Module LLLS0277: FURTHER CALCULUS

Department: FOUNDATION YEAR [Queen's Campus, Stockton]

LLLS0277: FURTHER CALCULUS

Type	Open	Level	0	Credits	10	Availability	Available in 2005/06	Module Cap	None.	Location	Queen's Campus Stockton

Prerequisites

• Extension Mathematics (LLLS0207) (or equivalent).

Corequisites

• None.

Excluded Combination of Modules

• None.

Aims

• To consolidate the basic concepts of Calculus in the Extension Mathematics module.
• to build on these concepts to include trigonometric and logarithmic functions.
• to introduce and develop understanding of a range of standard techniques for differentiation and integration.
• to improve confidence in algebraic manipulation through the study of additional mathematical techniques.

Content

• Factor Theorem for polynomials.
• differentiation of composite functions (chain rule) and of the sum, product or quotient of two functions.
• derivative of trigonometric and exponential functions.
• second derivatives of standard functions.
• integration of standard trigonometric functions (e.g. sin(squared)x, cos2x).
• the evaluation of integrals by using standard forms, by substitution, by partial fractions and by integration by parts.

Learning Outcomes

• By the end of the module the students will have acquired the skills to be able to:
• recall, select and use knowledge of appropriate integration and differentiation techniques as needed in a variety of contexts.
• confidently manipulate a range of algebraic expressions as required in problems appropriate to the syllabus.

• By the end of the module the students will:
• be able to communicate effectively in writing
• be able to apply number in the tackling of numerical problems
• have improved their own learning and performance
• be able to demonstrate problem solving skills

Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

• Theory, initial concepts and techniques will be introduced during lectures.
• Much of the learning, understanding and consolidation will take place through the use of structured worksheets during tutorials and students' own time.
• Ability to recall, select and use knowledge and to manipulate algebra will be tested by: a coursework portfolio containing students solutions to questions or tasks set by the tutor on a weekly basis.
• an end of year exam.

Teaching Methods and Learning Hours

Activity	Number	Frequency	Duration	Total/Hours
Lectures	11	Weekly	1 hour	11
Tutorials	11	Weekly	2 hours	22
Preparation and Reading				67
Total				100

Summative Assessment

End of module examination (60%); coursework portfolio: one worked answer or task per week (40%)

Formative Assessment:

Weekly self-testing units

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■ Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University