Table of contents for University calculus / Joel Hass, Maurice D. Weir, George B. Thomas, Jr.


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-l               Functions                                                                               1
1.1  Functions and Their Graphs  1
1.2  Combining Functions; Shifting and Scaling Graphs  14
1.3  Trigonometric Functions  22
1.4  Exponential Functions  30
1.5 Inverse Functions and Logarithms  36
1.6  Graphing with Calculators and Computers  50
-          Limits and Continuity                                                                 55
2.1  Rates of Change and Tangents to Curves  55
2.2  Limit of a Function and Limit Laws  62
2.3  The Precise Definition of a Limit  74
2.4  One-Sided Limits and Limits at Infinity  84
2.5 Infinite Limits and Vertical Asymptotes  97
2.6  Continuity  103
2.7  Tangents and Derivatives at a Point  115
QUESTIONS TO GUIDE YOUR REVIEW  119
PRACTICE EXERCISES  120
ADDITIONAL AND ADVANCED EXERCISES  122
-                Differentiation                                                                      125
3.1  The Derivative as a Function  125
3.2  Differentiation Rules for Polynomials, Exponentials, Products, and Quotients  134
3.3  The Derivative as a Rate of Change  146
3.4  Derivatives of Trigonometric Functions  157
3.5  The Chain Rule and Parametric Equations  164
3.6 Implicit Differentiation  177
3.7  Derivatives of Inverse Functions and Logarithms  183
3.8 Inverse Trigonometric Functions  194
3.9  Related Rates  201
3.10 Linearization and Differentials  209
3.11 Hyperbolic Functions  221
QUESTIONS TO GUIDE YOUR REVIEW  227
PRACTICE EXERCISES  228
ADDITIONAL AND ADVANCED EXERCISES  234
B         Applications of Derivatives                                                          237
4.1  Extreme Values of Functions  237
4.2  The Mean Value Theorem  245
4.3  Monotonic Functions and the First Derivative Test  254
4.4  Concavity and Curve Sketching  260
4.5  Applied Optimization  271
4.6 Indeterminate Forms and L'Hdpital's Rule  283
4.7  Newton's Method  291
4.8  Antiderivatives  296
QUESTIONS TO GUIDE YOUR REVIEW  306
PRACTICE EXERCISES  307
ADDITIONAL AND ADVANCED EXERCISES  311
-              Integration                                                                          315
5.1  Estimating with Finite Sums  315
5.2  Sigma Notation and Limits of Finite Sums  325
5.3  The Definite Integral  332
5.4  The Fundamental Theorem of Calculus  345
5.5 Indefinite Integrals and the Substitution Rule  354
5.6  Substitution and Area Between Curves  360
5.7  The Logarithm Defined as an Integral  370
QUESTIONS TO GUIDE YOUR REVIEW  381
PRACTICE EXERCISES  382
ADDITIONAL AND ADVANCED EXERCISES  386
B                Applications of Definite Integrals                                                   391
6.1  Volumes by Slicing and Rotation About an Axis  391
6.2  Volumes by Cylindrical Shells  401
6.3  Lengths of Plane Curves  408
6.4  Areas of Surfaces of Revolution  415
6.5  Exponential Change and Separable Differential Equations  421
6.6  Work   430
6.7  Moments and Centers of Mass  437
QUESTIONS TO GUIDE YOUR REVIEW  444
PRACTICE EXERCISES  444
ADDITIONAL AND ADVANCED EXERCISES  446
Techniques of Integration                                                            448
7.1 Integration by Parts  448
7.2  Trigonometric Integrals  455
7.3  Trigonometric Substitutions  461
7.4 Integration of Rational Functions by Partial Fractions  464
7.5 Integral Tables and Computer Algebra Systems  471
7.6  Numerical Integration  477
7.7 Improper Integrals  487
QUESTIONS TO GUIDE YOUR REVIEW  497
PRACTICE EXERCISES  497
ADDITIONAL AND ADVANCED EXERCISES  500
Infinite Sequences and Series                                                        502
8.1  Sequences  502
8.2 Infinite Series  515
