|Objective:||To provide students with a sound understanding of basic calculus in preparation for the degree courses.|
|Pre-Requisite:||PPC0016 - Pre-Calculus|
|Student Learning Time:||160 hours|
Final Examination: 50%
Limits and Continuity
Limits: Intuitive approach and computation. Limits at infinity. End behaviour of a function. Continuity. Continuity of trigonometric, exponential and inverse functions.
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.
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 second-order linear differential equations with constant coefficients.
At the completion of the subject, students should be able to: