Muutke küpsiste eelistusi

Casual Calculus: A Friendly Student Companion - Volume 2 [Pehme köide]

(Valparaiso Univ, Usa)
  • Formaat: Paperback / softback, 468 pages
  • Ilmumisaeg: 26-Sep-2022
  • Kirjastus: World Scientific Publishing Co Pte Ltd
  • ISBN-10: 9811241988
  • ISBN-13: 9789811241987
Teised raamatud teemal:
  • Formaat: Paperback / softback, 468 pages
  • Ilmumisaeg: 26-Sep-2022
  • Kirjastus: World Scientific Publishing Co Pte Ltd
  • ISBN-10: 9811241988
  • ISBN-13: 9789811241987
Teised raamatud teemal:
Yes, this is another Calculus book. However, I think it fits in a niche between the two predominant types of such texts. It could be used as a textbook, albeit a streamlined one it contains exposition on each topic, with an introduction, rationale, train of thought, and solved examples with accompanying suggested exercises. It could be used as a solution guide because it contains full written solutions to each of the hundreds of exercises posed inside. But its best position is right in between these two extremes. It is best used as a companion to a traditional text or as a refresher with its conversational tone, its "get right to it" content structure, and its inclusion of complete solutions to many problems, it is a friendly partner for students who are learning Calculus, either in class or via self-study.Exercises are structured in three sets to force multiple encounters with each topic. Solved examples in the text are accompanied by "You Try It" problems, which are similar to the solved examples; the students use these to see if they're ready to move forward. Then at the end of the section, there are "Practice Problems": more problems similar to the You Try It problems, but given all at once. Finally, each section has Challenge Problems these lean to being equally or a bit more difficult than the others, and they allow students to check on what they've mastered.My goal is to keep the students engaged with the text, and so the writing style is very informal, with attempts at humor along the way. Because we have large engineering and meteorology programs at my institution, and they make up the largest portion of our Calculus students; naturally, then, these sorts of STEM students are the target audience.
Preface vii
7 The Integration Dojo
1(80)
7.1 Integration by Substitution (Review)
1(8)
7.2 Integration by Parts
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)
7.6 Improper Integrals
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)
10 Approximation
161(74)
Interlude: Introduction to Approximation
161(12)
10.1 Taylor Polynomials
173(14)
10.2 Taylor Series Part 1
187(12)
10.3 Infinite Sequences
199(10)
10.4 Infinite Series
209(14)
10.5 Alternating Series
223(12)
11 The Fear of All Sums
235(50)
11.1 The Integral Test and p-Series
235(14)
11.2 The Ratio Test
249(6)
11.3 Power Series
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