Calculus

Calculus: Late Transcendentals, 11th EMEA Edition strives to increase student comprehension and conceptual understanding through a balance between rigor and clarity of explanations; sound mathematics; and excellent exercises, applications, and examples. Anton pedagogically approaches Calculus through the Rule of Four, presenting concepts from the verbal, algebraic, visual, and numerical points of view.

1 Limits and Continuity 1
1. 1 Limits (An Intuitive Approach) 1
1. 2 Computing Limits 13
1. 3 Limits at Infinity; End Behavior of a Function 22
1. 4 Limits (Discussed More Rigorously) 31
1. 5 Continuity 40
1. 6 Continuity of Trigonometric Functions 51
2 The Derivative 59
2. 1 Tangent Lines and Rates of Change 59
2. 2 The Derivative Function 69
2. 3 Introduction to Techniques of Differentiation 80
2. 4 The Product and Quotient Rules 88
2. 5 Derivatives of Trigonometric Functions 93
2. 6 The Chain Rule 98
2. 7 Implicit Differentiation 105
2. 8 Related Rates 112
2. 9 Local Linear Approximation; Differentials 119
3 The Derivative in Graphing and Applications 130
3. 1 Analysis of Functions I: Increase, Decrease, and Concavity 130
3. 2 Analysis of Functions II: Relative Extrema; Graphing Polynomials 139
3. 3 Analysis of Functions III: Rational Functions, Cusps, and Vertical Tangents 148
3. 4 Absolute Maxima and Minima 157
3. 5 Applied Maximum and Minimum Problems 164
3. 6 Rectilinear Motion 177
3. 7 Newton's Method 185
3. 8 Rolle's Theorem; Mean-Value Theorem 191
4 Integration 203
4. 1 An Overview of the Area Problem 203
4. 2 The Indefinite Integral 208
4. 3 Integration by Substitution 217
4. 4 The Definition of Area as a Limit; Sigma Notation 223
4. 5 The Definite Integral 233
4. 6 The Fundamental Theorem of Calculus 242
4. 7 Rectilinear Motion Revisited Using Integration 253
4. 8 Average Value of a Function and its Applications 262
4. 9 Evaluating Definite Integrals by Substitution 266
5 Applications of the Definite Integral in Geometry, Science, and Engineering 277
5. 1 Area Between Two Curves 277
5. 2 Volumes by Slicing; Disks and Washers 284
5. 3 Volumes by Cylindrical Shells 294
5. 4 Length of a Plane Curve 300
5. 5 Area of a Surface of Revolution 306
5. 6 Work 311
5. 7 Moments, Centers of Gravity, and Centroids 319
5. 8 Fluid Pressure and Force 328
6 Exponential, Logarithmic, and Inverse Trigonometric Functions 336
6. 1 Exponential and Logarithmic Functions 336
6. 2 Derivatives and Integrals Involving Logarithmic Functions 347
6. 3 Derivatives of Inverse Functions; Derivatives and Integrals Involving Exponential Functions 353
6. 4 Graphs and Applications Involving Logarithmic and Exponential Functions 360
6. 5 L'Hô pital's Rule; Indeterminate Forms 367
6. 6 Logarithmic and Other Functions Defined by Integrals 376
6. 7 Derivatives and Integrals Involving Inverse Trigonometric Functions 387
6. 8 Hyperbolic Functions and Hanging Cables 398
7 Principles of Integral Evaluation 412
7. 1 An Overview of Integration Methods 412
7. 2 Integration by Parts 415
7. 3 Integrating Trigonometric Functions 423
7. 4 Trigonometric Substitutions 431
7. 5 Integrating Rational Functions by Partial Fractions 437
7. 6 Using Computer Algebra Systems and Tables of Integrals 445
7. 7 Numerical Integration; Simpson's Rule 454
7. 8 Improper Integrals 467
8 Mathematical Modeling with Differential Equations 481
8. 1 Modeling with Differential Equations 481
8. 2 Separation of Variables 487
8. 3 Slope Fields; Euler's Method 498
8. 4 First-Order Differential Equations and Applications 504
9 Infinite Series 514
9. 1 Sequences 514
9. 2 Monotone Sequences 524
9. 3 Infinite Series 531
9. 4 Convergence Tests 539
