I took Calc 1 and 2 in high school and passed the AP exam to get credit in college for these courses. I am now in my second semester in college and I recently changed my major, which requires discrete math, linear algebra, and calc 3. The prerequisite at my university for discrete math is calc 1. I haven't had a calc class since senior year of high school (last year)
During the 2011 summer semester I plan on taking discrete math.
So should I do a full review of calc 1 or what parts of calc 1 should I review?
my humble opinion as to what parts of calculus are "important":
the definition of a limit (epsilon-delta). the definition of continuity. the definition of the derivative, you should be able to derive most of the basic formulae. the chain rule. the definition of infimum and supremum (greatest lower bound/least upper bound). the definition of (Riemann) integrable, and how to form some Riemann sums. the mean value theorem, and the intermediate value theorem. the fundamental theorem of calculus. some acquaintance with inverse functions. sequences, infinite series, and the more convergence tests you know, the better. familiarity with exponential, logarithm, trigonometric and polynomial functions. you should be able to differentiate and integrate most of these. Taylor series.
other stuff, if you have time: implicit differentiation, the inverse function theorem, exposure to a construction of the reals from the natural numbers. set theory is always useful. the binomial theorem. you should be comfortable with proofs by induction. some knowledge of complex numbers is helpful. know the difference between a relation, an equivalence relation, and a function. solids and surfaces of revolution (washer and shell methods).
i seriously recommend you give it a thorough going-over. i'll explain. i took AP calculus my junior year. i got a 5 on the test. my senior year i enrolled in calculus II and III at a local university. when i graduated from high school, i received college credit for a full year, and went straight to the second year course. it was called Calc II, and i thought: i've got this. been there, done that. i was so....lost...it took me almost 3 months to figure out what they were talking about. e1? what's this e1? where's x? where's y?
now, this might not happen to you. i don't know your school's program. but typically college math is on a whole different level than high school. they mean business.
It's not very important for introductory stuff. Calculus is based off of continuous things, where as discrete math is based off, well, discrete things. Of course, there are cases when you use calculus ideas like convergence, or the idea of fitting a continuous function to a discrete one and only looking at the points that you're interested in. Really, I don't think that you need to review too much, maby limits.
The best thing would be to talk to the lecturer for the upcoming Discrete Math course or for the past courses. Also, you could look through the textbook.
In the second-year Discrete Math course that I was involved in, we used very limited amount of calculus. The only topic that comes to mind is estimation of function growth and big-O notation. The definition of big-O uses several quantifiers in a row, which is often difficult to comprehend at first. In that, it is similar to the definition of a limit, which uses three quantifiers in a row. The definition of small-o notation does involve limits. In addition, one has to be comfortable proving inequalities involving polynomials, exponentiation and logarithms, but most more complicated facts, like when are given without a proof. Not all of this has to be covered in a Discrete Math course; I saw students struggling with these topics in the fourth-year Analysis of Algorithm course.