Advanced topics in calculus, including vectors and vector-valued functions, partial differentiation, Lagrange multipliers, multiple integrals, and Jacobians; application of the line integral, including Green's Theorem, the Divergence Theorem, and Stokes' Theorem.
Note: The notes will be based on a different version of the textbook. (LAST UPDATED JUNE 2025)
Calculus: Early Transcendentals 3rd Edition (Briggs) - Chapters 13-17
Textbook Link| Full Calculus 3 Notes |
| Chapter 1 - Vectors and the Geometry of Space (8/26/24 - 9/10/24) |
Three-Dimensional Coordinate Systems Vectors The Dot Product The Cross Product Equations of Lines & Planes Cylinders & Quadric Surfaces |
Notes |
| Chapter 2 - Vector-Valued Functions (9/11/24 - 9/23/24) |
Vector-Valued Functions Calculus of Vector-Valued Functions Motion in Space Length of Curves Curvature and Normal Vectors |
Notes |
| Chapter 3 - Functions of Several Variables (9/24/24 - 10/16/24) |
Graphs and Level Curves Limits and Continuity Partial Derivatives The Chain Rule Directional Derivatives and the Gradient Tangent Planes and Linear Approximation Maximum/Minimum Problems Lagrange Multipliers |
Notes |
| Chapter 4 - Multiple Integration (10/17/24 - 11/11/24) |
Double Integrals over Rectangular Regions Double Integrals over General Regions Double Integrals in Polar Coordinates Triple Integrals Triple Integrals in Cylindrical and Spherical Coordinates Integrals for Mass Calculations Change of Variables in Multiple Integration |
Notes |
| Chapter 5 - Vector Calculus (11/12/24 - 12/11/24) |
Vector Fields Line Integrals Conservative Vector Fields Green's Theorem Divergence and Curl Surface Integrals Stokes' Theorem Divergence Theorem |
Notes |