9. 5 The Comparison, Ratio, and Root Tests 547
9. 6 Alternating Series; Absolute and Conditional Convergence 553
9. 7 Maclaurin and Taylor Polynomials 563
9. 8 Maclaurin and Taylor Series; Power Series 573
9. 9 Convergence of Taylor Series 582
9. 10 Differentiating and Integrating Power Series; Modeling with Taylor Series 591
10 Parametric and Polar Curves; Conic Sections 605
10. 1 Parametric Equations; Tangent Lines and Arc Length for Parametric Curves 605
10. 2 Polar Coordinates 617
10. 3 Tangent Lines, Arc Length, and Area for Polar Curves 630
10. 4 Conic Sections 639
10. 5 Rotation of Axes; Second-Degree Equations 656
10. 6 Conic Sections in Polar Coordinates 661
11 Three-Dimensional Space; Vectors 674
11. 1 Rectangular Coordinates in 3-Space; Spheres; Cylindrical Surfaces 674
11. 2 Vectors 680
11. 3 Dot Product; Projections 691
11. 4 Cross Product 700
11. 5 Parametric Equations of Lines 710
11. 6 Planes in 3-Space 717
11. 7 Quadric Surfaces 725
11. 8 Cylindrical and Spherical Coordinates 735
12 Vector-Valued Functions 744
12. 1 Introduction to Vector-Valued Functions 744
12. 2 Calculus of Vector-Valued Functions 750
12. 3 Change of Parameter; Arc Length 759
12. 4 Unit Tangent, Normal, and Binormal Vectors 768
12. 5 Curvature 773
12. 6 Motion Along a Curve 781
12. 7 Kepler's Laws of Planetary Motion 794
13 Partial Derivatives 805
13. 1 Functions of Two or More Variables 805
13. 2 Limits and Continuity 815
13. 3 Partial Derivatives 824
13. 4 Differentiability, Differentials, and Local Linearity 837
13. 5 The Chain Rule 845
13. 6 Directional Derivatives and Gradients 855
13. 7 Tangent Planes and Normal Vectors 866
13. 8 Maxima and Minima of Functions of Two Variables 872
13. 9 Lagrange Multipliers 883
14 Multiple Integrals 894
14. 1 Double Integrals 894
14. 2 Double Integrals over Nonrectangular Regions 902
14. 3 Double Integrals in Polar Coordinates 910
14. 4 Surface Area; Parametric Surfaces 918
14. 5 Triple Integrals 930
14. 6 Triple Integrals in Cylindrical and Spherical Coordinates 938
14. 7 Change of Variables in Multiple Integrals; Jacobians 947
14. 8 Centers of Gravity Using Multiple Integrals 959
15 Topics in Vector Calculus 971
15. 1 Vector Fields 971
15. 2 Line Integrals 980
15. 3 Independence of Path; Conservative Vector Fields 995
15. 4 Green's Theorem 1005
15. 5 Surface Integrals 1013
15. 6 Applications of Surface Integrals; Flux 1021
15. 7 The Divergence Theorem 1030
15. 8 Stokes' Theorem 1039
A Appendices
A Trigonometry Review (Summary) A1
B Functions (Summary) A8
C New Functions from Old (Summary) A11
D Families of Functions (Summary) A16
E Inverse Functions (Summary) A23
Answers to Odd-Numbered Exercises A28
Index I-1
Web Appendices (online only)
Available for download at www. wiley. com/college/anton or at www. howardanton. com and in WileyPLUS.
A Trigonometry Review
B Functions
C New Functions from Old
D Families of Functions
E Inverse Functions
F Real Numbers, Intervals, and Inequalities
G Absolute Value
H Coordinate Planes, Lines, And Linear Functions
I Distance, Circles, And Quadratic Equations
J Solving Polynomial Equations
K Graphing Functions Using Calculators and Computer Algebra Systems
L Selected Proofs
M Early Parametric Equations Option
N Mathematical Models
O The Discriminant
P Second-Order Linear Homogeneous Differential Equations
Chapter Web Projects: Expanding the Calculus Horizon (online only)
Available for download at www. wiley. com/college/anton or at www. howardanton. com and in WileyPLUS.
Robotics - Chapter 2
Railroad Design - Chapter 7
Iteration and Dynamical Systems - Chapter 9
Comet Collision - Chapter 10
Blammo the Human Cannonball - Chapter 12
Hurricane Modeling - Chapter 15