| A Preview of Calculus |
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2 | (8) |
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10 | (56) |
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Four Ways to Represent a Function |
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11 | (13) |
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24 | (14) |
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New Functions from Old Functions |
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38 | (12) |
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Graphing Calculators and Computers |
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50 | (9) |
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56 | (3) |
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Principles of Problem Solving |
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59 | (7) |
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Limits and Rates of Change |
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66 | (62) |
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The Tangent and Velocity Problems |
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67 | (5) |
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72 | (12) |
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Calculating Limits Using the Limit Laws |
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84 | (10) |
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The Precise Definition of a Limit |
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94 | (10) |
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104 | (10) |
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Tangents, Velocities, and Other Rates of Change |
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114 | (12) |
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124 | (2) |
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126 | (2) |
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128 | (94) |
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129 | (7) |
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Writing Project Early Methods for Finding Tangents |
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135 | (1) |
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The Derivative as a Function |
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136 | (11) |
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147 | (11) |
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Rates of Change in the Natural and Social Sciences |
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158 | (12) |
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Derivatives of Trigonometric Functions |
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170 | (7) |
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177 | (8) |
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185 | (7) |
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192 | (7) |
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Applied Project *** Where Should a Pilot Start Descent? |
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199 | (1) |
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199 | (6) |
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Linear Approximations and Differentials |
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205 | (13) |
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Laboratory Project *** Taylor Polynomials |
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213 | (1) |
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214 | (4) |
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218 | (4) |
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Applications of Differentiation |
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222 | (90) |
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Maximum and Minimum Values |
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223 | (11) |
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Applied Project *** The Calculus of Rainbows |
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232 | (2) |
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234 | (6) |
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How Derivatives Affect the Shape of a Graph |
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240 | (9) |
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Limits at Infinity; Horizontal Asymptotes |
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249 | (14) |
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Summary of Curve Sketching |
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263 | (8) |
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Graphing with Calculus and Calculators |
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271 | (6) |
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277 | (11) |
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Applied Project *** The Shape of a Can |
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287 | (1) |
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Applications to Economics |
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288 | (5) |
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293 | (6) |
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299 | (11) |
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306 | (4) |
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310 | (2) |
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312 | (58) |
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313 | (11) |
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324 | (13) |
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Discovery Project *** Area Functions |
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336 | (1) |
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The Fundamental Theorem of Calculus |
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337 | (9) |
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Indefinite Integrals and the Total Change Theorem |
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346 | (10) |
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Writing Project *** Newton, Leibniz, and the Invention of Calculus |
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355 | (1) |
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356 | (11) |
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363 | (4) |
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367 | (3) |
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Applications of Integration |
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370 | (36) |
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371 | (7) |
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378 | (11) |
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Volumes by Cylindrical Shells |
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389 | (5) |
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394 | (4) |
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Average Value of a Function |
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398 | (5) |
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401 | (2) |
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403 | (3) |
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Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions |
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406 | (96) |
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407 | (9) |
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Instructors may cover either Sections 7.2--7.4 or Sections 7.2*--7.4*. See the Preface. |
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Exponential Functions and Their Derivatives |
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416 | (12) |
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428 | (7) |
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Derivatives of Logarithmic Functions |
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435 | (10) |
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The Natural Logarithmic Function |
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445 | (8) |
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The Natural Exponential Function |
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453 | (7) |
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General Logarithmic and Exponential Functions |
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460 | (9) |
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Inverse Trigonometric Functions |
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469 | (9) |
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Applied Project *** Where to Sit at the Movies |
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478 | (1) |
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478 | (7) |
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Indeterminate Forms and L'Hospital's Rule |
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485 | (15) |
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Writing Project *** The Origins of L'Hospital's Rule |
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496 | (1) |
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496 | (4) |
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500 | (2) |
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Techniques of Integration |
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502 | (72) |
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503 | (7) |
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510 | (7) |
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Trigonometric Substitution |
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517 | (7) |
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Integration of Rational Functions by Partial Fractions |
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524 | (9) |
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533 | (6) |
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Integration Using Tables and Computer Algebra Systems |
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539 | (7) |
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Discovery Project *** Patterns in Integrals |
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545 | (1) |
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546 | (11) |
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557 | (14) |
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568 | (3) |
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571 | (3) |
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Further Applications of Integration |
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574 | (40) |
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575 | (7) |
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Area of a Surface of Revolution |
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582 | (7) |
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Discovery Project *** Rotating on a Slant |
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588 | (1) |
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Applications to Physics and Engineering |
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589 | (9) |
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Applications to Economics and Biology |
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598 | (5) |
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603 | (9) |
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610 | (2) |
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612 | (2) |
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614 | (60) |
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Modeling with Differential Equations |
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615 | (5) |
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Direction Fields and Euler's Method |
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620 | (9) |
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629 | (8) |
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Applied Project *** Which Is Faster, Going Up or Coming Down? |
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636 | (1) |
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Exponential Growth and Decay |
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637 | (10) |
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Applied Project *** Calculus and Baseball |
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646 | (1) |
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647 | (9) |
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656 | (6) |
