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Thomas' Calculus 13th

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Entries: 180
George B.Thomas
calculus
pearson
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Thomas' Calculus 13th
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Entries
180
1. Functions
Theory
Page 15
1.1 Functions and Their Graphs
Theory
Page 15
1.2 Combining Functions, Shifting and Scaling Graphs
Theory
Page 28
1.3 Trigonometric Functions
Theory
Page 35
1.4 Graphing with Software
Theory
Page 43
1.5 Exponential Functions
Theory
Page 50
1.6 Inverse Functions and Logarithms
Theory
Page 55
Questions to Guide Your Review
Problem
Page 68
Practice Exercises
Problem
Page 68
Additional and Advanced Exercises
Problem
Page 71
2. Limits and Continuity
Theory
Page 73
2.1 Rates of Change and Tangents to Curves
Theory
Page 73
2.2 Limit of a Function and Limit Laws
Theory
Page 80
2.3 The Precise Definition of a Limit
Theory
Page 91
2.4 One-Sided Limits
Theory
Page 100
2.5 Continuity
Theory
Page 107
2.6 Limits Involving Infinity and Asymptotes of Graphs
Theory
Page 118
Questions to Guide Your Review
Problem
Page 132
Practice Exercises
Problem
Page 132
Additional and Advanced Exercises
Problem
Page 134
3. Derivatives
Theory
Page 137
3.1 Tangents and the Derivative at a Point
Theory
Page 137
3.2 The Derivative as a Function
Theory
Page 142
3.3 Differentiation Rules
Theory
Page 150
3.4 The Derivative as a Rate of Change
Theory
Page 160
3.5 Derivatives of Trigonometric Functions
Theory
Page 170
3.6 The Chain Rule
Theory
Page 177
3.7 Implicit Differentiation
Theory
Page 185
3.8 Derivatives of Inverse Functions and Logarithms
Theory
Page 191
3.9 Inverse Trigonometric Functions
Theory
Page 201
3.10 Related Rates
Theory
Page 211
3.11 Linearization and Differentials
Theory
Page 216
Questions to Guide Your Review
Problem
Page 228
Practice Exercises
Problem
Page 229
Additional and Advanced Exercises
Problem
Page 233
4. Applications of Derivatives
Theory
Page 237
4.1 Extreme Values of Functions
Theory
Page 237
4.2 The Mean Value Theorem
Theory
Page 245
4.3 Monotonic Functions and the First Derivative Test
Theory
Page 253
4.4 Concavity and Curve Sketching
Theory
Page 258
4.5 Indeterminate Forms and L'Hôpital's Rule
Theory
Page 269
4.6 Applied Optimization
Theory
Page 278
4.7 Newton's Method
Theory
Page 290
4.8 Antiderivatives
Theory
Page 295
Questions to Guide Your Review
Problem
Page 305
Practice Exercises
Problem
Page 305
Additional and Advanced Exercises
Problem
Page 309
5. Integrals
Theory
Page 313
5.1 Area and Estimating with Finite Sums
Theory
Page 313
5.2 Sigma Notation and Limits of Finite Sums
Theory
Page 323
5.3 The Definite Integral
Theory
Page 330
5.4 The Fundamental Theorem of Calculus
Theory
Page 342
5.5 Indefinite Integrals and the Substitution Method
Theory
Page 353
5.6 Definite Integral Substitutions and the Area Between Curves
Theory
Page 361
Questions to Guide Your Review
Problem
Page 371
Practice Exercises
Problem
Page 371
Additional and Advanced Exercises
Problem
Page 375
6. Applications of Definite Integrals
Theory
Page 379
6.1 Volumes Using Cross-Sections
Theory
Page 379
6.2 Volumes Using Cylindrical Shells
Theory
Page 390
6.3 Arc Length
Theory
Page 398
6.4 Areas of Surfaces of Revolution
Theory
Page 404
6.5 Work and Fluid Forces
Theory
Page 409
6.6 Moments and Centers of Mass
Theory
Page 418
Questions to Guide Your Review
Problem
Page 429
Practice Exercises
Problem
Page 430
Additional and Advanced Exercises
Problem
Page 431
7. Integrals and Transcendental Functions
Theory
Page 434
7.1 The Logarithm Defined as an Integral
Theory
Page 434
7.2 Exponential Change and Separable Differential Equations
Theory
Page 444
7.3 Hyperbolic Functions
Theory
Page 453
7.4 Relative Rates of Growth
Theory
Page 462
Questions to Guide Your Review
Problem
Page 467
Practice Exercises
Problem
Page 467
Additional and Advanced Exercises
Problem
Page 469
8. Techniques of Integration
Theory
Page 470
8.1 Using Basic Integration Formulas
Theory
Page 470
8.2 Integration by Parts
Theory
Page 475
8.3 Trigonometric Integrals
Theory
Page 483
8.4 Trigonometric Substitutions
Theory
Page 489
8.5 Integration of Rational Functions by Partial Fractions
Theory
Page 494
8.6 Integral Tables and Computer Algebra Systems
Theory
Page 503
8.7 Numerical Integration
Theory
Page 508
8.8 Improper Integrals
Theory
Page 518
8.9 Probability
Theory
Page 529
Questions to Guide Your Review
Problem
Page 542
Practice Exercises
Problem
Page 543
Additional and Advanced Exercises
Problem
Page 545
9. First-Order Differential Equations
Theory
Page 550
9.1 Solutions, Slope Fields, and Euler's Method
