Topics You Might Want to Learn
I will be filling in more and more as time goes on so if there isn't any help for the topic you need right now check back later. Each topic will have some sort of help... and explanation, and example, charts, a link... who knows. If you need other help, get back to me or check the sites I've linked to.
(many of
these links will lead to other sites)
Yes this is a lot... but heck you have all year... or well at least a semester right? So don't go crazy quite yet.
Limits and Continuity
algebraic techniques for solving limits
limit theorems: constant, sum, product, quotient
one-sided limits
infinite limits and limits at infinity
relationship between continuity and differentiability
Derivatives
definition of the derivative and at a point
derivative rules: power ... product ... quotient ... chain ... trig
derivation of two rules: d/dx(sin x)= cos x and d/dx(x^n)= nx^(n-1), n a positive integer
derivatives of inverse functions, including inverse trig functions
differentiability and continuity
Derivative Application
tangent and normal lines, slope of curve
average and instantaneous rates of change
curve sketching: increasing, decreasing, relative extrema, concavity, inflection points
differentials
optimization; absolute extrema
position/velocity/acceleration
Rolle's theorem and mean value theorem
relative extrema and the first derivative test
concavity and the second derivative test
Integral Calculus
Riemann sums
approximations for definite integrals: rectangles, trapezoids
fundamental theorems
Applications of Antidervatives and the Definite Integral
fundamental theorem of calculus
position/velocity/acceleration (PVA) in linear motion
differential equations (variables separable)
exponential growth/decay and its derivation: dy/dt = ky <=> y = Ce^kt
area under a curve and between curves
properties of definite integrals
definition of integrals
volume: solids of revolution and solids with known cross sections
average value at a function over an interval