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: 603
Contents
Preface
13. Mathematical Deja Vu
13.1 Life in Three Dimensions
13.2 Multivariable Functions
13.3 Three-Dimensional Surfaces
13.4 Limits of Multivariable Functions
13.5 Partial Derivatives
14. Can We All Agree That Just One Variable Was Lame?
14.1 The Chain Rule
14.2 Optimization
14.3 Double Integrals
14.4 Triple Integrals
15. And Can We Agree Rectangular Coordinates Are Rather Dull?
15.1 Double Integrals in Polar Coordinates
15.2 Cylindrical and Spherical Coordinates
15.3 The Calc 3 Boss Fight: Triple Integrals in Cylindrical & Spherical Coordinates
Interlude: Is Your Integral Zero?
16. Player V Has Entered the Game
16.1 Vector Basics
Interlude: Determinants
16.2 Dot and Cross Products
16.3 Vector Functions
16.4 Vector Fields and the Gradient
16.5 Planes and Tangent Planes
16.6 Directional Derivatives
17. We’ve Been Framed!
17.1 Arc Length Parameterization
17.2 Contours, Orientation, and Pointers
17.3 The Fresnet–Serret Frame
17.4 Lagrange Multipliers
17.5 Parametric Surfaces
18. Big Bang
18.1 Line Integrals
18.2 Conservative Vector Fields
18.3 Surface Integrals
18.4 Green’s Theorem
18.5 The Divergence Theorem
18.6 Stokes’ Theorem
Appendix A Conics, Quadrics, and Parametrics
A.1 Conic Sections
A.2 Quadric Surfaces
Appendix B Solutions to All Practice Problems
B.1 Chapter 13: Practice Problem Solutions
B.1.1 Life in Three-Dimensions — Practice — Solved
B.1.2 Multivariable Functions — Practice — Solved
B.1.3 3D Surfaces — Practice — Solved
B.1.4 Limits of MV Functions — Practice — Solved
B.1.5 Partial Derivatives — Practice — Solved
B.2 Chapter 14: Practice Problem Solutions
B.2.1 The Chain Rule — Practice — Solved
B.2.2 Optimization — Practice — Solved
B.2.3 Double Integrals — Practice — Solved
B.2.4 Triple Integrals — Practice — Solved
B.3 Chapter 15: Practice Problem Solutions
B.3.1 Double Ints in Polar Coords — Practice — Solved
B.3.2 Cylindrical and Spherical Coords — Practice — Solved
B.3.3 Triple Ints in Cyl. & Spher. Coords — Practice — Solved
B.4 Chapter 16: Practice Problem Solutions
B.4.1 Vector Basics — Practice — Solved
B.4.2 Dot and Cross Products — Practice — Solved
B.4.3 Vector Functions — Practice — Solved
B.4.4 Vector Fields and the Gradient — Practice — Solved
B.4.5 Planes and Tangent Planes — Practice — Solved
B.4.6 Directional Derivatives — Practice — Solved
B.5 Chapter 17: Practice Problem Solutions
B.5.1 Arc Length Parameterization — Practice — Solved
B.5.2 Contours, Orientation, Pointers — Practice — Solved
B.5.3 The Fresnet–Serret Frame — Practice — Solved
B.5.4 Lagrange Multipliers — Practice — Solved
B.5.5 Parametric Surfaces — Practice — Solved
B.6 Chapter 18: Practice Problem Solutions
B.6.1 Line Integrals — Practice — Solved
B.6.2 Conservative Vector Fields — Practice — Solved
B.6.3 Surface Integrals — Practice — Solved
B.6.4 Green’s Theorem — Practice Problems — Solutions
B.6.5 The Divergence Theorem — Practice — Solved
B.6.6 Stokes’ Theorem — Practice — Solved
Appendix C Solutions to All Challenge Problems
C.1 Chapter 13: Challenge Problem Solutions
C.1.1 Life in Three Dimensions — Challenge — Solved
C.1.2 Multivariable Functions — Challenge — Solved
C.1.3 3D Surfaces — Challenge — Solved
C.1.4 Limits of Multivariable Functions — Challenge — Solved
C.1.5 Partial Derivatives — Challenge — Solved
C.2 Chapter 14: Challenge Problem Solutions
C.2.1 The Chain Rule — Challenge — Solved
C.2.2 Optimization — Challenge — Solved
C.2.3 Double Integrals — Challenge — Solved
C.2.4 Triple Integrals — Challenge — Solved
C.3 Chapter 15: Challenge Problem Solutions
C.3.1 Double Ints in Polar Coords — Challenge — Solved
C.3.2 Cylindrical and Spherical Coords — Challenge — Solved
C.3.3 Triple Ints in Cyl. & Spher. Coords — Challenge — Solved
C.4 Chapter 16: Challenge Problem Solutions
C.4.1 Vector Basics — Challenge — Solved
C.4.2 Dot and Cross Products — Challenge — Solved
C.4.3 Vector Functions — Challenge — Solved
C.4.4 Vector Fields and the Gradient — Challenge — Solved
C.4.5 Planes and Tangent Planes — Challenge — Solved
C.4.6 Directional Derivatives — Challenge — Solved
C.5 Chapter 17: Challenge Problem Solutions
C.5.1 Arc Length Parameterization — Challenge — Solved
C.5.2 Contours, Orientation, Pointers — Challenge — Solved
C.5.3 The Fresnet–Serret Frame — Challenge — Solved
C.5.4 Lagrange Multipliers — Challenge — Solved
C.5.5 Parametric Surfaces — Challenge — Solved
C.6 Chapter 18: Challenge Problem Solutions
C.6.1 Line Integrals — Challenge — Solved
C.6.2 Conservative Vector Fields — Challenge — Solved
C.6.3 Surface Integrals — Challenge — Solved
C.6.4 Green’s Theorem — Challenge — Solved
C.6.5 The Divergence Theorem — Challenge — Solved
C.6.6 Stokes’ Theorem — Challenge — Solved
Index
