Math 213 Fall 2023

In-Class Lecture Notes

Here you will find lecture notes from Professor Perry's Fall 2023 Math 213 class. Further information, including syllabus, calendar, and assignments, can be found on this couse's canvas page.

Although I've made every effort to eliminate errors, please read carefully and critically!

If you have questions, corrections, or suggestions, please e-mail me at pperr0@uky.edu.

Peter Perry

Unit A: Vectors, Curves, and Surfaces in Space

• Lecture 1: Coordinates in Space
• Lecture 2: Vectors
• Lecture 3: Dot Products
• Lecture 4: Cross Products
• Lecture 5: Planes
• Lecture 6: Lines in Space
• Lecture 7: Curves in Space
• Lecture 8: Integrating along Curves, I
• Lecture 9: Integrating along Curves, II
• Lecture 10: Graphing Surfaces
• Lecture 11: Cylinders and Quadric Surfaces
• Lecture 12: Functions of Two Variables
• Lecture 13: Exam 1 Review

Unit B: Differential Calculus for Functions of Several Variables

• Lecture 14: Partial Derivatives
• Lecture 15: Higher-Order Derivatives
• Lecture 16: The Chain Rule
• Lecture 17: Tangent Planes
• Lecture 18: Approximation
• Lecture 19: Directional Derivatives and the Gradient
• Lecture 20: Local Maxima and Minima
• Lecture 21: Global Maxima and Minima
• Lecture 22: Lagrange Multipliers
• Lecture 25: Exam 2 Review

Unit C: Multiple Integrals

• Lecture 23: Double Integrals
• Lecture 24: Double Integrals in Polar Coordinates
• Lecture 26: Triple Integrals
• Lecture 27: Triple Integrals in Cylindrical Coordinates
• Lecture 28: Triple Integrals in Spherical Coordinates
• Lecture 28: The Cored Apple Problem
• Lecture 29: Double and Triple Integrals in General Coordinates
• Lecture 30: Vector Fields
• Lecture 31: Conservative Vector Fields
• Lecture 32: Line Integrals
• Lecture 36: Exam 3 Review

Unit D: Vector Calculus

• Lecture 33: Parametrized Surfaces
• Lecture 34: Tangent Planes
• Lecture 35: Surface Integrals
• Lecture 37: Gradient, Divergence, and Curl
• Lecture 38: The Divergence Theorem
• Lecture 39: Green's Theorem
• Lecture 40: Stokes' Theorem I
• Lecture 41: Stokes' Theorem II

Final Exam Review

• Lecture 42: Semester Review, Part I: Basics, Differentiation, Integration
• Lecture 43: Semester Review, Part II: Vector Calculus

Copyright © 2023 by Peter Perry