| A PREVIEW OF CALCULUS |
|
2 | (8) |
|
|
|
10 | (84) |
|
1.1 Four Ways to Represent a Function |
|
|
12 | (14) |
|
1.2 New Functions from Old Functions |
|
|
26 | (15) |
|
1.3 Graphing Calculators and Computers |
|
|
41 | (7) |
|
|
|
48 | (8) |
|
Laboratory Project: Families of Hypocycloids |
|
|
55 | (1) |
|
1.5 Exponential Functions |
|
|
56 | (7) |
|
1.6 Inverse Functions and Logarithms |
|
|
63 | (12) |
|
1.7 Models and Curve Fitting |
|
|
75 | (9) |
|
|
|
84 | (3) |
|
Principles of Problem Solving |
|
|
87 | (7) |
|
|
|
94 | (96) |
|
2.1 The Tangent and Velocity Problems |
|
|
96 | (5) |
|
2.2 The Limit of a Function |
|
|
101 | (10) |
|
2.3 Calculating Limits Using the Limit Laws |
|
|
111 | (9) |
|
|
|
120 | (10) |
|
2.5 Limits Involving Infinity |
|
|
130 | (12) |
|
2.6 Tangents, Velocities, and Other Rates of Change |
|
|
142 | (9) |
|
|
|
151 | (7) |
|
Writing Project: Early Methods for Finding Tangents |
|
|
157 | (1) |
|
2.8 The Derivative as a Function |
|
|
158 | (13) |
|
2.9 Linear Approximations |
|
|
171 | (4) |
|
2.10 What Does f' Say about f? |
|
|
175 | (7) |
|
|
|
182 | (4) |
|
|
|
186 | (4) |
|
|
|
190 | (76) |
|
3.1 Derivatives of Polynomials and Exponential Functions |
|
|
192 | (9) |
|
3.2 The Product and Quotient Rules |
|
|
201 | (6) |
|
3.3 Rates of Change in the Natural and Social Sciences |
|
|
207 | (13) |
|
3.4 Derivatives of Trigonometric Functions |
|
|
220 | (7) |
|
|
|
227 | (12) |
|
Laboratory Project: Bezier Curves |
|
|
237 | (1) |
|
Applied Project: Where Should a Pilot Start Descent? |
|
|
238 | (1) |
|
3.6 Implicit Differentiation |
|
|
239 | (8) |
|
3.7 Derivatives of Logarithmic Functions |
|
|
247 | (7) |
|
Discovery Project: Hyperbolic Functions |
|
|
253 | (1) |
|
3.8 Linear Approximations and Differentials |
|
|
254 | (6) |
|
Laboratory Project: Taylor Polynomials |
|
|
259 | (1) |
|
|
|
260 | (3) |
|
|
|
263 | (3) |
|
4 APPLICATIONS OF DIFFERENTIATION |
|
|
266 | (82) |
|
|
|
268 | (6) |
|
4.2 Maximum and Minimum Values |
|
|
274 | (9) |
|
Applied Project: The Calculus of Rainbows |
|
|
282 | (1) |
|
4.3 Derivatives and the Shapes of Curves |
|
|
283 | (11) |
|
4.4 Graphing with Calculus and Calculators |
|
|
294 | (7) |
|
4.5 Indeterminate Forms and L'Hospital's Rule |
|
|
301 | (9) |
|
Writing Project: The Origins of L'Hospital's Rule |
|
|
310 | (1) |
|
4.6 Optimization Problems |
|
|
310 | (12) |
|
Applied Project: The Shape of a Can |
|
|
321 | (1) |
|
4.7 Applications to Economics |
|
|
322 | (5) |
|
|
|
327 | (5) |
|
|
|
332 | (8) |
|
|
|
340 | (4) |
|
|
|
344 | (4) |
|
|
|
348 | (98) |
|
|
|
350 | (11) |
|
5.2 The Definite Integral |
|
|
