Reading the text:

• Read through the section before the material is covered in class. Even if you don't completely understand the section, at least you know what will be covered.
• After lecture, review your notes, and look back through the section that was covered; if you are still unsure about something, get clarification.
• If something is labeled Theorem, Definition, or has a box around it, it's important.
• Don't skip over the example problems.
• Keep a separate sheet of all the important formulas along with the page numbers so you can refer back to them later if you need to.
• If you plan to continue with math, don't skip over proofs!
• If you come across something you don't understand, make a note and ask the instructor or TA.

Homework:

• Form a study group or exchange emails and/or phone numbers early in the term.
• Give yourself at least a couple of days to do the homework. If you have questions, you'll have plenty of time to email classmates or discuss them during your study session.

Studying for a test and taking exams:

• Definitions are really important; know what they are and how to use them.
• Review homework and/or chapter review problems.
• Look through the examples in the chapters, and know how they arrived at each step. Also, know how, when given a word problem, to set up the equations. In other words, know the applications really well.

On the exam:

• If the formulas aren't given, write the important ones on the top before you look over the test. Formulas are sometimes hard to remember under pressure.
• If you have time at the end, double check your answers, no matter what!
• If you come across something you can't remember, move on; another problem/section of the test might jog your memory.
• Know how to use your calculator! The TI-89, for example, can be used to find derivatives and integrals. This doesn't mean you don't have to show work; it's just a great way to double check your work.

Things to have a firm grasp of:

Limits

• Definition of a limit
• Does a limit exist? ($\lim_{x \to c^+} f(x) = \lim_{x \to c^-} f(x)$; limit as x approaches c from the right is equal to the limit as x approaches c from the left).
• How to evaluate infinite and finite limits (i.e., $\lim_{x \to \infty} f(x)$ and $\lim_{x \to c} f(x)$ where c is a constant)
• Know the special cases (indeterminate forms and L'Hospital's Rule, removable discontinuities, etc.)
• Properties/Laws of limits

Continuity:

• Definition of continuity and discontinuity
• Test for continuity ($\lim_{x \to c^+} f(x) = \lim_{x \to c^-} f(x) = f(c)$ where c is constant)
• Left continuity vs. right continuity
• Continuity on an interval

Derivatives:

• Definition of a derivative
• When you can take a derivative (continuity must exist)
• Derivative of a function using limits ($f'(a) = \lim_{h \to 0} \frac{f(a+h) - f(a)}{h}$)
• Derivative rules: power rule, chain rule, constant multiple rule, difference rule, product/quotient rule, etc.
• Finding maximums and minimums (concavity, second derivatives)
• Derivatives of trig functions
• Implicit differentiation
• Special cases (derivative of e, logs, exponents, etc.)

Applications:

• Rate of change in volume/area/length/etc. are common applications of derivatives
• Optimization problems
• The chapters usually have great application examples; look through them carefully and know how they arrived at each step. The chapter problems are also great practice.