| A Word from the Authors |
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| Integrated Learning System for Calculus |
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| Features |
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xviii | |
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1 | (40) |
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2 | (8) |
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Linear Models and Rates of Change |
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10 | (9) |
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Functions and Their Graphs |
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19 | (12) |
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31 | (6) |
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37 | (2) |
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39 | (2) |
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Limits and Their Properties |
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41 | (54) |
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42 | (6) |
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Finding Limits Graphically and Numerically |
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48 | (11) |
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Evaluating Limits Analytically |
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59 | (11) |
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Continuity and One-Sided Limits |
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70 | (13) |
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83 | (7) |
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Section Project: Graphs and Limits of Trigonometric Functions |
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90 | (5) |
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91 | (2) |
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93 | (2) |
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95 | (68) |
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The Derivative and the Tangent Line Problem |
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96 | (11) |
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Basic Differentiation Rules and Rates of Change |
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107 | (12) |
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Product and Quotient Rules and Higher-Order Derivatives |
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119 | (11) |
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130 | (11) |
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141 | (7) |
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Section Project: Optical Illusions |
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148 | (15) |
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149 | (9) |
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158 | (3) |
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161 | (2) |
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Applications of Differentiation |
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163 | (84) |
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164 | (8) |
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Rolle's Theorem and the Mean Value Theorem |
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172 | (7) |
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Increasing and Decreasing Functions and the First Derivative Test |
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179 | (10) |
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Section Project: Rainbows |
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189 | (39) |
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Concavity and the Second Derivative Test |
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190 | (8) |
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198 | (11) |
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A Summary of Curve Sketching |
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209 | (9) |
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218 | (10) |
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Section Project: Connecticut River |
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228 | (19) |
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229 | (6) |
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235 | (7) |
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242 | (3) |
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245 | (2) |
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247 | (74) |
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Antiderivatives and Indefinite Integration |
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248 | (11) |
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259 | (12) |
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Riemann Sums and Definite Integrals |
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271 | (11) |
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The Fundamental Theorem of Calculus |
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282 | (12) |
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Section Project: Demonstrating the Fundamental Theorem |
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294 | (27) |
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Integration by Substitution |
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295 | (14) |
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309 | (7) |
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316 | (3) |
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319 | (2) |
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Logarithmic, Exponential, and Other Transcendental Functions |
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321 | (82) |
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The Natural Logarithmic Function: Differentiation |
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322 | (10) |
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The Natural Logarithmic Function: Integration |
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332 | (9) |
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341 | (9) |
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Exponential Functions: Differentiation and Integration |
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350 | (10) |
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Bases Other Than e and Applications |
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360 | (10) |
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Section Project: Using Graphing Utilities to Estimate Slope |
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370 | (28) |
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Inverse Trigonometric Functions: Differentiation |
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371 | (9) |
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Inverse Trigonometric Functions: Integration |
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380 | (8) |
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388 | (10) |
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Section Project: St. Louis Arch |
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398 | (5) |
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399 | (2) |
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401 | (2) |
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403 | (42) |
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Slope Fields and Euler's Method |
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404 | (9) |
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Differential Equations: Growth and Decay |
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413 | (8) |
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Separation of Variables and the Logistic Equation |
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421 | (11) |
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First-Order Linear Differential Equations |
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432 | (8) |
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Section Project: Weight Loss |
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440 | (5) |
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441 | (2) |
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443 | (2) |
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Applications of Integration |
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445 | (72) |
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Area of a Region Between Two Curves |
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446 | (10) |
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456 | (11) |
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467 | (8) |
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475 | (20) |
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Arc Length and Surfaces of Revolution |
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476 | (11) |
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487 | (8) |
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Section Project: Tidal Energy |
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495 | (22) |
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Moments, Centers of Mass, and Centroids |
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496 | (11) |
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Fluid Pressure and Fluid Force |
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507 | (6) |
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513 | (2) |
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515 | (2) |
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Integration Techniques, L'Hopital's Rule, and Improper Integrals |
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517 | (76) |
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518 | (7) |
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525 | (9) |
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534 | (8) |
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Section Project: Power Lines |
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542 | (51) |
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Trigonometric Substitution |
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543 | (9) |
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552 | (9) |
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Integration by Tables and Other Integration Techniques |
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561 | (6) |
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Indeterminate Forms and L'Hopital's Rule |
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567 | (11) |
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578 | (11) |
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589 | (2) |
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591 | (2) |
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593 | (100) |