361 | (11) |
|
5.3 Evaluating Definite Integrals |
|
|
372 | (11) |
|
Discovery Project: Area Functions |
|
|
382 | (1) |
|
5.4 The Fundamental Theorem of Calculus |
|
|
383 | (10) |
|
Writing Project: Newton, Leibniz, and the Invention of Calculus |
|
|
392 | (1) |
|
5.5 The Substitution Rule |
|
|
393 | (9) |
|
|
|
402 | (6) |
|
5.7 Integration Using Tables and Computer Algebra Systems |
|
|
408 | (8) |
|
Discovery Project: Patterns in Integrals |
|
|
414 | (2) |
|
5.8 Approximate Integration |
|
|
416 | (11) |
|
|
|
427 | (10) |
|
|
|
437 | (5) |
|
|
|
442 | (4) |
|
6 APPLICATIONS OF INTEGRATION |
|
|
446 | (56) |
|
|
|
448 | (7) |
|
|
|
455 | (9) |
|
|
|
464 | (5) |
|
6.4 Average Value of a Function |
|
|
469 | (4) |
|
Applied Project: Where to Sit at the Movies |
|
|
472 | (1) |
|
6.5 Applications to Physics and Engineering |
|
|
473 | (11) |
|
6.6 Applications to Economics and Biology |
|
|
484 | (5) |
|
|
|
489 | (7) |
|
|
|
496 | (3) |
|
|
|
499 | (3) |
|
|
|
502 | (56) |
|
7.1 Modeling with Differential Equations |
|
|
504 | (5) |
|
|
|
509 | (5) |
|
|
|
514 | (4) |
|
|
|
518 | (9) |
|
Applied Project: Which is Faster, Going Up or Coming Down? |
|
|
526 | (1) |
|
7.5 Exponential Growth and Decay |
|
|
527 | (10) |
|
Applied Project: Calculus and Baseball |
|
|
536 | (1) |
|
7.6 The Logistic Equation |
|
|
537 | (9) |
|
7.7 Predator-Prey Systems |
|
|
546 | (7) |
|
|
|
553 | (3) |
|
|
|
556 | (2) |
|
8 INFINITE SEQUENCES AND SERIES |
|
|
558 | |
|
|
|
560 | (10) |
|
Laboratory Project: Logistic Sequences |
|
|
569 | (1) |
|
|
|
570 | (9) |
|
8.3 The Integral and Comparison Tests; Estimating Sums |
|
|
579 | (10) |
|
8.4 Other Convergence Tests |
|
|
589 | (8) |
|
|
|
597 | (6) |
|
8.6 Representations of Functions as Power Series |
|
|
603 | (5) |
|
8.7 Taylor and Maclaurin Series |
|
|
608 | (11) |
|
|
|
619 | (5) |
|
Writing Project: How Newton Discovered the Binomial Series |
|
|
623 | (1) |
|
8.9 Applications of Taylor Polynomials |
|
|
624 | (9) |
|
Applied Project: Radiation from the Stars |
|
|
632 | (1) |
|
8.10 Using Series to Solve Differential Equations |
|
|
633 | (4) |
|
|
|
637 | (3) |
|
|
|
640 | |
| APPENDIXES |
|
A1 | (112) |
| A Intervals, Inequalities, and Absolute Values |
|
A2 | (5) |
| B Coordinate Geometry |
|
A7 | (12) |
| C Trigonometry |
|
A19 | (13) |
| D Precise Definitions of Limits |
|
A32 | (8) |
| E A Few Proofs |
|
A40 | (2) |
| F Integration of Rational Functions by Partial Fractions |
|
A42 | (9) |
| G Polar Coordinates |
|
A51 | (16) |
| H Complex Numbers |
|
A67 | (9) |
| I Answers to Odd-Numbered Exercises |
|
A76 | (37) |
| INDEX |
|
A113 | |
Shopping Cart
