Active Calculus – Multivariable Draft Table of Contents
- Chapter 9 Precalculus of Multivariable Functions
- 9.1 Why Multivariable?
- 9.2 Three Dimensional Space
- 9.3 Vectors
- 9.4 The Dot Product
- 9.5 The Cross Product
- 9.6 Lines and Planes in Space
- 9.7 Common Graphs in Two and Three Dimensions
- 9.8 Polar, Cylindrical, and Spherical Coordinates
- Chapter 10 Vector Valued Functions of One Variable
- 10.1 Vector-Valued Functions of One Variable
- 10.2 Calculus of Vector-Valued Functions of One Variable
- 10.3 Arc Length
- 10.4 The TNB Frame
- 10.5 Splitting the Acceleration Vector
- 10.6 Curvature
- Chapter 11 Derivatives of Multivariable Functions
- 11.1 Functions of Several Variables
- 11.2 Limits
- 11.3 First-Order Partial Derivatives
- 11.4 Second-Order Partial Derivatives
- 11.5 Linearization: Tangent Planes and Differentials
- 11.6 The Chain Rule
- 11.7 Directional Derivatives and the Gradient
- 11.8 Optimization
- 11.9 Constrained Optimization: Lagrange Multipliers
- Chapter 12 Multiple Integrals
- 12.1 Double Riemann Sums and Double Integrals over Rectangles
- 12.2 Iterated Integrals
- 12.3 Double Integrals over General Regions
- 12.4 Applications of Double Integrals
- 12.5 Double Integrals in Polar Coordinates
- 12.6 Surfaces Defined Parametrically and Surface Area
- 12.7 Triple Integrals
- 12.8 Triple Integrals in Cylindrical and Spherical Coordinates
- 12.9 Change of Variables
- Chapter 13 Vector Calculus
- 13.1 Vector Fields
- 13.2 The Idea of a Line Integral
- 13.3 Using Parametrizations to Calculate Line Integrals
- 13.4 Path-Independent Vector Fields and the Fundamental Theorem of Calculus for Line Integrals
- 13.5 Line Integrals of Scalar Functions
- 13.6 The Divergence of a Vector Field
- 13.7 The Curl of a Vector Field
- 13.8 Green’s Theorem
- 13.9 Flux Integrals
- 13.10 Surface Integrals of Scalar Valued Functions
- 13.11 Stokes’ Theorem
- 13.12 The Divergence Theorem
