Student's Solutions Manual Part Two for University Calculus

Front Cover
Title Page
Copyright Page
Preface to the Student
Table of Contents
8 Infinite Sequences and Series
8.1 Sequences
8.2 Infinite Series
8.3 The Integral Test
8.4 Comparison Tests
8.5 The Ratio and Root Tests
8.6 Alternating Series, Absolute and Conditional Convergence
8.7 Power Series
8.8 Taylor and Maclaurin Series
8.9 Convergence of Taylor Series
8.10 The Binomial Series
8 Practice Exercises
8 Additional and Advanced Exercises
9 Polar Coordinates and Conics
9.1 Polar Coordinates
9.2 Graphing in Polar Coordinates
9.3 Areas and Lengths in Polar Coordinates
9.4 Conic Sections
9.5 Conics in Polar Coordinates
9.6 Conics and Parametric Equations; The Cycloid
9 Practice Exercises
9 Additional and Advanced Exercises
10 Vectors and the Geometry of Space
10.1 Three-Dimensional Coordinate Systems
10.2 Vectors
10.3 The Dot Product
10.4 The Cross Product
10.5 Lines and Planes in Space
10.6 Cylinders and Quadric Surfaces
10 Practice Exercises
10 Additional and Advanced Exercises
11 Vector-Valued Functions and Motion in Space
11.1 Vector Functions and Their Derivatives
11.2 Integrals of Vector Functions
11.3 Arc Length in Space
11.4 Curvature of a Curve
11.5 Tangential and Normal Components of Acceleration
11.6 Velocity and Acceleration in Polar Coordinates
11 Practice Exercises
11 Additional and Advanced Exercises
12 Partial Derivatives
12.1 Functions of Several Variables
12.2 Limits and Continuity in Higher Dimensions
12.3 Partial Derivatives
12.4 The Chain Rule
12.5 Directional Derivatives and Gradient Vectors
12.6 Tangent Planes and Differentials
12.7 Extreme Values and Saddle Points
12.8 Lagrange Multipliers
12.9 Taylor's Formula for Two Variables
12 Practice Exercises
12 Additional and Advanced Exercises
13 Multiple Integrals
13.1 Double and Iterated Integrals over Rectangles
13.2 Double Integrals over General Regions
13.3 Area by Double Integration
13.4 Double Integrals in Polar Form
13.5 Triple Integrals in Rectangular Coordinates
13.6 Moments and Centers of Mass
13.7 Triple Integrals in Cylindrical and Spherical Coordinates
13.8 Substitutions in Multiple Integrals
13 Practice Exercises
13 Additional and Advanced Exercises
14 Integration in Vector Fields
14.1 Line Integrals
14.2 Vector Fields, Work, Circulation, and Flux
14.3 Path Independence, Potential Functions, and Conservative Fields
14.4 Green's Theorem in the Plane
14.5 Surfaces and Area
14.6 Surface Integrals and Flux
14.7 Stokes' Theorem
14.8 The Divergence Theorem and a Unified Theory
14 Practice Exercises
14 Additional and Advanced Exercises
Back Cover