This course begins with a discussion of functions, the limit concept and continuity. The concept of a derivative is introduced and the student learns to differentiate polynomial functions, rational functions, algebraic, exponential, logarithmic and trigonometric functions.
Differentiation is applied to extreme problems and to problems in related rates.
The integral as the unit of a sum is linked to the antiderivative by the Fundamental Theorem of Calculus and used to find areas and volumes. A graphics calculator is required for this course, and so is the use of a computer software, such as Mathematica. Derivatives The derivative definition and the rules for finding derivatives of polynomial, rational, exponential, logarithmic, trigonometric and algebraic functions. Logs and exponential functions Inverse functions, logs and exponential functions, derivatives of logs and exponential functions. Applications of Derivatives Applications of the derivative to maxima and minima, the relationships between distance, velocity and acceleration.