Jan 18, 2022
MATH& 264 - Calculus 4
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.
5 theory hours.
AA Specified Elective
Satisfies science distribution area F requirement or specified elective for the AA degree.
- 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
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