Theory
Page 550
9.2 First-Order Linear Equations
Theory
Page 558
9.3 Applications
Theory
Page 564
9.4 Graphical Solutions of Autonomous Equations
Theory
Page 570
9.5 Systems of Equations and Phase Planes
Theory
Page 577
Questions to Guide Your Review
Problem
Page 583
Practice Exercises
Problem
Page 583
Additional and Advanced Exercises
Problem
Page 584
10. Infinite Sequences and Series
Theory
Page 586
10.1 Sequences
Theory
Page 586
10.2 Infinite Series
Theory
Page 598
10.3 The Integral Test
Theory
Page 607
10.4 Comparison Tests
Theory
Page 614
10.5 Absolute Convergence, the Ratio and Root Tests
Theory
Page 618
10.6 Alternating Series and Conditional Convergence
Theory
Page 624
10.7 Power Series
Theory
Page 630
10.8 Taylor and Maclaurin Series
Theory
Page 640
10.9 Convergence of Taylor Series
Theory
Page 645
10.10 The Binomial Series and Applications of Taylor Series
Theory
Page 652
Questions to Guide Your Review
Problem
Page 661
Practice Exercises
Problem
Page 662
Additional and Advanced Exercises
Problem
Page 664
11. Parametric Equations and Polar Coordinates
Theory
Page 667
11.1 Parametrizations of Plane Curves
Theory
Page 667
11.2 Calculus with Parametric Curves
Theory
Page 675
11.3 Polar Coordinates
Theory
Page 685
11.4 Graphing Polar Coordinate Equations
Theory
Page 689
11.5 Areas and Lengths in Polar Coordinates
Theory
Page 693
11.6 Conic Sections
Theory
Page 697
11.7 Conics in Polar Coordinates
Theory
Page 706
Questions to Guide Your Review
Problem
Page 713
Practice Exercises
Problem
Page 713
Additional and Advanced Exercises
Problem
Page 715
12. Vectors and the Geometry of Space
Theory
Page 718
12.1 Three-Dimensional Coordinate Systems
Theory
Page 718
12.2 Vectors
Theory
Page 723
12.3 The Dot Product
Theory
Page 732
12.4 The Cross Product
Theory
Page 740
12.5 Lines and Planes in Space
Theory
Page 746
12.6 Cylinders and Quadric Surfaces
Theory
Page 754
Questions to Guide Your Review
Problem
Page 759
Practice Exercises
Problem
Page 760
Additional and Advanced Exercises
Problem
Page 762
13. Vector-Valued Functions and Motion in Space
Theory
Page 765
13.1 Curves in Space and Their Tangents
Theory
Page 765
13.2 Integrals of Vector Functions and Projectile Motion
Theory
Page 773
13.3 Arc Length in Space
Theory
Page 782
13.4 Curvature and Normal Vectors of a Curve
Theory
Page 786
13.5 Tangential and Normal Components of Acceleration
Theory
Page 792
13.6 Velocity and Acceleration in Polar Coordinates
Theory
Page 798
Questions to Guide Your Review
Problem
Page 802
Practice Exercises
Problem
Page 802
Additional and Advanced Exercises
Problem
Page 804
14. Partial Derivatives
Theory
Page 807
14.1 Functions of Several Variables
Theory
Page 807
14.2 Limits and Continuity in Higher Dimensions
Theory
Page 815
14.3 Partial Derivatives
Theory
Page 824
14.4 The Chain Rule
Theory
Page 835
14.5 Directional Derivatives and Gradient Vectors
Theory
Page 844
14.6 Tangent Planes and Differentials
Theory
Page 853
14.7 Extreme Values and Saddle Points
Theory
Page 862
14.8 Lagrange Multipliers
Theory
Page 871
14.9 Taylor's Formula for Two Variables
Theory
Page 880
14.10 Partial Derivatives with Constrained Variables
Theory
Page 884
Questions to Guide Your Review
Problem
Page 889
Practice Exercises
Problem
Page 890
Additional and Advanced Exercises
Problem
Page 893
15. Multiple Integrals
Theory
Page 896
15.1 Double and Iterated Integrals over Rectangles
Theory
Page 896
15.2 Double Integrals over General Regions
Theory
Page 901
15.3 Area by Double Integration
Theory
Page 910
15.4 Double Integrals in Polar Form
Theory
Page 914
15.5 Triple Integrals in Rectangular Coordinates
Theory
Page 920
15.6 Moments and Centers of Mass
Theory
Page 929
15.7 Triple Integrals in Cylindrical and Spherical Coordinates
Theory
Page 936
15.8 Substitutions in Multiple Integrals
Theory
Page 948
Questions to Guide Your Review
Problem
Page 958
Practice Exercises
Problem
Page 958
Additional and Advanced Exercises
Problem
Page 961
16. Integrals and Vector Fields
Theory
Page 964
16.1 Line Integrals
Theory
Page 964
16.2 Vector Fields and Line Integrals, Work, Circulation, and Flux
Theory
Page 971
16.3 Path Independence, Conservative Fields, and Potential Functions
Theory
Page 983
16.4 Green's Theorem in the Plane
Theory
Page 994
16.5 Surfaces and Area
Theory
Page 1006
16.6 Surface Integrals
Theory
Page 1017
16.7 Stokes' Theorem
Theory
Page 1028
16.8 The Divergence Theorem and a Unified Theory
Theory
Page 1041
Questions to Guide Your Review
Problem
Page 1053
Practice Exercises
Problem
Page 1054
Additional and Advanced Exercises
Problem
Page 1056
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