Math 223 - Vector Calculus

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.