Subject Code:  PCL0016 
Objective:  To provide students with a sound understanding of basic calculus in preparation for the degree courses. 
PreRequisite:  PPC0016  PreCalculus 
Credit Hours: 
4 
Student Learning Time:  160 hours 
Assessment:  Quizzes: 20%
Tests: 30% Final Examination: 50% 
References: 

Limits and Continuity
Limits: Intuitive approach and computation. Limits at
infinity. End behaviour of a function. Continuity. Continuity of
trigonometric, exponential and inverse functions.
The Derivative
Tangent lines and rates of
change. The derivative function. Introduction to techniques of
differentiation. Product and quotient rules. The chain rule.
Derivatives of trigonometric, exponential, logarithmic and inverse
trigonometric functions. Related rates. Differentials and local linear
approximation. Indeterminate forms. L’Hôpital’s Rule.
Applications of Differentiation
Analysis of functions. Increase, decrease and concavity.
Relative extrema, graphing polynomials. Rational functions, cusps and
vertical tangents. Absolute maxima and minima. Applied maximum and
minimum problems. Rectilinear motion.
Integration
The area problem. The definite integral. Integration by
substitution. Area in sigma notation and the definite integral. The
fundamental theorem of calculus. Integrals of trigonometric,
exponential and logarithmic functions. Rectilinear motion (revisited).
Average value and its applications. Evaluating definite integrals by
substitution. Integration by parts and partial fractions.
Applications of Integration
Area between two curves. Volumes of solids of revolution: slicing and
cylindrical shells. Length of a plane curve. Work.
Introduction to Differential Equations
Modeling with differential equations. First and secondorder linear
differential equations with constant coefficients.
At the completion of the subject, students should be able to: