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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) |
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) |
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'HÃ´pital's Rule, pp. 146-153 | Chapter 3 - complete (PDF - 3.3MB) Chapter 3 - sections: 3.1 - 3.4 (PDF - 1.5MB) |
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: |
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) |
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) |
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) |
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) |
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: |
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) |
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) |
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: |
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) |
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) |
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) |
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: |