Calculus hasn’t changed, but your students have. Many of today’s students have seen calculus before at the high school level. However, professors report nationwide that students come into their calculus courses with weak backgrounds in algebra and trigonometry, two areas of knowledge vital to the mastery of calculus. Thomas’ Calculus, Media Upgrade, Eleventh Edition, Part Two responds to the needs of today’s students by developing their conceptual understanding while maintaining a rigor appropriate to the calculus course.
Thomas’ Calculus, Media Upgrade, Eleventh Edition, Part Two is now available with an enhanced MyMathLab™ course–the ultimate homework, tutorial and study solution for today’s students. The enhanced MyMathLab course includes a rich and flexible set of course materials and features innovative Java™ Applets, Group Projects, and new MathXL® exercises. This text is also available with WebAssign® and WeBWorK®.
Table of Contents:
(Practice Exercises, Additional Exercises, and Questions to Guide Your Review appear at the end of each chapter.)
11. Infinite Sequences and Series
Sequences
Infinite Series
The Integral Test
Comparison Tests
The Ratio and Root Tests
Alternating Series, Absolute and Conditional Convergence
Power Series
Taylor and Maclaurin Series
Convergence of Taylor Series; Error Estimates
Applications of Power Series
Fourier Series
12. Vectors and the Geometry of Space
Three-Dimensional Coordinate Systems
Vectors
The Dot Product
The Cross Product
Lines and Planes in Space
Cylinders and Quadric Surfaces
13. Vector-Valued Functions and Motion in Space
Vector Functions
Modeling Projectile Motion
Arc Length and the Unit Tangent Vector T
Curvature and the Unit Normal Vector N
Torsion and the Unit Binormal Vector B
Planetary Motion and Satellites
14. Partial Derivatives
Functions of Several Variables
Limits and Continuity in Higher Dimensions
Partial Derivatives
The Chain Rule
Directional Derivatives and Gradient Vectors
Tangent Planes and Differentials
Extreme Values and Saddle Points
Lagrange Multipliers
*Partial Derivatives with Constrained Variables
Taylor's Formula for Two Variables
15. Multiple Integrals
Double Integrals
Areas, Moments and Centers of Mass*
Double Integrals in Polar Form
Triple Integrals in Rectangular Coordinates
Masses and Moments in Three Dimensions
Triple Integrals in Cylindrical and Spherical Coordinates
Substitutions in Multiple Integrals
16. Integration in Vector Fields
Line Integrals
Vector Fields, Work, Circulation, and Flux
Path Independence, Potential Functions, and Conservative Fields
Green's Theorem in the Plane
Surface Area and Surface Integrals
Parametrized Surfaces
Stokes' Theorem
The Divergence Theorem and a Unified Theory
Appendices
Mathematical Induction
Proofs of Limit Theorems
Commonly Occurring Limits
Theory of the Real Numbers
Complex Numbers
The Distributive Law for Vector Cross Products
Determinants and Cramer's Rule
The Mixed Derivative Theorem and the Increment Theorem
The Area of a Parallelogram's Projection on a Plane
