Calculus III -Math 241 E1H




Time/Location: MTWTh, 1.00-1.50 pm, Altgeld Henry 343

Instructor: Marius Junge, Altgeld  363,  Office hour, Wednesday 5pm-5.50pm

Text: Stewart: Calculus early transcendentls (mostly for exercises), and we will use webasign for homeworks.

Grading: Hw 30%, Midterm+ Quiz 40%, Final 30%.


Topics


1. Intro, Linear Algebra in 2D:
spanning vectors, matrices, areas, determinants, change of basis1,  
change of basis2


2. Curves:  Vector funtions,  paramatrization, derivatives, vector field, arclength, curvature, moving frame


3. Differentiation (parts of chapter 13 and 14):
Differentiation of vector functions, Curvature, Motion in Space
Differentiation of functions of several variables, Defintion, partial derivatives, Chain rule,
approximation, gradient vector, tangent planes, Lagrange multipliers
higher order derivatives

4. Linear algera in 3D: general independence and GS-method, cross and dot product
5. Integration: Integration of multivariate functions (this contains two approaches one with Riemann sums and one with upper and lower sums)
Examples, Fubini,  polar coordinates, domains  (cylindrical coordinates)

Triple Integrals and change of variables, Surface integrals.

6.
Vector claculus: Fudamental theoreom and its variations:  Green's theorem,  Stokes's theorem , Curl and Div, Surface areas
General Stokes and differential forms , graphsurfaces, Divergence theorem,
Differential forms and vector fields,Maxwell,Helmholtz












Course hotline (email to students and instructor):  Share your questions on homework, course material,  homework problems will only be
discussed after explicit request.

Homework (always Thursdays)

Hw1, Hw2, Hw3,  Hw4Hw5Hw6Hw7, Hw8Hw9Hw10Hw11, Hw12, Hw13, 

Material  Matrix multiplication,

 Examples


Practice problems


Updated solutions


Finalexamproblemsandsolutions



Courses webpage







Department of Mathematics