Ap Precalculus Textbook Pdf

The AP Calculus Problem Book Publication history: First edition, 2002 Second edition, 2003 Third edition, 2004 Third edition Revised and Corrected, 2005 Fourth edition, 2006, Edited by Amy Lanchester Fourth edition Revised and Corrected, 2007 Fourth edition, Corrected, 2008 This book was produced directly from the author’s LATEX files. The AP Calculus Problem Book Publication history: First edition, 2002 Second edition, 2003 Third edition, 2004 Third edition Revised and Corrected, 2005 Fourth edition, 2006, Edited by Amy Lanchester Fourth edition Revised and Corrected, 2007 Fourth edition, Corrected, 2008 This book was produced directly from the author’s LATEX files. This is the free digital calculus text by David R. Guichard and others. It was submitted to the Free Digital Textbook Initiative in California and will remain unchanged for at least two years. The book is in use at Whitman College and is occasionally updated to correct errors and add new material. The latest versions may be found.

Published in 1991 by Wellesley-Cambridge Press, the book is a useful resource for educators and self-learners alike. It is well organized, covers single variable and multivariable calculus in depth, and is rich with applications. There is also an online Instructor's Manual and a student Study Guide.

Ap Precalculus Textbook Pdf

The complete textbook is also available as a single file. (PDF - 38.5MB)

Precalculus Textbook Pdf

Highlights of Calculus

MIT Professor Gilbert Strang has created a series of videos to show ways in which calculus is important in our lives. The videos, which include real-life examples to illustrate the concepts, are ideal for high school students, college students, and anyone interested in learning the basics of calculus.

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Textbook Components

  • Table of Contents (PDF)
  • Answers to Odd-Numbered Problems (PDF - 2.4MB)
  • Equations (PDF)
ChapterSFILES
1: Introduction to Calculus, pp. 1-43
1.1 Velocity and Distance, pp. 1-7
1.2 Calculus Without Limits, pp. 8-15
1.3 The Velocity at an Instant, pp. 16-21
1.4 Circular Motion, pp. 22-28
1.5 A Review of Trigonometry, pp. 29-33
1.6 A Thousand Points of Light, pp. 34-35
1.7 Computing in Calculus, pp. 36-43

Chapter 1 - complete (PDF - 2.2MB)

Chapter 1 - sections:

1.1 - 1.4 (PDF - 1.6MB)
1.5 - 1.7 (PDF - 1.4MB)

2: Derivatives, pp. 44-90
2.1 The Derivative of a Function, pp. 44-49
2.2 Powers and Polynomials, pp. 50-57
2.3 The Slope and the Tangent Line, pp. 58-63
2.4 Derivative of the Sine and Cosine, pp. 64-70
2.5 The Product and Quotient and Power Rules, pp. 71-77
2.6 Limits, pp. 78-84
2.7 Continuous Functions, pp. 85-90

Chapter 2 - complete (PDF - 3.8MB)

Chapter 2 - sections:

2.1 - 2.4 (PDF - 2.3MB)
2.5 - 2.7 (PDF - 1.7MB)

3: Applications of the Derivative, pp. 91-153
3.1 Linear Approximation, pp. 91-95
3.2 Maximum and Minimum Problems, pp. 96-104
3.3 Second Derivatives: Minimum vs. Maximum, pp. 105-111
3.4 Graphs, pp. 112-120
3.5 Ellipses, Parabolas, and Hyperbolas, pp. 121-129
3.6 Iterations x[n+1] = F(x[n]), pp. 130-136
3.7 Newton's Method and Chaos, pp. 137-145
3.8 The Mean Value Theorem and l'Hôpital's Rule, pp. 146-153

Chapter 3 - complete (PDF - 3.3MB)

Chapter 3 - sections:

3.1 - 3.4 (PDF - 1.5MB)
3.5 - 3.8 (PDF - 2.0MB)

4: The Chain Rule, pp. 154-176
4.1 Derivatives by the Charin Rule, pp. 154-159
4.2 Implicit Differentiation and Related Rates, pp. 160-163
4.3 Inverse Functions and Their Derivatives, pp. 164-170
4.4 Inverses of Trigonometric Functions, pp. 171-176

Chapter 4 - complete (PDF - 1.1MB)

Chapter 4 - sections:

4.1 - 4.2 (PDF)
4.3 - 4.4 (PDF)

5: Integrals, pp. 177-227
5.1 The Idea of an Integral, pp. 177-181
5.2 Antiderivatives, pp. 182-186
5.3 Summation vs. Integration, pp. 187-194
5.4 Indefinite Integrals and Substitutions, pp. 195-200
5.5 The Definite Integral, pp. 201-205
5.6 Properties of the Integral and the Average Value, pp. 206-212
5.7 The Fundamental Theorem and Its Consequences, pp. 213-219
5.8 Numerical Integration, pp. 220-227

Chapter 5 - complete (PDF - 3.3MB)

Chapter 5 - sections:

5.1 - 5.4 (PDF - 1.1MB)
5.5 - 5.8 (PDF - 2.3MB)

6: Exponentials and Logarithms, pp. 228-282
6.1 An Overview, pp. 228-235
6.2 The Exponential e^x, pp. 236-241
6.3 Growth and Decay in Science and Economics, pp. 242-251
6.4 Logarithms, pp. 252-258
6.5 Separable Equations Including the Logistic Equation, pp. 259-266
6.6 Powers Instead of Exponentials, pp. 267-276
6.7 Hyperbolic Functions, pp. 277-282

