Yes, this is another Calculus book. However, 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.The 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. The target audience is STEM students including those in engineering and meteorology programs.
Author(s): Kenneth Luther
Publisher: World Scientific Publishing
Year: 2023
Language: English
Pages: 469
Contents
Preface
7. The Integration Dojo
7.1 Integration by Substitution (Review)
7.2 Integration by Parts
7.3 The Calc 2 Boss Fight: Integration by Partial Fractions
7.4 Trigonometric Integrals
7.5 Surprise Boss Fight: Trigonometric Substitution
7.6 Improper Integrals
8. The Mathematics Chainsaw Massacre
Introduction to Partitioning
8.1 The Area Between Two Curves
8.2 The Arc Length of a Curve
8.3 Average Value of a Function
8.4 Numerical Integration
9. Round and Round We Go: Solids of Revolution
9.1 Solids of Revolution: Surface Area
9.2 Volumes I: Disc-count Mathematics
9.3 Volumes II: The Shell Game
10. Approximation
Introduction to Approximation
10.1 Taylor Polynomials
10.2 Taylor Series Part 1
10.3 Infinite Sequences
10.4 Infinite Series
10.5 Alternating Series
11. The Fear of All Sums
11.1 The Integral Test and p-Series
11.2 The Ratio Test
11.3 Power Series
11.4 Functions in Disguise
11.5 Taylor Series Part 2
12. A Change in Graph Paper
12.1 Introduction to Parametric Equations
12.2 Calculus of Parametric Equations
12.3 Introduction to Polar Coordinates
12.4 Calculus of Polar Coordinates
Appendix A Solutions to All Practice Problems
A.1 Chapter 7: Practice Problem Solutions
A.1.1 Int. by Substitution — Practice — Solved
A.1.2 Int. by Parts — Practice — Solved
A.1.3 Int. by Partial Fracs. — Practice — Solved
A.1.4 Trig. Integrals — Practice — Solved
A.1.5 Trig. Substitution — Practice — Solved
A.1.6 Improper Integrals — Practice — Solved
A.2 Chapter 8: Practice Problem Solutions
A.2.1 Area Betw. Curves — Practice — Solved
A.2.2 Arc Length — Practice — Solved
A.2.3 Average Value — Practice — Solved
A.2.4 Numerical Integration — Practice — Solved
A.3 Chapter 9: Practice Problem Solutions
A.3.1 Solids of Rev.: Sfc Area — Practice — Solved
A.3.2 Vol. by Discs — Practice — Solved
A.3.3 Vol. by Shells — Practice — Solved
A.4 Chapter 10: Practice Problem Solutions
A.4.1 Taylor Polynomials — Practice — Solved
A.4.2 Taylor Series Pt. 1 — Practice — Solved
A.4.3 Infinite Sequences — Practice — Solved
A.4.4 Infinite Series — Practice — Solved
A.4.5 Alternating Series — Practice — Solved
A.5 Chapter 11: Practice Problem Solutions
A.5.1 Int. Test & p-Series — Practice — Solved
A.5.2 Ratio Test — Practice — Solved
A.5.3 Power Series — Practice — Solved
A.5.4 Funcs. in Disguise — Practice — Solved
A.5.5 Taylor Series Pt. 2 — Practice — Solved
A.6 Chapter 12: Practice Problem Solutions
A.6.1 Intro to Param. Eqs. — Practice — Solved
A.6.2 Calc. of Param. Eqs. — Practice — Solved
A.6.3 Intro to Polar Coords. — Practice — Solved
A.6.4 Calc. of Polar Coords. — Practice — Solved
Appendix B Solutions to All Challenge Problems
B.1 Chapter 7: Challenge Problem Solutions
B.1.1 Int. by Parts — Challenge — Solved
B.1.2 Int. by Partial Fracs. — Challenge — Solved
B.1.3 Trig. Integrals — Challenge — Solved
B.1.4 Trig. Substitution — Challenge — Solved
B.1.5 Improper Integrals — Challenge — Solved
B.2 Chapter 8: Challenge Problem Solutions
B.2.1 Area Betw. Curves — Challenge — Solved
B.2.2 Arc Length — Challenge — Solved
B.2.3 Average Value — Challenge — Solved
B.2.4 Numerical Int. — Challenge — Solved
B.3 Chapter 9: Challenge Problem Solutions
B.3.1 Solids of Rev.: Sfc. Area — Challenge — Solved
B.3.2 Vol. by Discs — Challenge — Solved
B.3.3 Vol. by Shells — Challenge — Solved
B.4 Chapter 10: Challenge Problem Solutions
B.4.1 Taylor Poly. — Challenge — Solved
B.4.2 Taylor Series Pt. 1 — Challenge — Solved
B.4.3 Infinite Sequences — Challenge — Solved
B.4.4 Infinite Series — Challenge — Solved
B.4.5 Alternating Series — Challenge — Solved
B.5 Chapter 11: Challenge Problem Solutions
B.5.1 Int. Test & p-Series — Challenge — Solved
B.5.2 Ratio Test — Challenge — Solved
B.5.3 Power Series — Challenge — Solved
B.5.4 Funcs. in Disguise — Challenge — Solved
B.5.5 Taylor Series Pt. 2 — Challenge — Solved
B.6 Chapter 12: Challenge Problem Solutions
B.6.1 Intro to Param. Eqs. — Challenge — Solved
B.6.2 Calc. of Param. Eqs. — Challenge — Solved
B.6.3 Intro to Polar Coords. — Challenge — Solved
B.6.4 Calc. of Polar Coords. — Challenge — Solved
Index
