SUNY Geneseo Department of Mathematics

Math 223 01, Calculus 3

Fall 2022
Prof. Doug Baldwin

A curved surface that bends up moving across it in one direction and down moving in the perpendicular direction

A “hyperbolic paraboloid” surface, plotted by Doug Baldwin using Wolfram Mathematica.

Welcome to Prof. Baldwin’s multivariable calculus course (or, more formally, SUNY Geneseo’s fall 2022 Math 223 01, Calculus 3). Use the links below to access the notes and other materials for this course.

Introduction
3D Analytic Geometry
- Topic: 3D Rectangular Coordinates
- Topic: Quadric Surfaces
  - 09/06 - Quadric Surfaces
- Topic: Other Coordinate Systems
  - 09/07 - Cylindrical and Spherical Coordinates
Vectors
- Topic: Introduction
  - 09/08 - Vectors in 3 Dimensions
  - Problem Set 2 - Introduction to Vectors
- Topic: The Dot Product
  - 09/12 - Dot Products
- Topic: The Cross Product
  - 09/13 - The Cross Product
- Topic: Lines and Planes
Vector-Valued Functions
- Topic: Introduction
  - 09/20 - Introduction to Vector-Valued Functions
- Topic: Limits of Vector-Valued Functions
  - 09/21 - Limits and Continuity
- Topic: Derivatives of Vector-Valued Functions
  - 09/23 - Derivatives
  - Problem Set 4 - Vector-Valued Functions
- Topic: Integrals of Vector-Valued Functions
  - 09/26 - Integrals
- Topic: Arc Length
  - 09/27 - Arc Length
- Topic: Curvature
  - 09/28 - Curvature
  - Problem Set 5 - Arc Length and Curvature
Derivatives of Multivariable Functions
- Topic: Introduction
  - 09/30 - Introduction to Multivariable Functions
  - 10/03 - Plotting Multivariable Functions
- Topic: Limits
  - 10/04 - Limits of Multivariable Functions
  - 10/05 - Limits that Don’t Exist
- Topic: Partial Derivatives
- Topic: Tangents
  - 10/14 - Tangent Planes
- Topic: The Chain Rule
  - 10/17 - The Chain Rule
  - Problem Set 7 - Partial Derivatives
- Topic: Directional Derivatives
  - 10/18 - Directional Derivatives
- Topic: Gradients
  - 10/19 - The Gradient
- Topic: Extreme Values
- Topic: Optimization
Integrals of Multivariable Functions
- Topic: Integration over Rectangular Regions
  - 10/31 - Introduction to Multivariable Integration
  - 11/01 - Applications of Integrals
- Topic: Integration over General Regions
- Topic: Polar Coordinates
  - 11/07 - Integration in Polar Coordinates
  - 11/08 - More Integration in Polar Coordinates
- Topic: Mass and Moment
  - 11/09 - Mass and Moment
- Topic: Scalar Line Integrals
Vector Calculus
- Topic: Vector Fields
  - 11/15 - Introduction to Vector Fields
  - 11/16 - Gradient Fields
- Topic: Vector Line Integrals
  - 11/18 - Vector Line Integrals
  - 11/21 - Flux and Circulation
- Topic: Potential Functions
- Topic: Green’s Theorem
  - 11/29 - Circulation Form of Green’s Theorem
  - 11/30 - Flux Form of Green’s Theorem
- Topic: Divergence and Curl
- Topic: Parametric Surfaces