Calculus+Essential+Learnings

= Essential Learnings and Indicators of Success =

== **EL 1** Students will demonstrate a sound understanding of limits both graphically and algebraically and be able to use limits to verify continuity of functions. == == **EL 2** Students will be able to derive functions and curves. ==
 * 1) Students can find limits of functions when given a graph.
 * 2) Students can find limits of function algebraically.
 * 3) Students demonstrate continuity of a function using limits.
 * 1) Students will be able to use both definitions of a derivative.
 * 2) Students will understand how a derivative relates to rates of change.
 * 3) Students will know and be able to use derivative rules.
 * 4) Students will be able to use implicit differentiation to find derivatives.
 * 5) Students will be able to find higher order derivatives.
 * 6) Students will be able to match graphs of functions with the first and second derivatives.
 * 7) Students can use derivatives to find critical points and points of inflection.
 * 8) Students can find absolute and relative extrema of functions.
 * 9) Students can determine where functions are increasing and decreasing using derivatives.
 * 10) Students can determine where functions are concave up and concave down using second derivatives.

== **EL 3** Students will apply their knowledge of derivatives to analyze and solve real world problems. == == **EL 4** Students will be able to antidifferentiate as well as use integrals to solve basic differential equations. == > == **EL 5** Students will be able to use integrals to analyze and solve real world problems. ==
 * 1) Students will understand how derivatives relate to physics.
 * 2) Students will understand how derivatives relate to economic principles.
 * 3) Students will be able to solve optimization problems.
 * 4) Students will be able to solve related rates problems.
 * 5) Students will be able to use derivatives to find slopes of curves, tangent lines, and normal lines at given points.
 * 6) Students will understand and apply the Mean Value Theorem.
 * 1) Students will use Rectangular Approximation Methods to estimate area under curves.
 * 2) Students will use the Trapezoidal Rule and Simpson's Rule for better approximation results.
 * 3) Students will use Riemann Sums to find areas.
 * 4) Students will use antiderivtives to solve simple definite and indefinite integrals.
 * 5) Students will use U-Substitution to solve more complex integrals.
 * 6) Students will use integrals to solve basic differential equations.
 * 1) Students will use integrals to solve physics problems.
 * 2) Students will use integrals to evalutes the area between curves.
 * 3) Students will use integrals to evaluate the volume of areas rotated around lines.