| CODE | FST0014 | ||||||||||||
| TITLE | Calculus | ||||||||||||
| UM LEVEL | 00 - Mod Pre-Tert, Foundation, Proficiency & DegreePlus | ||||||||||||
| MQF LEVEL | Not Applicable | ||||||||||||
| ECTS CREDITS | 5 | ||||||||||||
| DEPARTMENT | Science, Engineering and ICT | ||||||||||||
| DESCRIPTION | This study-unit introduces mathematical concepts to provide an introduction to calculus through the study of differentiation and integration. The students will be given the opportunity to apply differentiation and integration to solve simple problems on maxima and minima, rate of change, areas, volumes and length of arcs, and to solve first order and second order differential equations. Study-unit Aims: To provide: - A review of the gradient of a line and curve, of the equations of tangents and normals, and of simple curve sketching; - An introductory overview to limits, differentiation, integration and differential equations; - An outline of the applications of differentiation and integration to solving differential equations and other problems arising from real-life situations. Learning Outcomes: 1. Knowledge & Understanding: By the end of the study-unit the student will be able to: - Describe the derivative as a limit with particular reference to examples from mechanics and electrical theory; - Identify problems on rate of change, maxima and minima, and devise a method for solving these problems with particular reference to examples from mechanics and electrical theory; - View integration as a process of summation and as the inverse of differentiation; - Distinguish between first order and second order differential equations. 2. Skills: By the end of the study-unit the student will be able to: - Differentiate algebraic, trigonometric, exponential, logarithmic, implicit and parametric functions; - Differentiate sums, products, quotients and composition of functions; - Apply differentiation to gradients, tangents and normals, and to simple problems involving rates of change, maxima and minima; - Use trigonometric identities to integrate functions; - Evaluate integrals by means of standard forms, by substitution, by partial fractions and by parts; - Apply integration to calculate areas and mean values of functions; - Calculate volume of revolution, arc length and area of surface of revolution using Cartesian or parametric coordinates; - Use reduction formulae involving one parameter to evaluate integrals; - Solve first order differential equations (separable variables and linear) and second order differential equations (with constant coefficients); - Use the method of induction in problems involving differentiation and integration. Main Text/s and any supplementary readings: - L. Bostock and S. Chandler (2014). Mathematics The Core Course for A-Level. Stanley Thornes. ISBN: 9780859503068. - L. Bostock, S. Chandler and C. Rourke (1982). Further Pure Mathematics. Stanley Thornes. ISBN: 9780859501033. |
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| ADDITIONAL NOTES | This study-unit is offered only to the Certificate in Foundation Studies students. Please note that a pass in the Examination component is obligatory for an overall pass mark to be awarded. |
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| STUDY-UNIT TYPE | Lecture, Independent Study & Tutorial | ||||||||||||
| METHOD OF ASSESSMENT |
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| LECTURER/S | Agnetha Agius |
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The University makes every effort to ensure that the published Courses Plans, Programmes of Study and Study-Unit information are complete and up-to-date at the time of publication. The University reserves the right to make changes in case errors are detected after publication.
The availability of optional units may be subject to timetabling constraints. Units not attracting a sufficient number of registrations may be withdrawn without notice. It should be noted that all the information in the description above applies to study-units available during the academic year 2023/4. It may be subject to change in subsequent years. |
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