8.3  The Integral Test  523
8.4  Comparison Tests  529
8.5  The Ratio and Root Tests  533
8.6  Alternating Series, Absolute and Conditional Convergence  537
8.7  Power Series  543
8.8  Taylor and Maclaurin Series  553
8.9  Convergence of Taylor Series  559
8.10 The Binomial Series  569
QUESTIONS TO GUIDE YOUR REVIEW  572
PRACTICE EXERCISES  573
ADDITIONAL AND ADVANCED EXERCISES  575
Polar Coordinates and Conics                                                         577
9.1  Polar Coordinates  577
9.2  Graphing in Polar Coordinates  582
9.3  Areas and Lengths in Polar Coordinates  586
9.4  Conic Sections  590
9.5  Conics in Polar Coordinates  599
9.6  Conics and Parametric Equations; The Cycloid  606
QUESTIONS TO GUIDE YOUR REVIEW  610
PRACTICE EXERCISES  610
ADDITIONAL AND ADVANCED EXERCISES  612
Vectors and the Geometry of Space                                                      614
10.1 Three-Dimensional Coordinate Systems  614
10.2 Vectors  619
10.3 The Dot Product  628
10.4 The Cross Product  636
10.5 Lines and Planes in Space  642
10.6 Cylinders and Quadric Surfaces  652
QUESTIONS TO GUIDE YOUR REVIEW  657
PRACTICE EXERCISES  658
ADDITIONAL AND ADVANCED EXERCISES  660
Vector-Valued Functions and Motion in Space                                            663
11.1 Vector Functions and Their Derivatives  663
11.2 Integrals of Vector Functions  672
11.3 Arc Length in Space  678
11.4 Curvature of a Curve  683
11.5 Tangential and Normal Components of Acceleration  689
11.6 Velocity and Acceleration in Polar Coordinates  694
QUESTIONS TO GUIDE YOUR REVIEW  698
PRACTICE EXERCISES  698
ADDITIONAL AND ADVANCED EXERCISES  700
Partial Derivatives                                                                    702
12.1 Functions of Several Variables  702
12.2 Limits and Continuity in Higher Dimensions  711
12.3 Partial Derivatives  719
12.4 The Chain Rule  731
12.5 Directional Derivatives and Gradient Vectors  739
12.6 Tangent Planes and Differentials  747
12.7 Extreme Values and Saddle Points  756
12.8 Lagrange Multipliers  765
12.9 Taylor's Formula for Two Variables  775
QUESTIONS TO GUIDE YOUR REVIEW  779
PRACTICE EXERCISES  780
ADDITIONAL AND ADVANCED EXERCISES  783
Multiple Integrals                                                                     785
13.1 Double and Iterated Integrals over Rectangles  785
13.2 Double Integrals over General Regions  790
13.3 Area by Double Integration  799
13.4 Double Integrals in Polar Form  802
13.5 Triple Integrals in Rectangular Coordinates  807
13.6 Moments and Centers of Mass  816
13.7 Triple Integrals in Cylindrical and Spherical Coordinates  825
13.8 Substitutions in Multiple Integrals  837
QUESTIONS TO GUIDE YOUR REVIEW  846
PRACTICE EXERCISES  846
ADDITIONAL AND ADVANCED EXERCISES  848
I          Integration in Vector Fields                                                        851
14.1 Line Integrals  851
14.2 Vector Fields, Work, Circulation, and Flux  856
14.3 Path Independence, Potential Functions, and Conservative Fields  867
14.4 Green's Theorem in the Plane  877
14.5 Surfaces and Area  887
14.6 Surface Integrals and Flux  896
14.7 Stokes' Theorem  905
14.8 The Divergence Theorem and a Unified Theory  914
QUESTIONS TO GUIDE YOUR REVIEW  925
PRACTICE EXERCISES  925
ADDITIONAL AND ADVANCED EXERCISES  928
First-Order Differential Equations (online)
15.1 Solutions, Slope Fields, and Picard's Theorem
15.2 First-Order Linear Equations
15.3 Applications
15.4 Euler's Method
15.5 Graphical Solutions of Autonomous Equations
15.6 Systems of Equations and Phase Planes
Second-Order Differential Equations (online)
16.1 Second-Order Linear Equations
16.2 Nonhomogeneous Linear Equations
16.3 Applications
16.4 Euler Equations
16.5 Power Series Solutions



Library of Congress subject headings for this publication: Calculus Textbooks