MC
External
Multivariable Calculus
- Author
- Jessica Kuang
- Publisher
- Oxnard College
- Source
- LibreTexts
- License
- CC BY
- Language
- EN
- Category
- Basic Sciences
Contents· 83 sections
- 01: Vectors and the Geometry of Space
- 1.01: Vectors in the Plane
- 1.1E: Exercises for Vectors in the Plane
- 1.02: Vectors in Space
- 1.2E: Exercises for Vectors in Space
- 1.03: The Dot Product
- 1.3E: Exercises for The Dot Product
- 1.04: The Cross Product
- 1.4E: Exercises for The Cross Product
- 1.05: Equations of Lines and Planes in Space
- 1.5E: Exercises for Equations of Lines and Planes in Space
- 1.06: Quadric Surfaces
- 1.6E: Exercises for Quadric Surfaces
- 1.07: Cylindrical and Spherical Coordinates
- 1.7E: Exercises for Cylindrical and Spherical Coordinates
- 1.E: Chapter 1 Review Exercises
- 02: Functions of Multiple Variables and Partial Derivatives
- 2.01: Introduction to Functions of Multiple Variables
- 2.02: Functions of Multiple Variables
- 2.2E: Functions of Multiple Variables (Exercises)
- 2.03: Limits and Continuity
- 2.3E: Exercises for Limits and Continuity
- 2.04: Partial Derivatives
- 2.4E: Partial Derivatives (Exercises)
- 2.05: Tangent Planes Linear Approximations and the Total Differential
- 2.5E: Tangent Planes Linear Approximations and the Total Differential (Exercises)
- 2.06: The Chain Rule for Functions of Multiple Variables
- 2.6E: The Chain Rule for Functions of Multiple Variables (Exercises)
- 2.07: Directional Derivatives and the Gradient
- 2.7E: Directional Derivatives and the Gradient (Exercises)
- 2.08: Taylor Polynomials of Functions of Two Variables
- 2.8E: Taylor Polynomials of Functions of Two Variables (Exercises)
- 2.09: Optimization of Functions of Several Variables
- 2.9E: Optimization of Functions of Several Variables (Exercises)
- 2.10: Constrained Optimization
- 2.10E: Optimization of Functions of Several Variables (Exercises)
- 2.11: Lagrange Multipliers
- 2.11E: Exercises for Lagrange Multipliers
- 03: Multiple Integration
- 3.01: Iterated Integrals and Area
- 3.1E: Iterated Integrals and Area (Exercises)
- 3.02: Double Integrals Over Rectangular Regions
- 3.2.01: Double Integrals Part 1 (Exercises)
- 3.03: Double Integrals Over General Regions
- 3.3.01: Double Integrals Part 2 (Exercises)
- 3.04: Double Integration with Polar Coordinates
- 3.4b: Double Integrals in Polar Coordinates
- 3.4E: Double Integrals in Polar Coordinates (Exercises)
- 3.05: Triple Integrals
- 3.5E: Triple Integrals (Exercises)
- 3.06: Triple Integrals in Cylindrical and Spherical Coordinates
- 3.07: Calculating Centers of Mass and Moments of Inertia
- 3.08: Change of Variables in Multiple Integrals (Jacobians)
- 3.E: Chapter 3 Review Exercises
- 04: Vector-valued Functions
- 4.01: Vector-Valued Functions and Space Curves
- 4.1E: Exercises for Section 12.1
- 4.02: The Calculus of Vector-Valued Functions
- 4.2E: Exercises for Section 12.2
- 4.03: The Calculus of Vector-Valued Functions II
- 4.04: Motion in Space
- 4.4E: Exercises for Section 12.3
- 4.05: Arc Length and Curvature
- 4.5E: Exercises for Section 12.4
- 4.06: Acceleration and Kepler's Laws
- 4.6E: Exercises for Section 12.5
- 4.E: Chapter 4 Review Exercises
- 05: Vector Fields Line Integrals and Vector Theorems
- 5.01: Introduction to Vector Field Chapter
- 5.02: Vector Fields
- 5.2E: Vector Fields (Exercises)
- 5.03: Line Integrals
- 5.3.01: Line Integrals - Part 2
- 5.3E: Line Integrals (Exercises)
- 5.04: Conservative Vector Fields
- 5.4E: Conservative Vector Fields (Exercises)
- 5.05: Green's Theorem
- 5.5E: Green's Theorem (Exercises)
- 5.06: Divergence and Curl
- 5.6E: Divergence and Curl (Exercises)
- 5.07: Surface Integrals
- 5.08: Stokes' Theorem
- 5.09: The Divergence Theorem