| Preface |
|
vii | |
|
|
|
1 | (80) |
|
7.1 Integration by Substitution (Review) |
|
|
1 | (8) |
|
|
|
9 | (13) |
|
7.3 The Calc 2 Boss Fight: Integration by Partial Fractions |
|
|
22 | (20) |
|
7.4 Trigonometric Integrals |
|
|
42 | (12) |
|
7.5 Surprise Boss Fight: Trigonometric Substitution |
|
|
54 | (12) |
|
|
|
66 | (15) |
|
8 The Mathematics Chainsaw Massacre |
|
|
81 | (54) |
|
Interlude: Introduction to Partitioning |
|
|
81 | (7) |
|
8.1 The Area Between Two Curves |
|
|
88 | (12) |
|
8.2 The Arc Length of a Curve |
|
|
100 | (9) |
|
8.3 Average Value of a Function |
|
|
109 | (5) |
|
8.4 Numerical Integration |
|
|
114 | (21) |
|
9 Round and Round We Go: Solids of Revolution |
|
|
135 | (26) |
|
9.1 Solids of Revolution: Surface Area |
|
|
135 | (10) |
|
9.2 Volumes I: Disc-count Mathematics |
|
|
145 | (9) |
|
9.3 Volumes II: The Shell Game |
|
|
154 | (7) |
|
|
|
161 | (74) |
|
Interlude: Introduction to Approximation |
|
|
161 | (12) |
|
|
|
173 | (14) |
|
10.2 Taylor Series Part 1 |
|
|
187 | (12) |
|
|
|
199 | (10) |
|
|
|
209 | (14) |
|
|
|
223 | (12) |
|
|
|
235 | (50) |
|
11.1 The Integral Test and p-Series |
|
|
235 | (14) |
|
|
|
249 | (6) |
|
|
|
255 | (8) |
|
11.4 Functions in Disguise |
|
|
263 | (10) |
|
11.5 Taylor Series Part 2 |
|
|
273 | (12) |
|
12 A Change in Graph Paper |
|
|
285 | (36) |
|
12.1 Introduction to Parametric Equations |
|
|
285 | (8) |
|
12.2 Calculus of Parametric Equations |
|
|
293 | (10) |
|
12.3 Introduction to Polar Coordinates |
|
|
303 | (9) |
|
12.4 Calculus of Polar Coordinates |
|
|
312 | (9) |
|
Appendix A Solutions to All Practice Problems |
|
|
321 | (76) |
|
A.1 Chapter 7: Practice Problem Solutions |
|
|
321 | (22) |
|
A.1.1 Solutions to 7.1 Practice Problems |
|
|
321 | (6) |
|
A.1.2 Solutions to 7.2 Practice Problems |
|
|
327 | (3) |
|
A.1.3 Solutions to 7.3 Practice Problems |
|
|
330 | (3) |
|
A.1.4 Solutions to 7.4 Practice Problems |
|
|
333 | (3) |
|
A.1.5 Solutions to 7.5 Practice Problems |
|
|
336 | (3) |
|
A.1.6 Solutions to 7.6 Practice Problems |
|
|
339 | (4) |
|
A.2 Chapter 8: Practice Problem Solutions |
|
|
343 | (12) |
|
A.2.1 Solutions to 8.1 Practice Problems |
|
|
343 | (3) |
|
A.2.2 Solutions to 8.2 Practice Problems |
|
|
346 | (2) |
|
A.2.3 Solutions to 8.3 Practice Problems |
|
|
348 | (1) |
|
A.2.4 Solutions to 8.4 Practice Problems |
|
|
349 | (6) |
|
A.3 Chapter 9: Practice Problem Solutions |
|
|
355 | (6) |
|
A.3.1 Solutions to 9.1 Practice Problems |
|
|
355 | (3) |
|
A.3.2 Solutions to 9.2 Practice Problems |
|
|
358 | (2) |
|
A.3.3 Solutions to 9.3 Practice Problems |
|
|
360 | (1) |
|
A.4 Chapter 10: Practice Problem Solutions |
|
|
361 | (14) |
|
A.4.1 Solutions to 10.1 Practice Problems |
|
|
361 | (5) |
|
A.4.2 Solutions to 10.2 Practice Problems |
|
|
366 | (2) |
|
A.4.3 Solutions to 10.3 Practice Problems |
|
|
368 | (2) |
|
