Module Identifier MA13010  
Academic Year 2001/2002  
Co-ordinator Dr R Jones  
Semester Semester 2  
Pre-Requisite A or AS level Mathematics or equivalent.  
Mutually Exclusive May not be taken at the same time as, or after any of MA10020, MA11010, MA11110, MA12610, MA13510.  
Course delivery Lecture   22 x 1 hour lectures  
  Seminars / Tutorials   6 x 1hour example classes  
Assessment Exam   2-hour written examination   100%  
  Resit assessment   2-hour written examination   100%  

General description

This is a calculus course with the emphasis on methods, techniques and applications. The topics to be covered include differentiation, integration, Taylor and Mclaurin series, special functions, higher derivatives and partial differentiation.


To present the methods and techniques of the differential and the integral calculus so that they can be applied in a variety of contexts.

Learning outcomes

On completion of this module, a student should be able to:


1. FUNCTIONS: Curve sketching
2. INEQUALITIES: Simple inequalities
3. DIFFERENTIATION: Including differentiating from first principles. Function of a function rule, produce rule, quotient rule. Parametric differentiation, implicit differentiation
4. SPECIAL FUNCTIONS: Exponential, logarithmic, hyperbolic and trigonometric functions
5. HIGHER DERIVATIVES: Leibnitz' theorem
6. TAYLOR'S THEOREM: The mean-value theorem of the differential calculus and applications. Taylor and Maclaurin series. L'Hopital's rule
7. INTEGRATION: Integration techniques, integration by substitution and integration by parts
8. APPLICATIONS OF DIFFERENTIATION: Locate local maxima and minima of functions
9. APPLICATIONS OF INTEGRATION: Area under curve and volumes of solids of revolution
10. PARTIAL DIFFERENTIATION: First and second order partial derivatives of functions of two variables

Reading Lists

** Recommended Text
L Bostock & S Chandler. Mathematics - The Core Course for A-level. Thorne 0859503062
R Adams. (1999) Calculus - a complete course. 4th. Addison-Wesley 0201396076