Thomas Calculus 13th [Solutions]
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Entries: 111
George B.Thomas
calculus
pearson
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Thomas Calculus 13th [Solutions]
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111
1. Functions
Theory
Page 9
1.1 Functions and Their Graphs
Theory
Page 9
1.2 Combining Functions, Shifting and Scaling Graphs
Theory
Page 16
1.3 Trigonometric Functions
Theory
Page 26
1.4 Graphing with Software
Theory
Page 34
1.5 Exponential Functions
Theory
Page 39
1.6 Inverse Functions and Logarithms
Theory
Page 42
Practice Exercises
Problem
Page 51
Additional and Advanced Exercises
Problem
Page 60
2. Limits and Continuity
Theory
Page 67
2.1 Rates of Change and Tangents to Curves
Theory
Page 67
2.2 Limit of a Function and Limit Laws
Theory
Page 70
2.3 The Precise Definition of a Limit
Theory
Page 81
2.4 One-Sided Limits
Theory
Page 89
2.5 Continuity
Theory
Page 94
2.6 Limits Involving Infinity and Asymptotes of Graphs
Theory
Page 100
Practice Exercises
Problem
Page 110
Additional and Advanced Exercises
Problem
Page 116
3. Differentiation
Theory
Page 123
3.1 Tangents and the Derivative at a Point
Theory
Page 123
3.2 The Derivative as a Function
Theory
Page 129
3.3 Differentiation Rules
Theory
Page 139
3.4 The Derivative as a Rate of Change
Theory
Page 146
3.5 Derivatives of Trigonometric Functions
Theory
Page 152
3.6 The Chain Rule
Theory
Page 160
3.7 Implicit Differentiation
Theory
Page 170
3.8 Derivatives of Inverse Functions and Logarithms
Theory
Page 178
3.9 Inverse Trigonometric Functions
Theory
Page 188
3.10 Related Rates
Theory
Page 194
3.11 Linearization and Differentials
Theory
Page 200
Practice Exercises
Problem
Page 207
Additional and Advanced Exercises
Problem
Page 222
4. Applications of Derivatives
Theory
Page 227
4.1 Extreme Values of Functions
Theory
Page 227
4.2 The Mean Value Theorem
Theory
Page 241
4.3 Monotonic Functions and the First Derivative Test
Theory
Page 247
4.4 Concavity and Curve Sketching
Theory
Page 261
4.5 Indeterminate Forms and L'Hôpital's Rule
Theory
Page 288
4.6 Applied Optimization
Theory
Page 298
4.7 Newton's Method
Theory
Page 312
4.8 Antiderivatives
Theory
Page 317
Practice Exercises
Problem
Page 326
Additional and Advanced Exercises
Problem
Page 344
5. Integration
Theory
Page 351
5.1 Area and Estimating with Finite Sums
Theory
Page 351
5.2 Sigma Notation and Limits of Finite Sums
Theory
Page 356
5.3 The Definite Integral
Theory
Page 362
5.4 The Fundamental Theorem of Calculus
Theory
Page 377
5.5 Indefinite Integrals and the Substitution Method
Theory
Page 387
5.6 Substitution and Area Between Curves
Theory
Page 395
Practice Exercises
Problem
Page 415
Additional and Advanced Exercises
Problem
Page 430
6. Applications of Definite Integrals
Theory
Page 439
6.1 Volumes Using Cross-Sections
Theory
Page 439
6.2 Volumes Using Cylindrical Shells
Theory
Page 451
6.3 Arc Length
Theory
Page 462
6.4 Areas of Surfaces of Revolution
Theory
Page 470
6.5 Work and Fluid Forces
Theory
Page 476
6.6 Moments and Centers of Mass
Theory
Page 487
Practice Exercises
Problem
Page 500
Additional and Advanced Exercises
Problem
Page 509
7. Integrals and Transcendental Functions
Theory
Page 515
7.1 The Logarithm Defined as an Integral
Theory
Page 515
7.2 Exponential Change and Separable Differential Equations
Theory
Page 523
7.3 Hyperbolic Functions
Theory
Page 529
7.4 Relative Rates of Growth
Theory
Page 537
Practice Exercises
Problem
Page 543
Additional and Advanced Exercises
Problem
Page 548
8. Techniques of Integration
Theory
Page 551
8.1 Using Basic Integration Formulas
Theory
Page 551
8.2 Integration by Parts
Theory
Page 563
8.3 Trigonometric Integrals
Theory
Page 577
8.4 Trigonometric Substitutions
Theory
Page 585
8.5 Integration of Rational Functions by Partial Fractions
Theory
Page 593
8.6 Integral Tables and Computer Algebra Systems
Theory
Page 602
8.7 Numerical Integration
Theory
Page 615
8.8 Improper Integrals
Theory
Page 625
8.9 Probability
Theory
Page 637
Practice Exercises
Problem
Page 645
Additional and Advanced Exercises
Problem
Page 658
9. First-Order Differential Equations
Theory
Page 669
9.1 Solutions, Slope Fields, and Euler's Method
Theory
Page 669
9.2 First-Order Linear Equations
Theory
Page 678
9.3 Applications
Theory
Page 682
9.4 Graphical Solutions of Autonomous Equations
Theory
Page 686
9.5 Systems of Equations and Phase Planes
Theory
Page 694
Practice Exercises
Problem
Page 700
Additional and Advanced Exercises
Problem
Page 706
10. Infinite Sequences and Series
Theory
Page 709
10.1 Sequences
Theory
Page 709
10.2 Infinite Series
Theory
Page 720
10.3 The Integral Test
Theory
Page 728
10.4 Comparison Tests
Theory
Page 736
10.5 Absolute Convergence, the Ratio and Root Tests
Theory
Page 746
10.6 Alternating Series and Conditional Convergence
Theory
Page 752
10.7 Power Series
Theory
Page 760
10.8 Taylor and Maclaurin Series
Theory
Page 772
10.9 Convergence of Taylor Series
Theory
Page 777
10.10 The Binomial Series and Applications of Taylor Series
Theory
Page 785
Practice Exercises
Problem
Page 794
Additional and Advanced Exercises
Problem
Page 803
11. Parametric Equations and Polar Coordinates
Theory
Page 809
11.1 Parametrizations of Plane Curves
Theory
Page 809
11.2 Calculus with Parametric Curves
Theory
Page 817
11.3 Polar Coordinates
Theory
Page 827
11.4 Graphing Polar Coordinate Equations
Theory
Page 833
11.5 Areas and Lengths in Polar Coordinates
Theory
Page 840
11.6 Conic Sections
Theory
Page 846
11.7 Conics in Polar Coordinates
Theory
Page 857
Practice Exercises
Problem
Page 868
Additional and Advanced Exercises
Problem
Page 879
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