**Advanced Calculus II**

“Consider an infinitesimal paddle wheel…”

**Text: **(none)

**Prof:** Dr. Joel Feldman

Dr. Joel Feldman strikes a great balance between being really organized, while still pretty relaxed. He is very helpful, in that he is always available between classes for questions. He is also really knowledgeable about the field (as he is a mathematical physicist) which is great, though he did give us a particularly tragic expression when we said we didn’t know what curl was, halfway through the course and he had to explain it.

**Difficulty**

The weekly assignments are generally all straightforward. The questions vary from computational to small proofs. I missed the first midterm, but a lot of people got wrecked, and it looked tough so watch out. Each question in the second midterm was manageable, though it required thinking. The challenge is that there are only four questions, so the cost of getting one question completely wrong is quite high. The final was similar except it had more questions. The challenge then was that often it was not clear which of the various techniques we had learned in the course was the correct approach to a question.

**Key Concepts**

Analysing/ parameterizing curves in 2,3-space

Analysing/ parameterizing surfaces in 3-space

Analysing/ parameterizing vector fields in 3-space

Integrating over curves, vector fields, and surfaces

Integral Theorems

** Hard Concepts**

Applications of integral theorems: Hard to pick the right strategy that is going to work.

Biot-Savart Law: Really abstract, not sure if I understood it.

**Conclusion**

Feels like a fun physics course. Wish we had more time to discuss differential forms, but other than that pretty interesting class.