Pre-Calc Cncpts.    Calculus Cncpts.        Reference Sheet        Message Brd.

On this page, we've listed important concepts with which you should be comfortable.  For a basic understanding of Calculus I, you should be comfortable with the following concepts: The cartesian plane and functions The real number line The cartesian plane and the distance formula Lines in the plane; slope Circles Graphs of equations Functions Limits Limits Continuity Limits & asymptotes Curve sketching Differentiation The derivative as the slope of a curve Differentiability and continuity The derivative as a rate of change Higher order derivatives The product and quotient rules Position - velocity - acceleration functions The chain rule and the general power rule Implicit differentiation Related rates Applications of differentiation Extrema on an interval The mean value theorem Increasing and decreasing functions The first derivative test Concavity & the second derivative test Limits at infinity (horizontal asymptotes) Curve sketching (including extrema & concavity) Optimization problems (max/min problems) Newton's method Differentials Integration The indefinite integral U-substitution and the general power rule The fundamental theorem of calculus Area and the definite integral Trapezoid rule Applications of integration Average value of a function Area between two curves Volumes of revolution ("discs" & "shells") Volumes of solids with known cross section Exponential and logarithmic functions Exponential functions Differentiation and integration of exponentials Inverse functions Logarithmic functions Natural logarithmic differentiation Natural logarithmic integration Differential equations Growth and decay L'Hoptial's rule Trigonometric and inverse trigonometric functions Trigonometric graphs and limits Derivatives of trigonometric functions Integrals of trigonometric functions Inverse trigonometric functions and differentiation Inverse trigonometric functions and integration Integration techniques Review of integration formulas Integration by parts