Casual Calculus A Friendly Student Companion Volume 3

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