Chapter 6 - complete (PDF - 3.1MB)

Chapter 6 - sections:

6.1 - 6.4 (PDF - 2.1MB)
6.5 - 6.7 (PDF - 1.2MB)

7: Techniques of Integration, pp. 283-310
7.1 Integration by Parts, pp. 283-287
7.2 Trigonometric Integrals, pp. 288-293
7.3 Trigonometric Substitutions, pp. 294-299
7.4 Partial Fractions, pp. 300-304
7.5 Improper Integrals, pp. 305-310

Chapter 7 - complete (PDF - 1.7MB)

Chapter 7 - sections:

7.1 - 7.3 (PDF - 1.2MB)
7.4 - 7.5 (PDF)

8: Applications of the Integral, pp. 311-347
8.1 Areas and Volumes by Slices, pp. 311-319
8.2 Length of a Plane Curve, pp. 320-324
8.3 Area of a Surface of Revolution, pp. 325-327
8.4 Probability and Calculus, pp. 328-335
8.5 Masses and Moments, pp. 336-341
8.6 Force, Work, and Energy, pp. 342-347

Chapter 8 - complete (PDF - 2.1MB)

Chapter 8 - sections:

8.1 - 8.3 (PDF - 1.1MB)
8.4 - 8.6 (PDF - 1.1MB)

9: Polar Coordinates and Complex Numbers, pp. 348-367
9.1 Polar Coordinates, pp. 348-350
9.2 Polar Equations and Graphs, pp. 351-355
9.3 Slope, Length, and Area for Polar Curves, pp. 356-359
9.4 Complex Numbers, pp. 360-367

Chapter 9 - complete (PDF)

Chapter 9 - sections:

9.1 - 9.2 (PDF)
9.3 - 9.4 (PDF)

10: Infinite Series, pp. 368-391
10.1 The Geometric Series, pp. 368-373
10.2 Convergence Tests: Positive Series, pp. 374-380
10.3 Convergence Tests: All Series, pp. 325-327
10.4 The Taylor Series for e^x, sin x, and cos x, pp. 385-390
10.5 Power Series, pp. 391-397

Chapter 10 - complete (PDF - 2.0MB)

Chapter 10 - sections:

10.1 - 10.3 (PDF - 1.3MB)
10.4 - 10.5 (PDF)

11: Vectors and Matrices, pp. 398-445
11.1 Vectors and Dot Products, pp. 398-406
11.2 Planes and Projections, pp. 407-415
11.3 Cross Products and Determinants, pp. 416-424
11.4 Matrices and Linear Equations, pp. 425-434
11.5 Linear Algebra in Three Dimensions, pp. 435-445

Chapter 11 - complete (PDF - 3.3MB)

Chapter 11 - sections:

11.1 - 11.3 (PDF - 2.2MB)
11.4 - 11.5 (PDF - 1.2MB)

12: Motion along a Curve, pp. 446-471
12.1 The Position Vector, pp. 446-452
12.2 Plane Motion: Projectiles and Cycloids, pp. 453-458
12.3 Tangent Vector and Normal Vector, pp. 459-463
12.4 Polar Coordinates and Planetary Motion, pp. 464-471

Chapter 12 - complete (PDF - 1.2MB)

Chapter 12 - sections:

12.1 - 12.2 (PDF)
12.3 - 12.4 (PDF)

13: Partial Derivatives, pp. 472-520
13.1 Surface and Level Curves, pp. 472-474
13.2 Partial Derivatives, pp. 475-479
13.3 Tangent Planes and Linear Approximations, pp. 480-489
13.4 Directional Derivatives and Gradients, pp. 490-496
13.5 The Chain Rule, pp. 497-503
13.6 Maxima, Minima, and Saddle Points, pp. 504-513
13.7 Constraints and Lagrange Multipliers, pp. 514-520

Chapter 13 - complete (PDF - 3.9MB)

Chapter 13 - sections:

13.1 - 13.4 (PDF - 2.3MB)
13.5 - 13.7 (PDF - 1.5MB)

14: Multiple Integrals, pp. 521-548
14.1 Double Integrals, pp. 521-526
14.2 Changing to Better Coordinates, pp. 527-535
14.3 Triple Integrals, pp. 536-540
14.4 Cylindrical and Spherical Coordinates, pp. 541-548

Chapter 14 - complete (PDF - 1.9MB)

Chapter 14 - sections:

14.1 - 14.2 (PDF - 1.0MB)
14.3 - 14.4 (PDF)

15: Vector Calculus, pp. 549-598
15.1 Vector Fields, pp. 549-554
15.2 Line Integrals, pp. 555-562
15.3 Green's Theorem, pp. 563-572
15.4 Surface Integrals, pp. 573-581
15.5 The Divergence Theorem, pp. 582-588
15.6 Stokes' Theorem and the Curl of F, pp. 589-598

Chapter 15 - complete (PDF - 3.1MB)

Chapter 15 - sections:

15.1 - 15.3 (PDF - 1.5MB)
15.4 - 15.6 (PDF - 1.6MB)

16: Mathematics after Calculus, pp. 599-615
16.1 Linear Algebra, pp. 599-602
16.2 Differential Equations, pp. 603-610
16.3 Discrete Mathematics, pp. 611-615

Chapter 16 - complete (PDF)

Chapter 16 - sections:

16.1 - 16.2 (PDF)
16.3 (PDF)

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