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: 722
Contents
Preface
0. Prelude: Your Mathematics Pep Talk
1. Years of Work in One Chapter
1.1 The Basics of Functions
1.2 Essential Types of Functions
1.3 Exponential and Logarithmic Functions
1.4 Compositions and Inverses
1.5 The Pre-Calc Boss Fight: Trigonometric Functions (and Their Inverses)
1.6 The Greatest Functions Ever!
2. Take It to the Limit
2.1 Introduction to Limits
2.2 Computation of Limits
2.3 Limits Involving Infinity
2.4 Limits and Continuity
2.5 Secant Lines and Tangent Lines
Interlude: The Formal Definition of Limits
3. Embrace the Change
3.1 The Rate of Change of a Function
3.2 The Derivative at a Point
3.3 The Derivative Function
3.4 Simple Derivatives and Antiderivatives
3.5 The Power Rule
3.6 The Power Rule on Steroids
4. Abandon Hope All Ye Who Enter Here
4.1 How to Make Exponential and Logarithmic Functions Worse
4.2 How to Make Trigonometric Functions Worse
4.3 The Product and Quotient Rules
4.4 The Chain Rule
4.5 Implicit Differentiation
4.6 Antiderivatives Using Substitution
5. Calculus Has Its Ups and Downs
5.1 The Calc 1 Boss Fight: Related Rates
5.2 Derivatives and Graphs
5.3 Optimization
5.4 Local Linear Approximation and L-Hopital’s Rule
5.5 Calc Offers Good Value When It Gets on a Rolle
6. The Best Mathematics Symbol There Is ... So Far
6.1 Sigma Notation
6.2 The Area Under a Curve
6.3 Definite Integrals
6.4 The Fundamental Theorem of Calculus
6.5 Definite Integrals With Substitution
Appendix A Solutions to All Practice Problems
A.1 Chapter 1: Practice Problem Solutions
A.1.1 Basics of Functions — Practice — Solved
A.1.2 Essential Types — Practice — Solved
A.1.3 Exp and Log Functions — Practice — Solved
A.1.4 Compositions & Inverses — Practice — Solved
A.1.5 Trig Functions & Inverses — Practice — Solved
A.1.6 Hyperbolic Funcs — Practice — Solved
A.2 Chapter 2: Practice Problem Solutions
A.2.1 Intro to Limits — Practice — Solved
A.2.2 Computation of Limits — Practice — Solved
A.2.3 Limits w/ Infinity — Practice — Solved
A.2.4 Limits & Continuity — Practice — Solved
A.2.5 Secant & Tangent Lines — Practice — Solved
A.3 Chapter 3: Practice Problem Solutions
A.3.1 The Rate of Change — Practice — Solved
A.3.2 Derivative at a Point — Practice — Solved
A.3.3 The Derivative Function — Practice — Solved
A.3.4 Simple Derivs and Antiderivs — Practice — Solved
A.3.5 Power Rule — Practice — Solved
A.3.6 Power Rule Pt 2 — You Try It — Solved
A.4 Chapter 4: Practice Problem Solutions
A.4.1 Exp & Log Function Derivs — Practice — Solved
A.4.2 Trig Functions Derivs — Practice — Solved
A.4.3 Product & Quotient Rules — Practice — Solved
A.4.4 Chain Rule — Practice — Solved
A.4.5 Implicit Differentiation — Practice — Solved
A.4.6 Antiderivs Using Substitution — Practice — Solved
A.5 Chapter 5: Practice Problem Solutions
A.5.1 Related Rates — Practice — Solved
A.5.2 Derivatives and Graphs — Practice — Solved
A.5.3 Optimization — Practice — Solved
A.5.4 Local Lin Approx & L-Hopital’s Rule — Practice — Solved
A.5.5 Good Value — Practice — Solved
A.6 Chapter 6: Practice Problem Solutions
A.6.1 Sigma Notation — Practice — Solved
A.6.2 Area Under a Curve — Practice — Solved
A.6.3 Definite Integrals — Practice — Solved
A.6.4 FTOC — Practice — Solved
A.6.5 Def Ints With Substitution — Practice — Solved
Appendix B Solutions to All Challenge Problems
B.1 Chapter 1: Challenge Problem Solutions
B.1.1 Basics of Functions — Challenge — Solved
B.1.2 Essential Types — Challenge — Solved
B.1.3 Exp and Log Functions — Challenge — Solved
B.1.4 Compositions and Inverses — Challenge — Solved
B.1.5 Trig Functions & Their Inverses — Challenge — Solved
B.1.6 Hyperbolic Funcs — Challenge — Solved
B.2 Chapter 2: Challenge Problem Solutions
B.2.1 Intro to Limits — Challenge — Solved
B.2.2 Computation of Limits — Challenge — Solved
B.2.3 Limits Involving Infinity — Challenge — Solved
B.2.4 Limits and Continuity — Challenge — Solved
B.2.5 Secant & Tangent Lines — Challenge — Solved
B.3 Chapter 3: Challenge Problem Solutions
B.3.1 Rate of Change — Challenge — Solved
B.3.2 Derivative at a Point — Challenge — Solved
B.3.3 The Derivative Function — Challenge — Solved
B.3.4 Simple Derivs and Antiderivs — Challenge — Solved
B.3.5 Power Rule — Challenge — Solved
B.3.6 Power Rule Pt 2 — Challenge — Solved
B.4 Chapter 4: Challenge Problem Solutions
B.4.1 Exp & Log Function Derivs — Challenge — Solved
B.4.2 Trig Function Derivs — Challenge — Solved
B.4.3 Product & Quotient Rules — Challenge — Solved
B.4.4 Chain Rule — Challenge — Solved
B.4.5 Implicit Differentiation — Challenge — Solved
B.4.6 Antiderivs Using Substitution — Challenge — Solved
B.5 Chapter 5: Challenge Problem Solutions
B.5.1 Related Rates — Challenge — Solved
B.5.2 Derivatives and Graphs — Challenge — Solved
B.5.3 Optimization — Challenge — Solved
B.5.4 Local Lin Approx & L-Hopital’s Rule — Challenge — Solved
B.5.5 Good Value — Challenge — Solved
B.6 Chapter 6: Challenge Problem Solutions
B.6.1 Sigma Notation — Challenge — Solved
B.6.2 Area Under A Curve — Challenge — Solved
B.6.3 Definite Integrals — Challenge — Solved
B.6.4 FTOC — Challenge — Solved
B.6.5 Def Ints With Substitution — Challenge — Solved
Index
