## Section 3 Course Objectives and Student Learning Outcomes

The main objective of Calculus 3 is to combine ideas of calculus and geometry to deal with functions whose values are a point in the plane or space (a vector), and functions whose arguments are several variables or a vector. These ideas are applied to study curves in space, motion, minimizing functions of several variables and functions defined on surfaces in space, and integrals over solids and surfaces. This material is covered in Chapters 12 to 16 of the text

*Calculus: Early Transcendentals*(6th Ed.) by James Stewart, except omitting Section 15.5. Students are expected to prepare for class by doing the reading assignments described below, and to practice what is learnt in class by doing all the recommended homework exercises, not just the ones to be handed in for grading.By the end of the course, students should be able to:

- Identify, sketch and parametrize surfaces and space curves. Identify and plot vector fields.
- Algebraically manipulate vectors using the dot product, scalar product and cross product to answer geometric questions.
- Apply differentiation and integration to parametrized curves to draw conclusions about the geometry of the curve or about the trajectory of a particle.
- Compute, interpret, and apply various kinds of derivatives of multi-variable functions (whether scalar functions or vector functions).
- Solve multi-variable optimization problems, both constrained and unconstrained.
- Set up, evaluate, and apply integrals over two or three dimensional regions, using various coordinate systems and various orders of integration.
- Convert multiple integrals between different orders of integration and/or different coordinate systems.
- Evaluate and apply line integrals and surface integrals of both scalar functions and vector fields.
- Evaluate integrals by selecting an appropriate version of the Fundamental Theorem of Calculus (FTC for Vector Fields, Green's Theorem, Stokes' Theorem, or the Divergence Theorem) to transform the integral into an easier one with a domain of integration having a different dimension.

These outcomes will be assessed on the final exam.