The student is able to (especially w.r.t. functions of two or three variables):
- work with partial derivatives and applications.
- define and evaluate double and triple integrals over bounded regions
Calculus 2 is the continuation of Calculus 1A and 1B, and is followed by Vector Calculus course in Module 5.
The course introduces material and techniques needed in topics such as classical mechanics, thermodynamics, fluid dynamics, and probability theory. In this course, the main subjects are differentiation and integration of functions that depend on more than one independent variable.
The first part of the course focuses on differentiation. More specifically, the topics are partial differentiation, its definition, computation techniques (such as the chain rule, implicit differentiation). Applications such as linearizing and approximating multivariate functions via Taylor's formula, finding tangent planes and normal lines to a surface. Finally, detecting and classifying critical points and computing extreme values of a function.
The second part of the course focuses on multiple integrals, which are defined as limits of Riemann sums. Multiple integration is used, for example, to find areas or volumes of bounded regions in the plane or in the space. Emphasis is given on the description of bounded and unbounded regions in different coordinate systems.
Finally, the course focuses on finding the center of mass of a body with emphasis on how to detect and employ symmetries to simplify computations.