2.3 understanding the derivative homework

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. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike License. We recommend using aĪuthors: Gilbert Strang, Edwin “Jed” Herman Use the information below to generate a citation. Then you must include on every digital page view the following attribution: If you are redistributing all or part of this book in a digital format,

Then you must include on every physical page the following attribution: If you are redistributing all or part of this book in a print format, Want to cite, share, or modify this book? This book uses theĬreative Commons Attribution-NonCommercial-ShareAlike License

2.3 understanding the derivative homework