| CODE | IFS0011 | ||||||||||||
| TITLE | Algebraic Techniques, Trigonometry and Vectors | ||||||||||||
| UM LEVEL | 00 - Mod Pre-Tert, Foundation, Proficiency & DegreePlus | ||||||||||||
| MQF LEVEL | 4 | ||||||||||||
| ECTS CREDITS | 5 | ||||||||||||
| DEPARTMENT | Engineering and ICT | ||||||||||||
| DESCRIPTION | This study-unit introduces mathematical concepts to provide an introduction to algebraic techniques, needed for advanced mathematical computations and manipulations; vectors; trigonometric and hyperbolic functions, equations and identities. The topics covered offer the necessary algebraic foundations to work in calculus, trigonometry and geometry. The range of techniques developed in this study-unit are aimed to equip the students with the necessary tools to be in a better position to undertake further study-units in Mathematics and in other related subjects. Study-unit Aims: To provide: - A review of the mathematical techniques and topics covered at a lower level and the consolidation of this knowledge; - An introductory overview to advanced mathematical techniques and topics; - An outline of the applications of algebraic techniques (equations, inequalities and functions), indices and logarithms; - A review of trigonometric ratios; - An introductory overview to trigonometric and hyperbolic functions, equations, and identities, and to their use and applications; - An introductory overview to vector algebra. Learning Outcomes: 1. Knowledge & Understanding: By the end of the study-unit the student will be able to: - Describe and distinguish between polynomials and rational functions; - Explain the factor theorem and the remainder theorem; - Describe the relation between the roots and the coefficients of a quadratic equation; - State and prove the laws of indices and the laws of logarithms; - Describe trigonometric functions and their inverses for any angle and sketch their graphs; - Recall the values in surd form of cosine, sine and tangent of standard angles given in degrees and radians; - Explain what the general solutions of trigonometric equations represent; - Define hyperbolic functions and inverse hyperbolic functions, describe their basic properties and sketch their graphs; - Explain the use of vectors in two and three dimensions, and represent vectors using different notations; - Recognise skew lines and intersecting lines in three dimensions. 2. Skills: By the end of the study-unit the student will be able to: - Simplify rational expressions; - Express rational functions into partial fractions; - Use and manipulate indices, logarithms and surds; - Form new quadratic equations with roots related to those of another quadratic equation; - Sketch curves of polynomials (up to three stationary points), and of exponential and logarithmic functions; - Solve inequalities graphically and algebraically; - Solve trigonometric identities by making use of the general solution; - Find the length of an arc and the area of a sector of a circle; - Manipulate trigonometric identities, including compound angle, double angle and half angle identities; - Use inverse trigonometric and hyperbolic functions and their graphs; - Find the vector equation of a line and of a plane; - Find the scalar product and the vector product of two vectors; - Use vectors in two and three dimensional geometry to find the area of a parallelogram and triangle. 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 | Please note that a pass in the Examination component is obligatory for an overall pass mark to be awarded. | ||||||||||||
| 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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