Spring 2023 Math 223 Outline

A saddle-shaped surface

Hyperbolic paraboloid plotted in Mathematica by Doug Baldwin.

Welcome to Prof. Baldwin’s multivariable calculus course (or, more formally, SUNY Geneseo’s spring 2023 Math 223, Calculus III). Use the links below to access the elements of the course.

Introduction
3D Analytic Geometry
- Topic: 3D Coordinates
- Topic: Quadric Surfaces
  - 01/31 - Quadric Surfaces (and Cylinders)
  - 02/01 - Quadric Surfaces (and Cylinders), Part 2
- Topic: Cylindrical and Spherical Coordinates
  - 02/03 - Cylindrical and Spherical Coordinates
  - Problem Set 2 - 3D Surfaces
Vectors
- Topic: Introduction
  - 02/06 - Vectors in 3 Dimensions
- Topic: The Dot Product
  - 02/07 - Vectors and Dot Products
  - 02/08 - Dot Product Applications
- Topic: The Cross Product
  - 02/10 - The Cross Product
  - Problem Set 3 - Vectors
- Topic: Lines
  - 02/13 - Lines in Space
  - 02/14 - More About Lines
- Topic: Planes
Vector-Valued Functions
- Topic: Introduction
  - 02/20 - Introduction to Vector-Valued Functions
- Topic: Limits
  - 02/21 - Limits of Vector-Valued Functions
- Topic: Derivatives
  - 02/22 - Derivatives of Vector-Valued Functions
- Topic: Integrals
- Topic: Arc Length
  - 03/01 - Arc Length
- Topic: Curvature
  - 03/03 - Curvature
  - Problem Set 6 - Arc Length and Curvature
Derivatives of Multivariable Functions
- Topic: Multivariable Functions
  - 03/06 - Introduction to Multivariable Functions
- Topic: Limits of Multivariable Functions
  - 03/07 - Limits
  - 03/08 - Limits that Don’t Exist
- Topic: Partial Derivatives
  - 03/10 - Partial Derivatives
  - Problem Set 7 - Multivariable Functions
- Topic: Higher-Order Derivatives
  - 03/20 - Higher-Order Derivatives
- Topic: Tangents
- Topic: The Chain Rule
  - 03/24 - The Chain Rule
- Topic: Directional Derivatives
  - 03/27 - Directional Derivatives
  - 03/28 - Directional Derivatives Part 2
- Topic: The Gradient
  - 03/29 - The Gradient
  - Problem Set 9 - Gradients and Directional Derivatives
- Topic: Extreme Values
- Topic: Lagrange Multipliers
  - 04/05 - Lagrange Multipliers
  - Problem Set 10 - Optimization
Integrals of Multivariable Functions
- Topic: Rectangular Regions
  - 04/07 - Introduction to Multiple Integrals
  - 04/10 - Integrals and Volume
- Topic: General Regions
- Topic: Polar Coordinates
  - 04/17 - Double Integrals in Polar Coordinates
- Topic: Scalar Line Integrals
Vector Calculus
- Topic: Vector Fields
  - 04/21 - Vector Fields
- Topic: Vector Line Integrals
  - 04/24 - Line Integrals and Vector Fields
  - 04/25 - Flux
- Topic: Conservative Fields
  - 04/28 - Conservative Fields (and Circulation)
  - Problem Set 13 - Conservative Vector Fields
- Topic: Potential Functions
  - 05/01 - Finding Potential Functions
- Topic: The Fundamental Theorem of Line Integrals
  - 05/02 - The Fundamental Theorem for Line Integrals
- Topic: Green’s Theorem
- Topic: Divergence and Curl
  - 05/10 - Divergence and Curl