Survival Guide to Calculus

by O. Hald

Students may have taken calculus in high school and have done well. So they might expect university-level calculus to be straightforward. However, a majority of the students find themselves struggling and every year many students fail. Why? Because college is not high school.

To do well, students must change their mindsets. Memorization is not enough! Don't expect to be spoon-fed by the professors. To succeed, students must pay attention to the theory and be able to work by themselves.

Students' Expectations Professors' Response
Professors should explain everything in class and go over the materials slowly so that we can understand every detail. Unfortunately, we can't teach everything because there isn't enough time. It is your responsibility to learn the materials outside of class. The pace of the class is dictated by the syllabus and is at least twice as fast as high school.
Since I know calculus from high school, I don't need to read the book. This is the easiest trap to fall into and the hardest ot get out of. High school calculus tends to be superficial. At Berkeley, we demand much more every inch of the way. But students don't realize it until it is too late. Advice: Read the textbook as if you are learning it for the first time.
I know how to differentiate, why should I bother with the theory? The course is more than just differentiating a few functions. You might scrape by without a clear grasp of the theory but you can't solve ``never before seen'' problems. Real-world problems do not come in nice packages. To formulate such problems clearly, you need a firm grasp of the theoretical concepts. Without that, you'll do poorly on the exams.
If I attend the lectures and do the homework, I should do well on the exams. Only if you understand the lectures, understand the theory behind the homework solutions, and understand why each homework problem is solved in that particular way. Exams test your knowledge and understanding of the theory and not your memorizations skills. Not all the exam problems are similar to the homework.
In high school we solved problems like: Let y=x-2x2. Which x gives the biggest y? That's good. Can you also solve: Let y2=x-2x2y. Find (x,y) so that y is as large as possible.