Calculus 3

What you will learn

• •The evaluations of line integrals, double integrals, and triple integrals and the application of these evaluations (to e.g., electromagnetic topics in physics).
• •For double integrals and triple integrals, the change of variables (coordinates). The evaluations of triple integrals using (rectangular), cylindrical coordinates, and spherical coordinates.
• •Gradient theorem, i.e., the fundamental theorem of calculus for line integrals, and certain conservative fields: seeing the Newton-Leibniz formula as a special case; applying the theorem to calculate certain line integrals; application to gravity field and electric field (understand and calculate potential energy).
• •Green-Gauss theorem, i.e., divergence theorem: seeing the Newton-Leibniz formula as a special case; applying the theorem to calculate line integrals and surface integrals; flux integral over curves and surfaces; applying the theorem to get Gauss law for electric field.
• •Stokes' theorem, i.e., the fundamental theorem for curls: seeing that Newton-Leibniz, Gradient, Green-Gauss and Stokes' theorems are essentially the same thing; calculation of certain line integrals; getting the Maxwell–Faraday equation from Faraday's law of induction; getting the Maxwell–Ampère equation from its integral form.

How it is graded

Week by week