Advanced Calculus with Physical Applications
A course to follow
differential and integral calculus
Week 
Topic(s) 
Quiz 

Problem set 
Problem set 
1 
Parametric equations and curves 
09/0309/13 

2 
Polar coordinates 
09/0909/13 

3 
Conic sections 
09/1609/20 

4 
3D coordinate systems, vectors 
09/2309/27 

5 
Dot product and cross product 
10/0110/04 

6 
Equations of lines and planes 
10/0710/11 

7 
Equations of cylinders and quadratic surfaces 
10/1610/18 

8 
Vector functions and their derivatives 
10/2110/25 

9 
Arc length and curvature,
motion in space 
10/2811/01 

10 
Functions of several
variables 
11/0411/08 

11 
Partial derivatives 
11/1211/15 

12 
Tangent planes and linear
approximations 
11/1811/22 

13 
The chain rule 
12/0212/06 

14 
Directional derivatives and
the gradient vector 
12/0912/13 

15 
Minimum and maximum values,
Lagrange multipliers 
12/1612/20 

16 
Introduction to double
integrals and iterated integrals 
01/0201/03 

17 
Double integrals 
01/0601/10 

18 
Applications of double
integrals and surface area 
01/1301/16 

19 
Triple integrals 
01/2101/24 

20 
Vector fields 
01/2701/31 

21 
Line integrals 
02/0302/07 
Questions 
Answers 

22 
Green’s theorem 
02/1002/14 
Questions 
Answers 

23 
Curl and divergence 
02/2402/28 
Questions 
Answers 

24 
Parametric surfaces 
03/0203/06 
Questions 
Answers 

25 
Surface integrals 
03/0903/12 
Questions 
Answers 

26 
Stokes’ theorem 
03/1603/20 
Questions 
Answers 

27 
Divergence theorem 
03/2303/27 
Questions 
Answers 

28 
Gauss’s laws 
03/3004/03 
Questions 
Answers 

29 
Faraday’s law 
04/0604/09 
Questions 
Answers 

30 
AmpereMaxwell law 
04/1304/17 
Questions 
Answers 

31 
The speed of light 
04/2705/01 
Questions 
Answers 

32 
Firstorder linear
differential equations 
05/0405/08 
Questions 
Answers 

33 
Applications 
05/1105/15 
Questions 
Answers 

34 
Secondorder linear
differential equations 
05/1805/22 
Questions 
Answers 

35 
Applications 
05/2605/29 
Questions 
Answers 