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594 | (12) |
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606 | (10) |
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Section Project: Cantor's Disappearing Table |
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616 | (7) |
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The Integral Test and p-Series |
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617 | (6) |
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Section Project: The Harmonic Series |
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623 | (7) |
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624 | (6) |
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Section Project: Solera Method |
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630 | (63) |
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631 | (8) |
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639 | (9) |
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Taylor Polynomials and Approximations |
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648 | (11) |
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659 | (10) |
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Representation of Functions by Power Series |
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669 | (7) |
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Taylor and Maclaurin Series |
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676 | (12) |
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688 | (3) |
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691 | (2) |
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Conics, Parametric Equations, and Polar Coordinates |
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693 | (68) |
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694 | (15) |
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Plane Curves and Parametric Equations |
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709 | (9) |
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Section Project: Cycloids |
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718 | (20) |
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Parametric Equations and Calculus |
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719 | (10) |
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Polar Coordinates and Polar Graphs |
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729 | (9) |
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Section Project: Anamorphic Art |
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738 | (23) |
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Area and Arc Length in Polar Coordinates |
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739 | (9) |
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Polar Equations of Conics and Kepler's Laws |
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748 | (8) |
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756 | (3) |
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759 | (2) |
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Vectors and the Geometry of Space |
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761 | (70) |
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762 | (11) |
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Space Coordinates and Vectors in Space |
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773 | (8) |
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The Dot Product of Two Vectors |
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781 | (9) |
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The Cross Product of Two Vectors in Space |
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790 | (8) |
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Lines and Planes in Space |
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798 | (11) |
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Section Project: Distances in Space |
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809 | (22) |
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810 | (10) |
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Cylindrical and Spherical Coordinates |
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820 | (7) |
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827 | (2) |
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829 | (2) |
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831 | (52) |
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832 | (7) |
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Section Project: Witch of Agnesi |
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839 | (44) |
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Differentiation and Integration of Vector-Valued Functions |
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840 | (8) |
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Velocity and Acceleration |
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848 | (9) |
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Tangent Vectors and Normal Vectors |
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857 | (10) |
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867 | (12) |
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879 | (2) |
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881 | (2) |
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Functions of Several Variables |
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883 | (98) |
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Introduction to Functions of Several Variables |
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884 | (12) |
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896 | (10) |
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906 | (9) |
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Section Project: Moire Fringes |
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915 | (36) |
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916 | (7) |
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Chain Rules for Functions of Several Variables |
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923 | (8) |
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Directional Derivatives and Gradients |
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931 | (12) |
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Tangent Planes and Normal Lines |
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943 | (8) |
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Section Project: Wildflowers |
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951 | (16) |
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Extrema of Functions of Two Variables |
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952 | (8) |
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Applications of Extrema of Functions of Two Variables |
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960 | (7) |
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Section Project: Building a Pipeline |
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967 | (14) |
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968 | (8) |
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976 | (3) |
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979 | (2) |
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981 | (72) |
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Iterated Integrals and Area in the Plane |
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982 | (8) |
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Double Integrals and Volume |
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990 | (11) |
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Change of Variables: Polar Coordinates |
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1001 | (8) |
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Center of Mass and Moments of Inertia |
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1009 | (7) |
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Section Project: Center of Pressure on a Sail |
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1016 | (7) |
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1017 | (6) |
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Section Project: Capillary Action |
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1023 | (18) |
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Triple Integrals and Applications |
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1024 | (11) |
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Triple Integrals in Cylindrical and Spherical Coordinates |
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1035 | (6) |
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Section Project: Wrinkled and Bumpy Spheres |
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1041 | (12) |
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Change of Variables: Jacobians |
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1042 | (6) |
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1048 | (3) |
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1051 | (2) |
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1053 | |
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1054 | (11) |
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1065 | (14) |
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Conservative Vector Fields and Independence of Path |
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1079 | (10) |
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1089 | (8) |
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Section Project: Hyperbolic and Trigonometric Functions |
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1097 | (22) |
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1098 | (10) |
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1108 | (11) |
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Section Project: Hyperboloid of One Sheet |
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1119 | (17) |
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1120 | (8) |
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1128 | (6) |
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1134 | (2) |
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Section Project: The Planimeter |
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1136 | |
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1137 | |
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Appendix A Proofs of Selected Theorems |
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1 | (19) |
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Appendix B Integration Tables |
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20 | (7) |
| Answers to Odd-Numbered Exercises |
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27 | (116) |
| Index of Applications |
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143 | (4) |
| Index |
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147 | |