A.4.4 Solutions to 10.4 Practice Problems |
|
|
370 | (2) |
|
A.4.5 Solutions to 10.5 Practice Problems |
|
|
372 | (3) |
|
A.5 Chapter 11: Practice Problem Solutions |
|
|
375 | (12) |
|
A.5.1 Solutions to 11.1 Practice Problems |
|
|
375 | (4) |
|
A.5.2 Solutions to 11.2 Practice Problems |
|
|
379 | (1) |
|
A.5.3 Solutions to 11.3 Practice Problems |
|
|
380 | (2) |
|
A.5.4 Solutions to 11.4 Practice Problems |
|
|
382 | (2) |
|
A.5.5 Solutions to 11.5 Practice Problems |
|
|
384 | (3) |
|
A.6 Chapter 12: Practice Problem Solutions |
|
|
387 | (10) |
|
A.6.1 Solutions to 12.1 Practice Problems |
|
|
387 | (2) |
|
A.6.2 Solutions to 12.2 Practice Problems |
|
|
389 | (2) |
|
A.6.3 Solutions to 12.3 Practice Problems |
|
|
391 | (2) |
|
A.6.4 Solutions to 12.4 Practice Problems |
|
|
393 | (4) |
|
Appendix B Solutions to All Challenge Problems |
|
|
397 | (56) |
|
B.1 Chapter 7: Challenge Problem Solutions |
|
|
397 | (14) |
|
B.1.1 Solutions to 7.2 Challenge Problems |
|
|
397 | (3) |
|
B.1.2 Solutions to 7.3 Challenge Problems |
|
|
400 | (3) |
|
B.1.3 Solutions to 7.4 Challenge Problems |
|
|
403 | (2) |
|
B.1.4 Solutions to 7.5 Challenge Problems |
|
|
405 | (3) |
|
B.1.5 Solutions to 7.6 Challenge Problems |
|
|
408 | (3) |
|
B.2 Chapter 8: Challenge Problem Solutions |
|
|
411 | (10) |
|
B.2.1 Solutions to 8.1 Challenge Problems |
|
|
411 | (2) |
|
B.2.2 Solutions to 8.2 Challenge Problems |
|
|
413 | (4) |
|
B.2.3 Solutions to 8.3 Challenge Problems |
|
|
417 | (2) |
|
B.2.4 Solutions to 8.4 Challenge Problems |
|
|
419 | (2) |
|
B.3 Chapter 9: Challenge Problem Solutions |
|
|
421 | (4) |
|
B.3.1 Solutions to 9.1 Challenge Problems |
|
|
421 | (2) |
|
B.3.2 Solutions to 9.2 Challenge Problems |
|
|
423 | (1) |
|
B.3.3 Solutions to 9.3 Challenge Problems |
|
|
424 | (1) |
|
B.4 Chapter 10: Challenge Problem Solutions |
|
|
425 | (10) |
|
B.4.1 Solutions to 10.1 Challenge Problems |
|
|
425 | (3) |
|
B.4.2 Solutions to 10.2 Challenge Problems |
|
|
428 | (2) |
|
B.4.3 Solutions to 10.3 Challenge Problems |
|
|
430 | (1) |
|
B.4.4 Solutions to 10.4 Challenge Problems |
|
|
431 | (2) |
|
B.4.5 Solutions to 10.5 Challenge Problems |
|
|
433 | (2) |
|
B.5 Chapter 11: Challenge Problem Solutions |
|
|
435 | (10) |
|
B.5.1 Solutions to 11.1 Challenge Problems |
|
|
435 | (2) |
|
B.5.2 Solutions to 11.2 Challenge Problems |
|
|
437 | (2) |
|
B.5.3 Solutions to 11.3 Challenge Problems |
|
|
439 | (2) |
|
B.5.4 Solutions to 11.4 Challenge Problems |
|
|
441 | (2) |
|
B.5.5 Solutions to 11.5 Challenge Problems |
|
|
443 | (2) |
|
B.6 Chapter 12: Challenge Problem Solutions |
|
|
445 | (8) |
|
B.6.1 Solutions to 12.1 Challenge Problems |
|
|
445 | (1) |
|
B.6.2 Solutions to 12.2 Challenge Problems |
|
|
446 | (3) |
|
B.6.3 Solutions to 12.3 Challenge Problems |
|
|
449 | (2) |
|
B.6.4 Solutions to 12.4 Challenge Problems |
|
|
451 | (2) |
| Index |
|
453 | |