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

Problem set 
Problem set 
1 
Parametric equations and curves 


2 
Polar coordinates 


3 
Conic sections 


4 
3D coordinate systems, vectors 


5 
Dot product and cross product 


6 
Equations of lines and planes 


7 
Equations of cylinders and quadratic surfaces 


8 
Vector functions and their derivatives 


9 
Arc length and curvature,
motion in space 


10 
Functions of several
variables 


11 
Partial derivatives 


12 
Tangent planes and linear
approximations 


13 
The chain rule 


14 
Directional derivatives and
the gradient vector 


15 
Minimum and maximum values,
Lagrange multipliers 


16 
Introduction to double
integrals and iterated integrals 


17 
Double integrals 


18 
Applications of double
integrals and surface area 


19 
Triple integrals 


20 
Vector fields 

Questions 
Answers 

21 
Line integrals 

Questions 
Answers 

22 
Green’s theorem 

Questions 
Answers 

23 
Curl and divergence 

Questions 
Answers 

24 
Parametric surfaces 

Notes 
Questions 
Answers 
25 
Surface integrals 

Notes 
Questions 
Answers 
26 
Stokes’ theorem 

Notes 
Questions 
Answers 
27 
Divergence theorem 

Notes 
Questions 
Answers 
28 
Firstorder differential
equations 

Notes 
Questions 
Answers 
29 
Firstorder linear
equations 

Notes 
Questions 
Answers 
30 
Secondorder linear
equations 

Notes 
Questions 
Answers 
31 
Nonhomogenous linear
equations 

Notes 
Questions 
Answers 
32 
Gauss’s law for electricity 

Notes 
Questions 
Answers 
33 
Gauss’s law for magnetism 

Notes 
Questions 
Answers 
34 
Faraday’s law 

Notes 
Questions 
Answers 
35 
AmpereMaxwell law 

Notes 
Questions 
Answers 
36 
The speed of light 

Notes 
Questions 
Answers 