| A Preview of Calculus |
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2 | (8) |
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10 | (82) |
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Four Ways to Represent a Function |
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11 | (14) |
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Mathematical Models: A Catalog of Essential Functions |
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25 | (13) |
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New Functions from Old Functions |
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38 | (11) |
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Graphing Calculators and Computers |
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49 | (6) |
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55 | (8) |
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Inverse Functions and Logarithms |
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63 | (11) |
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74 | (18) |
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Laboratory Project Running Circles around Circles |
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82 | (1) |
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83 | (3) |
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Principles of Problem Solving |
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86 | (6) |
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92 | (90) |
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The Tangent and Velocity Problems |
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93 | (5) |
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98 | (10) |
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Calculating Limits Using the Limit Laws |
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108 | (9) |
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117 | (11) |
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Limits Involving Infinity |
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128 | (11) |
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Tangents, Velocities, and Other Rates of Change |
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139 | (9) |
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148 | (7) |
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Writing Project Early Methods for Finding Tangents |
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155 | (1) |
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The Derivative as a Function |
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155 | (13) |
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What Does f' Say about f? |
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168 | (14) |
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175 | (4) |
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179 | (3) |
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182 | (80) |
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Derivatives of Polynomials and Exponential Functions |
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183 | (10) |
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Applied Project - Building a Better Roller Coaster |
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192 | (1) |
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The Product and Quotient Rules |
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193 | (7) |
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Rates of Change in the Natural and Social Sciences |
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200 | (13) |
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Derivatives of Trigonometric Functions |
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213 | (7) |
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220 | (12) |
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Laboratory Project Bezier Curves |
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231 | (1) |
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Applied Project Where Should a Pilot Start Descent? |
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232 | (1) |
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232 | (8) |
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Derivatives of Logarithmic Functions |
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240 | (7) |
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Discovery Project Hyperbolic Functions |
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246 | (1) |
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Linear Approximations and Differentials |
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247 | (15) |
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Laboratory Project Taylor Polynomials |
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254 | (1) |
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255 | (3) |
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258 | (4) |
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Applications of Differentiation |
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262 | (80) |
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263 | (6) |
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Maximum and Minimum Values |
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269 | (9) |
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Applied Project The Calculus of Rainbows |
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277 | (1) |
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Derivatives and the Shapes of Curves |
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278 | (11) |
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Graphing with Calculus and Calculators |
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289 | (8) |
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Indeterminate Forms and I'Hospital's Rule |
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297 | (9) |
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Writing Project The Origins of l'Hospital's Rule |
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305 | (1) |
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306 | (11) |
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Applied Project The Shape of a Can |
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316 | (1) |
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Applications to Business and Economics |
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317 | (5) |
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322 | (5) |
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327 | (15) |
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335 | (4) |
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339 | (3) |
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342 | (98) |
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343 | (11) |
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354 | (12) |
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Evaluating Definite Integrals |
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366 | (11) |
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Discovery Project Area Functions |
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376 | (1) |
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The Fundamental Theorem of Calculus |
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377 | (9) |
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Writing Project Newton, Leibniz, and the Invention of Calculus |
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385 | (1) |
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386 | (7) |
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393 | (7) |
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Additional Techniques of Integration |
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400 | (5) |
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Integration Using Tables and Computer Algebra Systems |
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405 | (7) |
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Discovery Project Patterns in Integrals |
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411 | (1) |
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412 | (11) |
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423 | (17) |
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433 | (4) |
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437 | (3) |
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Applications of Integration |
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440 | (58) |
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441 | (6) |
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447 | (14) |
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Discovery Project Rotating on a Slant |
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460 | (1) |
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461 | (6) |
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Discovery Project Arc Length Contest |
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466 | (1) |
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Average Value of a Function |
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467 | (4) |
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Applied Project Where to Sit at the Movies |
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470 | (1) |
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Applications to Physics and Engineering |
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471 | (11) |
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Applications to Economics and Biology |
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482 | (4) |
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486 | (12) |
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493 | (3) |
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496 | (2) |
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498 | (58) |
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Modeling with Differential Equations |
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499 | (5) |
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Direction Fields and Euler's Method |
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504 | (9) |
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513 | (11) |
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Applied Project How Fast Does a Tank Drain? |
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521 | (2) |
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Applied Project Which Is Faster. Going Up or Coming Down? |
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523 | (1) |
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Exponential Growth and Decay |
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524 | (11) |
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Applied Project Calculus and Baseball |
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534 | (1) |
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535 | (9) |
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544 | (12) |
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551 | (3) |
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554 | (556) |
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Infinite Sequences and Series |
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556 | |
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557 | (10) |
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Laboratory Project Logistic Sequences |
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567 | (1) |
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567 | (10) |
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The Integral and Comparison Tests; Estimating Sums |
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577 | (9) |
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586 | (8) |
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594 | (5) |
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Representations of Functions as Power Series |
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599 | (6) |
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Taylor and Maclaurin Series |
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605 | (12) |
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Laboratory Project An Elusive Limit |
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617 | (1) |
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617 | (4) |
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Writing Project How Newton Discovered the Binomial Series |
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621 | (1) |
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Applications of Taylor Polynomials |
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621 | |
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Applied Project Radiation from the Stars |
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630 | (1) |
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631 | (3) |
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634 | |
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1 | (115) |
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A Intervals, Inequalities, and Absolute Values |
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2 | (5) |
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7 | (11) |
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18 | (11) |
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D Precise Definitions of Limits |
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29 | (9) |
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38 | (3) |
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41 | (5) |
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G Integration of Rational Functions by Partial Fractions |
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46 | (8) |
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54 | (16) |
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70 | (9) |
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J Answers to Odd-Numbered Exercises |
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79 | (37) |
| Index |
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116 | |
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