I will take advancad calculus next semester, in this course, after completing the coverage of basic theorems about integration on R^n, the fundamental theorems of vector calculus are presented. Some of the topics are: Chage of Variables Theorem, Green, Gauss and Stokes's Theorems on parametric curves/surfaces (in 2 and 3 dimensions), tensors, differential forms, the general form of Stokes's Theorem.
Course content: change of variables, parametric curves and surfaces, Green, Gauss and Stokes's Theorems (in 2 and 3 dimensions), Tensors, Differential forms ,exterior derivative, Revisiting Stokes's Theorem.
Can you reccommend books for beginners, online notes and can you give me advice that how should I study this course? Thanks...
We used Marsden and Tromba's Vector Calculus my second semester at Berkeley. It covers most if not all of the mentioned topics. I would recommend it.
Make sure and attend all of the lectures. Work lots of examples. Go over the problems with fellow students, a TA, or anyone else in the know. It helps to have people to talk to.