# Calculus

Topics: Derivative, Integral, Fundamental theorem of calculus Pages: 5 (489 words) Published: July 20, 2013
No 1. 2. 3. 4. 5. 6. 7. 8. Code: UCCM1153 Status: Credit Hours: 3 Semester and Year Taught:

Information on Every Subject Name of Subject: Introduction to Calculus and Applications

Pre-requisite (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: One-sided 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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5

1.5

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7.25

13.75

Topic 3: Differentiation Rules • Derivatives of polynomials, exponential, trigonometric and logarithmic functions • Rules of differentiation • Product, quotient and chain rules • Implicit differentiation • Linear approximations and differentials Topic 4: Applications of Differentiation • Related rates • Maximum and minimum values • Critical numbers • Mean value theorem • Increasing and decreasing functions • Concavity • Indeterminate forms and l'Hospital's rule • Optimization problems • Applications to economics • Newton’s method to find roots of equation • Antiderivatives Topic 5: Integrals • Area under a curve • Definition integrals • Riemann sum • Properties of definite integral • Evaluating definite integrals • Fundamental theorem of calculus • Integration by substitution and by parts • Additional technique of integration – partial fractions • Approximate integration by Trapezoidal and Simpson's rules • Error bound for Trapezoidal and Simpson's rule

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3

1

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4.5

8.5

3

10

3

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14.5

27.5

4, 5

10

3

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14.5

27.5

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31

Assessment Includes Tests/Quizes/Assignments/Lab Assignments/Final actual exam time and self learning time

Total Credit Hours

32

10

0 3

78

120

Main Reference(s): 1. Stewart, J. (2006). Calculus: Concepts and Contexts, Metric Version. (3rd ed.). Belmont, CA: Thomson Brooks/Cole. Additional Reference(s): 1. Anton, H., Bivens, I., & Davis, S. (2002). Calculus. (7th ed.). New York: John Wiley & Sons. 2. Adams, R. A. (2006). Calculus: A Complete Course. Toronto: Addison-Wesley.

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