| Objectives: |
The objective is for students to become familiar with multivariable functions, apply the concepts of limits, continuity, and derivatives—which they have learned in the context of single-variable functions—to multivariable functions, interpret their graphs, and calculate surface area and volume using various methods involving integrals. |
| Content: |
Definite and Indefinite Integrals: Solutions and Applications, Area Between Curves, Lengths of Curves in the Plane, Finding Volume by Slicing and Rotation Around an Axis, Finding Volume Using Cylindrical Shells, Areas of Surfaces of Revolution, Generalized Integrals, Multivariable Functions, Limits and Continuity in Higher Dimensions, Partial Derivatives, the Chain Rule, Directional Derivatives and Gradient Vectors, Tangent Planes and Differentials, Extremum Values and Saddle Points, the Second Derivative Test for Extremum Values Translated with DeepL.com (free version) |