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 - 4.1 MB)
Chapter 1 - sections:
1.1 - 1.4 (PDF - 2.8 MB)
1.5 - 1.7 (PDF - 1.6 MB) |
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 - 4.3 MB)
Chapter 2 - sections:
2.1 - 2.4 (PDF - 2.6 MB)
2.5 - 2.7 (PDF - 2.0 MB) |
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'Hopital's Rule, pp. 146-153
| Chapter 3 - complete (PDF - 5.9 MB)
Chapter 3 - sections:
3.1 - 3.4 (PDF - 3.2 MB)
3.5 - 3.8 (PDF - 3.3 MB) |
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 - 2.0 MB)
Chapter 4 - sections:
4.1 - 4.2 (PDF - 1.0 MB)
4.3 - 4.4 (PDF - 1.2 MB) |
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 - 4.8 MB)
Chapter 5 - sections:
5.1 - 5.4 (PDF - 2.2 MB)
5.5 - 5.8 (PDF - 2.8 MB) |
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 - 4.9 MB)
Chapter 6 - sections:
6.1 - 6.4 (PDF - 3.0 MB)
6.5 - 6.7 (PDF - 2.2 MB) |
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 - 2.6 MB)
Chapter 7 - sections:
7.1 - 7.3 (PDF - 1.7 MB)
7.4 - 7.5 (PDF - 1.0 MB) |
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 - 3.4 MB)
Chapter 8 - sections:
8.1 - 8.3 (PDF - 1.7 MB)
8.4 - 8.6 (PDF - 2.0 MB) |
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 - 1.7 MB)
Chapter 9 - sections:
9.1 - 9.2 (PDF)
9.3 - 9.4 (PDF - 1.0 MB) |
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 - 2.9 MB)
Chapter 10 - sections:
10.1 - 10.3 (PDF - 1.9 MB)
10.4 - 10.5 (PDF - 1.2 MB) |
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 - 4.0 MB)
Chapter 11 - sections:
11.1 - 11.3 (PDF - 2.5 MB)
11.4 - 11.5 (PDF - 1.7 MB) |
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 - 2.2 MB)
Chapter 12 - sections:
12.1 - 12.2 (PDF - 1.2 MB)
12.3 - 12.4 (PDF - 1.1 MB) |
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 - 4.9 MB)
Chapter 13 - sections:
13.1 - 13.4 (PDF - 2.7 MB)
13.5 - 13.7 (PDF - 2.5 MB) |
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 - 2.5 MB)
Chapter 14 - sections:
14.1 - 14.2 (PDF - 1.4 MB)
14.3 - 14.4 (PDF - 1.3 MB) |
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 - 4.3 MB)
Chapter 15 - sections:
15.1 - 15.3 (PDF - 2.1 MB)
15.4 - 15.6 (PDF - 2.3 MB) |
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 - 1.8 MB)
Chapter 16 - sections:
16.1 - 16.2 (PDF - 1.5 MB)
16.3 (PDF) |
