Homework 2 (due Wednesday Jan 20 at 6pm ) Homework 0 ( review of 20C - NOT to be turned in) ![]() Gauss's theorem (FTC for divergence in 3d) Conservative fields (idea of scalar and vector potential)Ĩ.4. Stokes's theorem (FTC for curl in 3d)Ĩ.3. Integral of F.dA (e.g for computing flux of a vector field through a surface)Ĩ.1. for computing average value of f over a surface)ħ.6. ![]() for computing average value of f over a curve)ħ.5. work done by force as object moves along a path)ħ.2. Divergence and curl: in 3d space, the only two geometrically-meaningful kinds of derivative other than gradientħ.1. The change of variables formula for integrals (multivariable "integration by substitution")Ĥ.4. Maps between Euclidean spaces changes of coordinate systemĦ.2. Triple integrals over funny-shaped regions.Ħ.1. The trick of switching the order of integrationĥ.5. Double integrals over more complicated shapes. Taylor series for multivariable functionsĥ.3. ![]() The derivative of a function of several variables.ģ.2. Basic stuff about differentiation - mostly revision, but very important!Ģ.3. Scalar- and vector-valued multivariable functions, graphs and level setsī. Cylindrical and spherical coordinatesĢ.1. ![]() Revision of prerequisites from 20C. (I won't lecture on this, but check you understand it by doing HW 0 (not for credit) below.)ġ.4. The same techniques are incredibly useful in all parts of the physical sciences.Ī. The language of vector calculus gives us powerful methods for writing and working with these equations in a way that doesn't depend on what coordinate system we use and lets us understand the intrinsic geometrical meaning of the various terms. The main ideas all originated from the 19th century study of electromagnetism, and the culmination of the course is seeing how to combine various simple experimental observations about EM fields to arrive at Maxwell's equations, the partial differential equations governing EM theory. This course continues directly on from 20C and concerns calculus primarily in three dimensions. In 20C you learned about functions of several variables and their partial derivatives.
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