# Module Information

Module Identifier
MA13010
Module Title
Basic Calculus
2013/2014
Co-ordinator
Semester
Intended for use in future years
Mutually Exclusive
May not be taken at the same time as, or after, MA10020.
Pre-Requisite
A or AS level Mathematics or equivalent.

#### Course Delivery

Delivery Type Delivery length / details
Lecture 22 Hours. (22 x 1 hour lectures)
Seminars / Tutorials 6 Hours. (6 x 1 hour example classes)

#### Assessment

Assessment Type Assessment length / details Proportion
Semester Exam 2 Hours   (written examination)  100%
Supplementary Assessment 2 Hours   (written examination)  100%

### Learning Outcomes

On completion of this module, a student should be able to:
1. sketch graphs of elementary functions;
2. solve inequalities by routine methods;
3. explain the geometrical significance of the derivative of a function at a point as the slope of the tangent to a curve;
4. differentiate elementary functions from first principles;
5. differentiate using the function of a function rule, the product rule, and the quotient rule;
6. differentiate parametrically and differentiate implicit functions;
7. differentiate repeatedly including using Leibnitz' theorem;
8. obtain the Taylor and Maclaurin expansions of a function;
9. evaluate indeterminate limits using L'Hopital's rule;
10. integrate using the method of substitution and integration by parts;
11. apply the theory of integration to determine the area of regions in a plane and volumes of solids of revolution;
12. locate critical points and determine their nature;
13. determine the first and second partial derivatives of functions of two variables.

### Brief 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.

### Aims

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

### Content

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

### Notes

This module is at CQFW Level 4