Calculus 1 (Math 220) Tips

I would just say to do lots of problems. I got a lot better in my calculus classes once I resolved to do all of the problems in the textbook in each section as we were covering it. Some of the problems you can skip over if they are just re-hashing the same thing that you've solved in other problems in that section, but be sure to do all of the last ones, which are usually the hardest. :-)

 

Drakkith, you're going to be spending a lot of time with the derivative. Some important concepts are the slope of the tangent line to a curve, and the slope of a secant line joining two points on a curve. The derivative (which is the slope of a tangent line at some point on a curve) is the limit of the slopes of a secant line as one point is moved toward a particular point.

After the derivative is presented, as the limit of a difference quotient (the difference quotient gives the slope of a secant line), you will see a bunch of shorthand techniques, including the sum rule, constant multiple rule, product rule, power rule, quotient rule, and chain rule, plus some specialized rules for dealing with functions such as the sine and cosine, exponential and log functions. An important thing to remember is, Always use the simplest rule you can get away with.

For example, if the function is f(x) = x²/2, you might be tempted to use the quotient rule, as it is, after all, a quotient. Resist that urge, and realize that this function is a constant multiple (i.e., multiplied by 1/2) of x². Although the quotient rule is applicable here, it is more complicated, and thus presents more opportunities for mistakes.