SCS1106 Calculus

This course is designed to develop the topics of differential and integral calculus. Emphasis is placed on limits, continuity, derivatives and integrals of algebraic and transcendental functions of one variable.

Course Objectives
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
• appreciate the concept of a derivative and compute derivative of a function [ X]
• apply differentiation to solve real life problems
• evaluate the definite integral of a function as a limit of Riemann sums
• apply integration to solve real life problems

Learning Outcomes
Upon completion, students should be able to:

• Apply the definition of limit to evaluate limits by multiple methods and use it to derive the definition and rules for differentiation and integration.
• Use derivatives to analyze and graph algebraic and transcendental functions.
• Select and apply appropriate models and differentiation techniques to solve problems involving algebraic and transcendental functions; these problems will include but are not limited to applications involving optimization and related rates.
• Apply the definition of indefinite integral to solve basic differential equations.
• Apply the definition of definite integral to evaluate basic integrals.
• Use the fundamental theorem of calculus to evaluate integrals involving algebraic and transcendental functions.