Calculus I

This course introduces the two main branches of Calculus: Differential and Integral Calculus. Differential Calculus studies rates of change in one quantity relative to rate of change in another quantity and Integral Calculus studies the accumulation of quantities such as distance travelled or area under a curve. The two processes are inversely related as specified by the Fundamental Theorem of Calculus.At the end of this course the student should be able to:

• demonstrate a good overall conceptual understanding of functions and their graphical, numerical, analytical, and verbal representations
• state and prove theorems on limits; compute limit of a function
• identify functions that are continuous
• compute derivative of a function from first principles
• apply differentiation to solve real life problems
• evaluate the definite integral of a function as a limit of Riemann sums
• apply integration to compute area of region, volume of a solid