Calculus 3

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)

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