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.

Frequently Asked Questions

Q:How much should I study?
A:That depends on the individual. In one study, successful students put in about 14-15 hours per week outside of class to get an A; some more, some less. Keep up with the class. Cramming doesn't work.
Q:I don't like my Graduate Student Instructor (GSI). Can I get into another section?
A:No, it is normally impossible to switch sections during the semester. Instead, you should find another student to work with. You can ask the Student Learning Center (SLC) if they have study groups for your class. They also provide free drop-in tutoring during the day. In addition, free drop-in tutoring is available at the Academic Centers located in the dorms.
Q:I thought I knew the material, but I did poorly on the midterm. Can I still get an A?
A:Not necessarily, ask your GSI how you're doing. Remember, it's hard to get an A. If you decide to stay, change your study habits, join a study group, and solve lots of extra problems.
Q:My professor goes too fast in lecture and I get lost. What should I do?
A:If you are behind, catch up on your reading. In addition, it's amazing how much reading before the lecture helps. You don't have to know it all; skimming the main ideas will enable you to follow the lecture.
Q:The lectures are useless because the professor doesn't show me how to do the homework problems.
A:The purpose of the lecture is not to show you how to solve simple problems, but to give you the tools to attack difficult problems. Typically these involve a combination of techniques from several sections and require theoretical understanding. On the exams, some or even all of the problems may be of this type. It is inefficient (as well as foolish) to try to memorize solutions to problems. What matters is the attack.
Q:I'm terrified of my professor and afraid to go to office hours; my professor seems impatient and will not show me how to do the problems.
A:Most math professors are happy to help you if you have struggled with the problem. However, do not expect them to solve the problem for you. They want to see that you've spent more than two minutes on in and looked at the theory in the book so you can ask a precise question. ``I can't do #5'' will not advance the conversation.