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662 | (10) |
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668 | (4) |
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672 | (2) |
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Parametric Equations and Polar Coordinates |
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674 | (52) |
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Curves Defined by Parametric Equations |
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675 | (7) |
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Laboratory Project *** Families of Hypocycloids |
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682 | (1) |
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682 | (7) |
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Laboratory Project *** Bezier Curves |
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689 | (1) |
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Arc Length and Surface Area |
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689 | (5) |
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694 | (10) |
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Areas and Lengths in Polar Coordinates |
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704 | (5) |
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709 | (7) |
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Conic Sections in Polar Coordinates |
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716 | (8) |
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722 | (2) |
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724 | (2) |
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Infinite Sequences and Series |
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726 | (90) |
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727 | (11) |
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Laboratory Project *** Logistic Sequences |
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738 | (1) |
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738 | (10) |
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The Integral Test and Estimates of Sums |
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748 | (7) |
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755 | (5) |
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760 | (5) |
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Absolute Convergence and the Ratio and Root Tests |
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765 | (7) |
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Strategy for Testing Series |
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772 | (2) |
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774 | (5) |
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Representations of Functions as Power Series |
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779 | (6) |
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Taylor and Maclaurin Series |
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785 | (11) |
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796 | (4) |
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Writing Project *** How Newton Discovered the Binomial Series |
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799 | (1) |
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Applications of Taylor Polynomials |
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800 | (12) |
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Applied Project *** Radiation from the Stars |
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808 | (1) |
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809 | (3) |
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812 | (4) |
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Vectors and the Geometry of Space |
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816 | (54) |
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Three-Dimensional Coordinate Systems |
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817 | (5) |
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822 | (8) |
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830 | (7) |
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837 | (9) |
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Discovery Project *** The Geometry of a Tetrahedron |
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845 | (1) |
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Equations of Lines and Planes |
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846 | (9) |
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Cylinders and Quadric Surfaces |
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855 | (6) |
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Cylindrical and Spherical Coordinates |
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861 | (8) |
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Laboratory Project *** Families of Surfaces |
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866 | (1) |
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866 | (3) |
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869 | (1) |
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870 | (36) |
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Vector Functions and Space Curves |
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871 | (6) |
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Derivatives and Integrals of Vector Functions |
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877 | (6) |
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883 | (8) |
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Motion in Space: Velocity and Acceleration |
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891 | (13) |
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Applied Project *** Kepler's Laws |
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900 | (1) |
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901 | (3) |
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904 | (2) |
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906 | (94) |
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Functions of Several Variables |
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907 | (14) |
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921 | (8) |
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929 | (13) |
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Tangent Planes and Linear Approximations |
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942 | (9) |
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951 | (9) |
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Directional Derivatives and the Gradient Vector |
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960 | (13) |
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Maximum and Minimum Values |
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973 | (12) |
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Applied Project *** Designing a Dumpster |
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983 | (1) |
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Discovery Project *** Quadratic Approximations and Critical Points |
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984 | (1) |
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985 | (13) |
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Applied Project *** Rocket Science |
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992 | (1) |
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Applied Project *** Hydro-Turbine Optimization |
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993 | (1) |
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994 | (4) |
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998 | (2) |
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1000 | (74) |
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Double Integrals over Rectangles |
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1001 | (9) |
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1010 | (5) |
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Double Integrals over General Regions |
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1015 | (8) |
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Double Integrals in Polar Coordinates |
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1023 | (6) |
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Applications of Double Integrals |
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1029 | (10) |
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1039 | (3) |
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1042 | (10) |
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Discovery Project *** Volumes of Hyperspheres |
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1052 | (1) |
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Triple Integrals in Cylindrical and Spherical Coordinates |
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1052 | (8) |
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Applied Project *** Roller Derby |
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1058 | (1) |
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Discovery Project *** The Intersection of Three Cylinders |
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1059 | (1) |
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Change of Variables in Multiple Integrals |
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1060 | (12) |
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1068 | (4) |
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1072 | (2) |
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1074 | (84) |
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1075 | (6) |
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1081 | (12) |
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The Fundamental Theorem for Line Integrals |
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1093 | (9) |
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1102 | (7) |
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1109 | (8) |
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Parametric Surfaces and Their Areas |
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1117 | (10) |
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1127 | (12) |
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1139 | (6) |
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Writing Project *** Three Men and Two Theorems |
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1144 | (1) |
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1145 | (7) |
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1152 | (4) |
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1153 | (3) |
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1156 | (2) |
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Second-Order Differential Equations |
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1158 | (26) |
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Second-Order Linear Equations |
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1159 | (6) |
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Nonhomogeneous Linear Equations |
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1165 | (7) |
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Applications of Second-Order Differential Equations |
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1172 | (8) |
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1180 | (4) |
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1184 | |
| Appendixes |
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1 | (118) |
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A Intervals, Inequalities, and Absolute Values |
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2 | (8) |
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B Coordinate Geometry and Lines |
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10 | (6) |
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C Graphs of Second-Degree Equations |
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16 | (8) |
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24 | (10) |
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34 | (5) |
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39 | (9) |
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48 | (8) |
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H Answers to Odd-Numbered Exercises |
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56 | (63) |
| Index |
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119 | |
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