| CODE | ENR0001 | ||||||||||||
| TITLE | Algebraic Techniques, Coordinate Geometry and Differentiation | ||||||||||||
| UM LEVEL | 00 - Mod Pre-Tert, Foundation, Proficiency & DegreePlus | ||||||||||||
| ECTS CREDITS | 6 | ||||||||||||
| DEPARTMENT | Faculty of Engineering | ||||||||||||
| DESCRIPTION | The study-unit introduces the basic algebraic concepts of surds, indices, logarithms, partial fractions and quadratic equations which are the essential building blocks for more complex mathematical computations. The unit then introduces the mathematics of functions and coordinate geometry and finally presents the concepts and applications of differentiation. Study-Unit Aims: The study-unit aims to provide students with the mathematical skills necessary for more advanced mathematical techniques required in Engineering. Through this study-unit, the student will become proficient in the use of surds, indices, logarithms, solving quadratic equations and inequalities and the use of partial fractions. The unit will also introduce functions and teach students how to work with straight lines, loci and circles in a Cartesian coordinate system. The study unit also aims to provide an understanding of the concepts and rules of differentiation and the skills necessary to perform differentiation of basic functions. Various applications of differentiation will be presented. Learning Outcomes: 1. Knowledge & Understanding: By the end of the study-unit the student will be able to: a. describe the laws of surds, indices and logarithms, distinguish between polynomials and rational functions; b. explain the use of the factor theorem and the remainder theorem; c. describe the relation between the roots and the coefficients of a quadratic equation; d. express simple inequalities in one variable; e. describe functions in terms of their domain, co-domain and range; f. distinguish between odd, even and periodic functions; g. understand the geometry related to straight lines, loci and circles; h. work with horizontal, vertical and oblique asymptotes; i. describe the derivative of a function as the limit of the gradient of a chord on a curve of the function; j. identify problems where differentiation should be applied to determine the rate of change or to identify stationary points. 2. Skills: By the end of the study-unit the student will be able to: a. use and manipulate indices, logarithms and surds, simplify rational expressions, express rational functions into partial fractions, find solutions to quadratic equations and find graphical and algebraic solutions to inequalities; b. find the domain and range of a function, the inverse function and the composition of two functions; c. write the equations of lines and circles and find intersection points between multiple lines and/or circles; d. sketch rational functions which may include horizontal, vertical and oblique asymptotes; e. differentiate algebraic, trigonometric, exponential and logarithmic functions; f. differentiate implicit functions and functions defined by parametric equations; g. apply differentiation rules to determine the derivative of sums, products and quotients of functions and the derivative of a function of a function; h. apply differentiation to evaluate the gradient of a function and to determine the equations of tangents and normals. Main Text/s and any supplementary readings: - 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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