# Module Information

#### 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

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