Description
Book SynopsisWilliam Briggs has been on the mathematics faculty at the University of Colorado at Denver for twenty-three years. He received his BA in mathematics from the University of Colorado and his MS and PhD in applied mathematics from Harvard University. He teaches undergraduate and graduate courses throughout the mathematics curriculum with a special interest in mathematical modeling and differential equations as it applies to problems in the biosciences. He has written a quantitative reasoning textbook, Using and Understanding Mathematics; an undergraduate problem solving book, Ants, Bikes, and Clocks; and two tutorial monographs, The Multigrid Tutorial and The DFT: An Owner's Manual for the Discrete Fourier Transform. He is the Society for Industrial and Applied Mathematics (SIAM) Vice President for Education, a University of Colorado President's Teaching Scholar, a recipient of the Outstanding Teacher Awar
Table of Contents
Table of Contents
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Sequences and Infinite Series
- 10.1 An Overview
- 10.2 Sequences
- 10.3 Infinite Series
- 10.4 The Divergence and Integral Tests
- 10.5 Comparison Tests
- 10.6 Alternating Series
- 10.7 The Ratio and Root Tests
- 10.8 Choosing a Convergence Test
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Power Series
- 11.1 Approximating Functions with Polynomials
- 11.2 Properties of Power Series
- 11.3 Taylor Series
- 11.4 Working with Taylor Series
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Parametric and Polar Curves
- 12.1 Parametric Equations
- 12.2 Polar Coordinates
- 12.3 Calculus in Polar Coordinates
- 12.4 Conic Sections
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Vectors and the Geometry of Space
- 13.1 Vectors in the Plane
- 13.2 Vectors in Three Dimensions
- 13.3 Dot Products
- 13.4 Cross Products
- 13.5 Lines and Planes in Space
- 13.6 Cylinders and Quadric Surfaces
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Vector-Valued Functions
- 14.1 Vector-Valued Functions
- 14.2 Calculus of Vector-Valued Functions
- 14.3 Motion in Space
- 14.4 Length of Curves
- 14.5 Curvature and Normal Vectors
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Functions of Several Variables
- 15.1 Graphs and Level Curves
- 15.2 Limits and Continuity
- 15.3 Partial Derivatives
- 15.4 The Chain Rule
- 15.5 Directional Derivatives and the Gradient
- 15.6 Tangent Planes and Linear Approximation
- 15.7 Maximum/Minimum Problems
- 15.8 Lagrange Multipliers
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Multiple Integration
- 16.1 Double Integrals over Rectangular Regions
- 16.2 Double Integrals over General Regions
- 16.3 Double Integrals in Polar Coordinates
- 16.4 Triple Integrals
- 16.5 Triple Integrals in Cylindrical and Spherical Coordinates
- 16.6 Integrals for Mass Calculations
- 16.7 Change of Variables in Multiple Integrals
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Vector Calculus
- 17.1 Vector Fields
- 17.2 Line Integrals
- 17.3 Conservative Vector Fields
- 17.4 Green’s Theorem
- 17.5 Divergence and Curl
- 17.6 Surface Integrals
- 17.7 Stokes’ Theorem
- 17.8 Divergence Theorem
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D2 Second-Order Differential Equations ONLINE
- D2.1 Basic Ideas
- D2.2 Linear Homogeneous Equations
- D2.3 Linear Nonhomogeneous Equations
- D2.4 Applications
- D2.5 Complex Forcing Functions
Appendix A. Proofs of Selected Theorems Appendix B. Algebra Review ONLINE Appendix C. Complex Numbers ONLINE Answers Index Table of Integrals
