CLEP Calculus

This calculus course has been carefully curated to teach you about the methods of differentiation and the applications of integration. You will be introduced to the concepts of limits, as well as how to find them from tables or graphs. The derivative and notation are key concepts to understand when dealing with differentiation. The relationship between differentiability and continuity will also be highlighted. You will also learn about the relationship between limits and asymptotes. See how the absolute extrema is related to both absolute minima and maxima and why the Sandwich theorem is a useful tool in calculating some types of limits. Study how to use a chart to find the absolute extrema of a curve. Upon the successful completion of this course, you should be able to differentiate between concave up and concave down curves. 

The mean value and Rolle’s theorem are important to understand when working with derivatives. The first and second derivative tests will also be explained. You will learn about the concepts of integration and the constant of integration. The relationship between Riemann sums and area under a curve will be highlighted. U-substitution allows for an immediate reversal of the process of differentiation and you will become familiar with how to find integrals using this method. The optimization problem seeks the best value for a variable quantity - you delve into the steps needed to solve it. You will also become familiar with linear approximations and differentials. Did you know that there are three sigma laws? Prepare to learn about their differences, as well as their appropriate use to simplify calculations.

This course teaches you how to integrate the six trigonometric functions because, when integrating certain binomials, trig substitutions can be useful. You will also be able to discuss integration using lnx if you are working with natural logarithmic functions. The technique of integration by parts will also be highlighted in the material. You will see how to integrate inverse trigonometric and natural exponential functions. The relationship between velocity and the position function is analyzed. You will also be able to calculate the surface of revolution and how to find the arc length. Exponential growth and decomposition are key concepts in calculus and you will become familiar with their various applications.