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MATH& 264 - Calculus 4

5 credits

Prerequisites
A grade of “C” or better in MATH& 163 . MATH& 264 is the fourth course of the standard calculus sequence.

Content includes: infinite sequences and series (builds on coverage in MATH& 152 ); cylindrical and spherical coordinates; the general chain rule for functions of several variables; triple integrals in rectangular, cylindrical and sphericle coordinates; vector fields; line integrals; surface integrals; Green’s theorem; Stokes’ theorem; and the Divergence Theorem. Applications are taken from the natural sciences and engineering.

Theory Hours
5 theory hours.

AA Specified Elective
Satisfies science distribution area F requirement or specified elective for the AA degree.

Course Outcomes
• Use the chain rule to compute derivatives and verify formulas
• Compute definite triple integrals in rectangular, cylindrical and spherical coordinates
• Convert between rectangular, cylindrical and spherical coordinates when computing triple integrals
• Use double and triple integrals to compute center of mass, and moments of inertia
• Compute potential functions for conservative fields
• Determine whether a field is conservative or not
• Compute scalar and vector line integrals
• Calculate Work and Flux across a curve using line integrals
• Use the Fundamental Theorem for Conservative Vector Fields appropriately to solve problems
• Compute surface areas using integration
• Compute surface integrals of real functions
• Compute surface integrals of vector fields
• Apply surface integrals to basic fluid mechanics and electric and magnetic fields
• Use Green’s theorem to evaluate line integrals and areas
• Use Green’s theorem to compute the circulation of a vector field
• Use Stokes’ theorem to compute the flux of a vector field through a surface
• Use Stokes’ theorem to compute the circulation of a vector field around the boundary of a surface
• Compute the divergence of a field
• Use the divergence theorem to compute the flux of a vector field through a surface
• Use the divergence theorem to solve basic problems in electrostatics