Calculus
Information on Every Subject Name of Subject: Introduction to Calculus and Applications
Prerequisite (if applicable): None Mode of Delivery: Lecture and Tutorial Valuation: Course Work Final Examination 40% 60%
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Teaching Staff: Objective(s) of Subject: • Review the notion of function and its basic properties. • Understand the concepts of derivatives. • Understand linear approximations. • Understand the relationship between integration and differentiation and continuity. Learning Outcomes: After completing this unit, students will be able to: 1. describe the basic ideas concerning functions, their graphs, and ways of transforming and combining them; 2. use the concepts of derivatives to solve problems involving rates of change and approximation of functions; 3. apply the differential calculus to solve optimization problems; 4. relate the integral to the derivative; 5. use the integral to solve problems concerning areas.
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Subject Synopsis: This unit covers topics on Functions and Models, Limits and Derivatives, Differentiation Rules, Applications of Differentiation and Integrals.
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Subject Outline and Notional Hours: Topic Learning Outcomes 1 L 4 T 1.5 P SL 6.25 TLT 11.75
Topic 1: Functions and Models
• • • • • • Functions Models and curve fitting Transformations, combinations, composition and graphs of functions Exponential functions Inverse functions and logarithms Parametric curves
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Topic 2: Limits and Derivatives
• • • • • • • Limits: Onesided limits; laws of limit; limits involving infinity Squeeze theorem Continuity, Intermediate value theorem Tangents and other rates of change Derivatives The derivative as a function Second derivatives
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1.5

7.25
13.75
Topic 3: Differentiation Rules • Derivatives of polynomials, exponential, trigonometric and logarithmic functions • Rules of