| 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 I'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 | (2) |
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Infinite Sequences and Series |
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556 | (80) |
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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 | (15) |
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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 | (2) |
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Vectors and the Geometry of Space |
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636 | (58) |
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Three-Dimensional Coordinate Systems |
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637 | (5) |
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642 | (9) |
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651 | (6) |
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657 | (9) |
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Discovery Project • The Geometry of a Tetrahedron |
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665 | (1) |
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Equations of Lines and Planes |
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666 | (10) |
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Laboratory Project • Putting 3D in Perspective |
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675 | (1) |
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676 | (9) |
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Cylindrical and Spherical Coordinates |
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685 | (9) |
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Laboratory Project • Families of Surfaces |
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690 | (1) |
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690 | (3) |
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693 | (1) |
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694 | (44) |
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Vector Functions and Space Curves |
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695 | (7) |
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Derivatives and Integrals of Vector Functions |
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702 | (6) |
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708 | (8) |
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Motion in Space: Velocity and Acceleration |
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716 | (12) |
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Applied Project • Kepler's Laws |
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727 | (1) |
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728 | (10) |
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734 | (2) |
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736 | (2) |
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738 | (90) |
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Functions of Several Variables |
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739 | (11) |
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750 | (6) |
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756 | (13) |
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Tangent Planes and Linear Approximations |
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769 | (11) |
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780 | (8) |
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Directional Derivatives and the Gradient Vector |
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788 | (13) |
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Maximum and Minimum Values |
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801 | (12) |
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Applied Project • Designing a Dumpster |
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811 | (1) |
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Discovery Project • Quadratic Approximations and Critical Points |
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812 | (1) |
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813 | (15) |
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Applied Project • Rocket Science |
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820 | (1) |
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Applied Project • Hydro-Turbine Optimization |
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821 | (1) |
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822 | (4) |
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826 | (2) |
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828 | (76) |
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Double Integrals over Rectangles |
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829 | (8) |
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837 | (6) |
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Double Integrals over General Regions |
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843 | (8) |
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Double Integrals in Polar Coordinates |
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851 | (6) |
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Applications of Double Integrals |
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857 | (10) |
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867 | (5) |
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872 | (10) |
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Discovery Project • Volumes of Hyperspheres |
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881 | (1) |
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Triple Integrals in Cylindrical and Spherical Coordinates |
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882 | (7) |
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Applied Project • Roller Derby |
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888 | (1) |
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Discovery Project • The Intersection of Three Cylinders |
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889 | (1) |
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Change of Variables in Multiple Integrals |
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889 | (15) |
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898 | (4) |
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902 | (2) |
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904 | |
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905 | (7) |
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912 | (12) |
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The Fundamental Theorem for Line Integrals |
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924 | (9) |
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933 | (7) |
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940 | (8) |
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948 | (11) |
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959 | (7) |
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Writing Project • Three Men and Two Theorems |
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965 | (1) |
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966 | (7) |
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973 | |
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974 | (3) |
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977 | |
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1 | (134) |
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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 | (10) |
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39 | (5) |
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44 | (6) |
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G Integration of Rational Functions by Partial Fractions |
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50 | (8) |
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58 | (16) |
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74 | (9) |
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J Answers to Odd-Numbered Exercises |
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83 | (52) |
| Index |
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135 | |
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