Vector Calculus (MATH 223)

The Math Department offers free online tutoring for Math 223, Monday-Friday. Click here to see the schedule.

COURSE OBJECTIVES AND LEARNING OUTCOMES:

Course Objectives

• Recognize and sketch surfaces in three-dimensional space;

• Recognize and apply the algebraic and geometric properties of vectors and vector functions in two and three dimensions;

• Compute dot products and cross products and interpret their geometric meaning;

• Compute partial derivatives of functions of several variables and explain their meaning;

• Compute directional derivatives and gradients of scalar functions and explain their meaning;

• Compute and classify the critical points;

• Parameterize curves in 2- and 3-space;

• Set up and evaluate double and triple integrals using a variety of coordinate systems;

• Evaluate integrals through scalar or vector fields and explain some physical interpretation of these integrals;

• Recognize and apply Fundamental theorem of line integrals, Green’s theorem, Divergence Theorem, and Stokes’ theorem correctly.

Expected Learning Outcomes

Upon completion of this course, students should be able to:

• Perform vector operations, determine equations of lines and planes, parametrize 2D & 3D curves.

• Graphically and analytically synthesize and apply multivariable and vector-valued functions and their derivatives, using correct notation and mathematical precision.

• Synthesize the key concepts differential, integral and multivariate calculus.

• Evaluate double integrals in Cartesian and polar coordinates; evaluate triple integrals in rectangular, cylindrical, and spherical coordinates; and calculate areas and volumes using multiple integrals.

• Use double, triple and line integrals in applications, including Green's Theorem, Stokes' Theorem, Divergence Theorem and Fundamental theorem of line integrals.