MATH& 264 Calculus 4

• Find local and absolute extrema of functions of two variables using the Second Derivatives Test, substitution, and the Lagrange Multiplier Method.
• Use double integrals to represent areas of regions, and compute them in rectangular and polar coordinates.
• Use triple integrals to represent volumes of solids, and evaluate them in Cartesian, cylindrical, and spherical coordinates.
• Apply double and triple integrals to basic physics, such as finding mass and center of mass.
• Perform general change of variables in double and triple integrals.
• Sketch and interpret vector fields in two and three dimensions, and calculate and interpret their curl and divergence.
• Compute and interpret line integrals of scalar and vector fields, and apply the Fundamental Theorem for Line Integrals and Green’s Theorem.
• Describe surfaces parametrically and calculate their surface areas. Calculate and interpret surface integrals of scalar and vector fields.
• Apply Stokes’ Theorem and the Divergence Theorem to evaluate line, surface, and multiple integrals and to describe behavior in velocity, electric, and other fields.