Created on: September 9, 2014

Website Address: https://library.curriki.org/oer/Curriki-Calculus-

TABLE OF CONTENTS

This collection provides learning materials for all topics in the College Board’s course description for an AP Calculus AB course, as well as a small number of additional topics, such as L’Hopital’s Rule. The standards contained here are modeled after the Indiana Academic Standards for Mathematics – Calculus (Adopted April 2014 – Standards Correlation Guide Document 5-28-2014).

Notes regarding this course:

• There is content which is beyond what is currently contained in the AP Calculus AB course description, i.e. Logarithmic Differentiation and L’Hopital’s Rule. Both of these are useful topics to cover, and L’Hopital’s Rule, while not now a part of AP CalculusAB, will be added to the AP Calculus AB course description for the 2016-2017 academic year.

• The collection is organized into five broad categories: Limits & Continuity (LC),

Derivatives (D), Applications of Derivatives (AD), Integrals (I), and Applications

of Integrals (AI). This categorization aligns closely, but not exactly, with the

AP course description. Some specific topics could be placed in more than one

category, e.g. Slope Fields could be placed in Applications of Derivatives or Integrals. Regardless of the categorization, all content in the AP Calculus AB Course Description is covered in this course.

• The sequencing of the topics generally, but not rigidly, follows the sequence in

which the course would be taught. While the categories would generally be covered in the order presented, specific content within the categories could be effectively covered in a number of different sequences.

In this, the third section of the course, the topics include:Applications of derivatives• Analysis of curves, including the notions of monotonicity and concavity.• Optimization, both absolute (global) and relative (local) extrema.• Modeling rates of change, including related rates problems.• Use of implicit differentiation to find the derivative of an inverse function.• Interpretation of the derivative as a rate of change in varied applied contexts, including velocity, speed, and acceleration.• Geometric interpretation of differential equations via slope fields and the relationship between slope fields and solution curves for differential equations.Computation of derivatives• Knowledge of derivatives of basic functions, including power, exponential, logarithmic, trigonometric, and inverse trigonometric functions.• Derivative rules for sums, products, and quotients of functions.• Chain rule and implicit differentiation.

In this, the fourth section of the course, the topics include:Interpretations and properties of definite integrals• Definite integral as a limit of Riemann sums.• Definite integral of the rate of change of a quantity over an interval interpreted as the change of the quantity over the interval.• Basic properties of definite integrals (examples include additivity and linearity).Fundamental Theorem of Calculus• Use of the Fundamental Theorem to evaluate definite integrals.• Use of the Fundamental Theorem to represent a particular antiderivative and the analytical and graphical analysis of functions so defined.Techniques of antidifferentiation• Antiderivatives following directly from derivatives of basic functions.• Antiderivatives by substitution of variables (including change of limits for definite integrals).Numerical approximations to definite integrals.• Use of Riemann sums (using left, right, and midpoint evaluation points) and trapezoidal sums to approximate definite integrals of functions represented algebraically, graphically, and by tables of values.