factorization. Subspaces, Basis, Dimension, and Rank. Introduction to Linear Transformations. Vignette: Robotics. Applications.

4. EIGENVALUES AND EIGENVECTORS.

Introduction: A Dynamical System on Graphs. Introduction to Eigenvalues and Eigenvectors. Determinants. Writing Project: Which Came First-the Matrix or the Determinant? Vignette: Lewis Carroll's Condensation Method. Exploration: Geometric Applications of Determinants. Eigenvalues and Eigenvectors of n x n Matrices. Writing Project: The History of Eigenvalues. Similarity and Diagonalization. Iterative Methods for Computing Eigenvalues. Applications and the Perron-Frobenius Theorem.

Vignette: Ranking Sports Teams and Searching the Internet.

5. ORTHOGONALITY.

Introduction: Shadows on a Wall. Orthogonality in Rn. Orthogonal Complements and Orthogonal Projections. The Gram-Schmidt Process and the QR Factorization. Explorations: The Modified QR Factorization; Approximating Eigenvalues with the QR Algorithm. Orthogonal Diagonalization of Symmetric Matrices. Applications.

6. VECTOR SPACES.

Introduction: Fibonacci in (Vector) Space. Vector Spaces and Subspaces. Linear Independence, Basis, and Dimension. Writing Project: The Rise of Vector Spaces. Exploration: Magic Squares. Change of Basis. Linear Transformations. The Kernel and Range of a Linear Transformation. The Matrix of a Linear Transformation. Exploration: Tilings, Lattices and the Crystallographic Restriction. Applications.

7. DISTANCE AND APPROXIMATION.

Introduction: Taxicab Geometry. Inner Product Spaces. Explorations: Vectors and Matrices with Complex Entries; Geometric Inequalities and Optimization Problems. Norms and Distance Functions. Least Squares Approximation. The Singular Value Decomposition. Vignette: Digital Image Compression. Applications.

8. CODES. (Online)

Code Vectors. Vignette: The Codabar System. Error-Correcting Codes. Dual Codes. Linear Codes. The Minimum Distance of a Code.

Appendix A: Mathematical Notation and Methods of Proof.

Appendix B: Mathematical Induction.

Appendix C: Complex Numbers.

Appendix D: Polynomials.



Calculus, International Metric Version


Preface.

To the Student.

Diagnostic Tests.

A Preview of Calculus.

1. FUNCTIONS AND LIMITS.

Four Ways to Represent a Function. Mathematical Models: A Catalog of Essential Functions. New Functions from Old Functions. The Tangent and Velocity Problems. The Limit of a Function. Calculating Limits Using the Limit Laws. The Precise Definition of a Limit. Continuity. Review. Principles of Problem Solving.

2. DERIVATIVES.

Derivatives and Rates of Change. Writing Project: Early Methods for Finding Tangents. The Derivative as a Function. Differentiation Formulas. Applied Project: Building a Better Roller Coaster. Derivatives of Trigonometric Functions. The Chain Rule. Applied Project: Where Should a Pilot Start Descent? Implicit Differentiation. Laboratory Project: Families of Implicit Curves. Rates of Change in the Natural and Social Sciences. Related Rates. Linear Approximations and Differentials. Laboratory Project: Taylor Polynomials. Review. Problems Plus.

3. APPLICATION OF DIFFERENTIATION.

Maximum and Minimum Values. Applied Project: The Calculus of Rainbows. The Mean Value Theorem. How Derivatives Affect the Shape of a Graph. Limits at Infinity; Horizontal Asymptotes. Summary of Curve Sketching. Graphing with Calculus and Calculators. Optimization Problems. Applied Project: The Shape of a Can. Applied Project: Planes and Birds: Minimizing Energy. Newton’s Method. Antiderivatives. Review. Problems Plus.

4. INTEGRALS.

Areas and Distances. The Definite Integral. Discovery Project: Area Functions. The Fundamental Theorem of Calculus. Indefinite Integrals and the Net Change Theorem. Writing Project: Newton, Leibniz, and the Invention of Calculus. The Substitution Rule. Review. Problems Plus.

5. APPLICATIONS OF INTEGRATION.

Areas Between Curves. Applied Project: The Gini Index. Volumes. Volumes by Cylindrical Shells. Work. Average Value of a Function. Applied Project: Calculus and Baseball. Review. Problems Plus.

6. INVERSE FUNCTIONS: EXPONENTIAL, LOGARITHMIC, AND INVERSE TRIGONOMETRIC FUNCTIONS.

Inverse Functions. Instructors may cover either Sections 6.2-6.4 or Sections 6.2*-6.4* Exponential Functions and Their Derivatives. Logarithmic Functions. Derivatives of Logarithmic Functions. The Natural Logarithmic Function The Natural Exponential Function. General Logarithmic and Exponential Functions. Exponential Growth and Decay. Applied Project: Controlling Red Blood Cell Loss During Surgery. Inverse Trigonometric Functions. Applied Project: Where to Sit at the Movies. Hyperbolic Functions. Indeterminate Forms and l’Hospital’s Rule. Writing Project: The Origins of l’ Hospital’s Rule Review. Problems Plus.

7. TECHNIQUES OF INTEGRATION.

Integration by Parts. Trigonometric Integrals. Trigonometric Substitution. Integration of Rational Functions by Partial Fractions. Strategy for Integration. Integration Using Tables and Computer Algebra Systems. Discovery Project: Patterns in Integrals. Approximate Integration. Improper Integrals. Review. Problems Plus.

8. FURTHER APPLICATIONS OF INTEGRATION.

Arc Length. Discovery Project: Arc Length Contest. Area of a Surface of Revolution. Discovery Project: Rotating on a Slant. Applications to Physics and Engineering. Discovery Project: Complementary Coffee Cups. Applications to Economics and Biology. Probability. Review. Problems Plus.

9. DIFFERENTIAL EQUATIONS.

Modeling with Differential Equations. Direction Fields and Euler’s Method. Separable Equations. Applied Project: How Fast Does a Tank Drain? Applied Project: Which is Faster, Going Up or Coming Down? Models for Population Growth. Linear Equations. Predator-Prey Systems. Review. Problems Plus.

10. PARAMETRIC EQUATIONS AND POLAR COORDINATES.

Curves Defined by Parametric Equations. Laboratory Project: Running Circles Around Circles. Calculus with Parametric Curves. Laboratory Project: Bézier Curves. Polar Coordinates. Laboratory Project: Families of Polar Curves. Areas and Lengths in Polar Coordinates. Conic Sections. Conic Sections in Polar C

ISBN: 9780170276603
ISBN-10: 0170276600
Audience: Tertiary; University or College
Format: Book with Other Items
Language: English
Published: 15th October 2015
Publisher: Cengage Learning EMEA
Country of Publication: GB
Dimensions (cm): 26.0 x 23.0  x 8.0
Weight (kg): 4.2
Edition Number: 1
Edition Type: New edition

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