MCC: MTH 212 Calculus III

A standard course in multivariable calculus that starts with vectors operations and vector-valued functions, continues through functions of multiple variables, partial derivatives, multiple integration, vector fields, and vector theorems.

Mathematics

Author: Paul Seeburger
Publisher: Monroe Community College
Source: LibreTexts
License: CC BY-NC-SA
Language: EN
Category: Basic Sciences

Read online Download PDF (open licence)

Contents· 92 sections

Chapter 11: Vectors and the Geometry of Space
11.1: Vectors in the Plane
11.1E: Exercises for Vectors in the Plane
11.2: Vectors in Space
11.2E: Exercises for Vectors in Space
11.3: The Dot Product
11.3E: Exercises for The Dot Product
11.4: The Cross Product
11.4E: Exercises for The Cross Product
11.5: Equations of Lines and Planes in Space
11.5E: Exercises for Equations of Lines and Planes in Space
11.6: Quadric Surfaces
11.6E: Exercises for Quadric Surfaces
11.7: Cylindrical and Spherical Coordinates
11.7E: Exercises for Cylindrical and Spherical Coordinates
11R: Chapter 11 Review Exercises
Chapter 12: Vector-valued Functions
12.1: Vector-Valued Functions and Space Curves
12.1E: Exercises for Section 12.1
12.2: The Calculus of Vector-Valued Functions
12.2E: Exercises for Section 12.2
12.2B: The Calculus of Vector-Valued Functions II
12.3: Motion in Space
12.3E: Exercises for Section 12.3
12.4: Arc Length and Curvature
12.4E: Exercises for Section 12.4
12.5: Acceleration and Kepler's Laws
12.5E: Exercises for Section 12.5
12R: Review Exercises for Chapter 12
12Rz: More Review Exercises for Chapter 12
Chapter 13: Functions of Multiple Variables and Partial Derivatives
13.0: Introduction to Functions of Multiple Variables
13.1: Functions of Multiple Variables
13.1E: Functions of Multiple Variables (Exercises)
13.2: Limits and Continuity
13.2E: Exercises for Limits and Continuity
13.3: Partial Derivatives
13.3E: Partial Derivatives (Exercises)
13.4: Tangent Planes Linear Approximations and the Total Differential
13.4E: Tangent Planes Linear Approximations and the Total Differential (Exercises)
13.5: The Chain Rule for Functions of Multiple Variables
13.5E: The Chain Rule for Functions of Multiple Variables (Exercises)
13.6: Directional Derivatives and the Gradient
13.6E: Directional Derivatives and the Gradient (Exercises)
13.7: Taylor Polynomials of Functions of Two Variables
13.7E: Taylor Polynomials of Functions of Two Variables (Exercises)
13.8: Optimization of Functions of Several Variables
13.8E: Optimization of Functions of Several Variables (Exercises)
13.9: Applications of Optimization Constrained Optimization and Absolute Extrema
13.9E: Optimization of Functions of Several Variables (Exercises)
13.A: Lagrange Multipliers
13.10E: Exercises for Lagrange Multipliers
13R: Chapter 13 Review Exercises
Chapter 14: Multiple Integration
14.1: Iterated Integrals and Area
14.1E: Iterated Integrals and Area (Exercises)
14.2a: Double Integrals Over Rectangular Regions
14.2aE: Double Integrals Part 1 (Exercises)
14.2b: Double Integrals Over General Regions
14.2bE: Double Integrals Part 2 (Exercises)
14.3: Double Integration with Polar Coordinates
14.3b: Double Integrals in Polar Coordinates
14.3E: Double Integrals in Polar Coordinates (Exercises)
14.4: Triple Integrals
14.4E: Triple Integrals (Exercises)
14.5: Triple Integrals in Cylindrical and Spherical Coordinates
14.5E: Exercises for Section 14.5
14.6: Calculating Centers of Mass and Moments of Inertia
14.6E: Exercises for Section 14.6
14.7: Change of Variables in Multiple Integrals (Jacobians)
14.7E: Exercises for Section 14.7
14R: Review Exercises for Chapter 14
More Chapter 14 Review Exercises
Chapter 15: Vector Fields Line Integrals and Vector Theorems
15.0: Introduction to Vector Field Chapter
15.1: Vector Fields
15.1E: Exercises for Section 15.1
15.2: Line Integrals
15.2: Line Integrals - Part 2
15.2E: Exercises for Section 15.2
15.3: Conservative Vector Fields
15.3E: Exercises for Section 15.3
15.4: Green's Theorem
15.4E: Exercises for Section 15.4
15.5: Divergence and Curl
15.5E: Divergence and Curl (Exercises)
15.6: Surface Integrals
15.6E: Exercises for Section 15.6
15.7: Stokes' Theorem
15.7E: Exercises for Section 15.7
15.8: The Divergence Theorem
15.8E: Exercises for Section 15.8