| CODE | ENR0004 | ||||||||||||
| TITLE | Further Calculus, Polar Coordinates and Series | ||||||||||||
| UM LEVEL | 00 - Mod Pre-Tert, Foundation, Proficiency & DegreePlus | ||||||||||||
| ECTS CREDITS | 6 | ||||||||||||
| DEPARTMENT | Faculty of Engineering | ||||||||||||
| DESCRIPTION | This study-unit presents techniques for simple curve sketching and introduces the polar coordinate system. It also introduces the students to the concepts and applications of integration. Specifically, the study-unit covers the application of integration to determine the area under a curve, the mean value of a function, surface areas and volumes. Students will also apply differentiation and integration techniques to solve first and second order differential equations. The study-unit will also include the study of sequences and series and the summation of series. Study-Unit Aims: This study-unit aims to provide the necessary skills to draw curves using both the Cartesian as well as the polar coordinate system. It also provides an understanding of the concepts and rules of integration and the skills necessary to perform integration of basic functions. Various applications of integration will also be presented. The unit will also provide the mathematical skills for finding the solutions of first-order and second-order differential equations. Finally, an introduction will also be given to finite and infinite series, as well as arithmetic and geometric series. Learning Outcomes: 1. Knowledge & Understanding: By the end of the study-unit the student will be able to: a. sketch curves and perform simple transformations of graphs; b. describe the relation between polar and rectangular coordinates; c. work with a polar coordinate system; d. describe integration as the limit of a summation and the inverse of differentiation; e. recognise standard derivative forms, useful for performing integration as the reverse of differentiation; f. distinguish between first order and second order differential equations; g. identify arithmetic series, and finite and infinite geometric series. 2. Skills: By the end of the study-unit the student will be able to: a. sketch curves of exponential and logarithmic functions; b. sketch curves of polynomials (up to three stationary points) and their transformations; c. convert between rectangular and polar coordinates and plot points in polar coordinates; d. find the intersection of polar curves and the area enclosed by a polar curve; e. integrate algebraic, trigonometric, exponential and logarithmic functions by the reversal of the differentiation of standard functions; f. determine integrals by substitution, by parts, and by using partial fractions and trigonometric identities; g. solve first order differential equations and second order differential equations with constant coefficients; h. apply integration to calculate the area under a curve and the mean value of a function; i. apply integration to evaluate volume of revolution, arc length and surface area for Cartesian or parametric coordinates; j. determine the general term of an arithmetic and geometric series and evaluate the sum of arithmetic and geometric series; k. determine the sum of arithmetic and geometric progressions, apply the condition for convergence of an infinite geometric series and find its sum to infinity; l. find the Maclaurin's series of simple functions, including the general term in simple cases; m. evaluate the summation of simple finite series and simple infinite series; n. expand (a + bx)^n using the bionomial expansion in either ascending or descending powers of x. Main Text/s and any supplementary readings: Main Texts: - Bostock, L., & Chandler, S. (1981). Mathematics : The core course for A-level. Thornes. - Bostock, L., Chandler, S., & Rourke, C. (1982). Further pure mathematics. Thornes. |
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| STUDY-UNIT TYPE | Lecture, Independent Study & Tutorial | ||||||||||||
| METHOD OF ASSESSMENT |
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| LECTURER/S | Karl Frendo Cumbo |
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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 2024/5. It may be subject to change in subsequent years. |
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