Thomas' Calculus, 15th edition

11. Parametric Equations and Polar Coordinates

• 11.1 Parametrizations of Plane Curves
• 11.2 Calculus with Parametric Curves
• 11.3 Polar Coordinates
• 11.4 Graphing Polar Coordinate Equations
• 11.5 Areas and Lengths in Polar Coordinates
• 11.6 Conic Sections
• 11.7 Conics in Polar Coordinates
• Questions to Guide Your Review
• Practice Exercises
• Additional and Advanced Exercises
• Technology Application Projects

12. Vectors and the Geometry of Space

• 12.1 Three-Dimensional Coordinate Systems
• 12.2 Vectors
• 12.3 The Dot Product
• 12.4 The Cross Product
• 12.5 Lines and Planes in Space
• 12.6 Cylinders and Quadric Surfaces
• Questions to Guide Your Review
• Practice Exercises
• Additional and Advanced Exercises
• Technology Application Projects

13. Vector-Valued Functions and Motion in Space

• 13.1 Curves in Space and Their Tangents
• 13.2 Integrals of Vector Functions; Projectile Motion
• 13.3 Arc Length in Space
• 13.4 Curvature and Normal Vectors of a Curve
• 13.5 Tangential and Normal Components of Acceleration
• 13.6 Velocity and Acceleration in Polar Coordinates
• Questions to Guide Your Review
• Practice Exercises
• Additional and Advanced Exercises
• Technology Application Projects

14. Partial Derivatives

• 14.1 Functions of Several Variables
• 14.2 Limits and Continuity in Higher Dimensions
• 14.3 Partial Derivatives
• 14.4 The Chain Rule
• 14.5 Directional Derivatives and Gradient Vectors
• 14.6 Tangent Planes and Differentials
• 14.7 Extreme Values and Saddle Points
• 14.8 Lagrange Multipliers
• 14.9 Taylor's Formula for Two Variables
• 14.10 Partial Derivatives with Constrained Variables
• Questions to Guide Your Review
• Practice Exercises
• Additional and Advanced Exercises
• Technology Application Projects

15. Multiple Integrals

• 15.1 Double and Iterated Integrals over Rectangles
• 15.2 Double Integrals over General Regions
• 15.3 Area by Double Integration
• 15.4 Double Integrals in Polar Form
• 15.5 Triple Integrals in Rectangular Coordinates
• 15.6 Applications
• 15.7 Triple Integrals in Cylindrical and Spherical Coordinates
• 15.8 Substitutions in Multiple Integrals
• Questions to Guide Your Review
• Practice Exercises
• Additional and Advanced Exercises
• Technology Application Projects

16. Integrals and Vector Fields

• 16.1 Line Integrals of Scalar Functions
• 16.2 Vector Fields and Line Integrals: Work, Circulation, and Flux
• 16.3 Path Independence, Conservative Fields, and Potential Functions
• 16.4 Green's Theorem in the Plane
• 16.5 Surfaces and Area
• 16.6 Surface Integrals
• 16.7 Stokes' Theorem
• 16.8 The Divergence Theorem and a Unified Theory
• Questions to Guide Your Review
• Practice Exercises
• Additional and Advanced Exercises
• Technology Application Projects

17. Second-Order Differential Equations

• 17.1 Second-Order Linear Equations
• 17.2 Nonhomogeneous Linear Equations
• 17.3 Applications
• 17.4 Euler Equations
• 17.5 Power-Series Solutions
• Questions to Guide Your Review
• Practice Exercises
• Additional and Advanced Exercises
• Technology Application Projects

18. Complex Functions (online)

• 18.1 Complex Numbers
• 18.2 Limits and Continuity
• 18.3 Complex Derivatives
• 18.4 The Cauchy-Riemann Equations
• 18.5 Complex Series
• 18.6 Conformal Maps

19. Fourier Series and Wavelets (online)

• 19.1 Periodic Functions
• 19.2 Summing Sines and Cosines
• 19.3 Vectors and Approximation in Three and More Dimensions
• 19.4 Approximation of Functions
• 19.5 Advanced Topic: The Haar System and Wavelets

Appendix A

• A.1 Real Numbers and the Real Line
• A.2 Mathematical Induction
• A.3 Lines, Circles, and Parabolas
• A.4 Proofs of Limit Theorems
• A.5 Commonly Occurring Limits
• A.6 Theory of the Real Numbers
• A.7 The Distributive Law for Vector Cross Products
• A.8 The Mixed Derivative Theorem and the Increment Theorem

Appendix B (online)

• B.1 Determinants
• B.2 Extreme Values and Saddle Points for Functions of More than Two Variables
• B.3 The Method of Gradient Descent

Answers to Odd-Numbered Exercises

Applications Index

Subject Index

A Brief Table of Integrals

Credits