| CODE | FST0013 | ||||||||||||
| TITLE | Trigonometry and Numerical Methods | ||||||||||||
| 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 trigonometric and hyperbolic functions, equations and identities. The students will also be introduced to the polar coordinate system and to polar curve sketching. Numerical methods to find approximate values of roots of equations, of series, and of definite integrals will be also explored and implemented. Study-unit Aims: To provide: - A review of trigonometric ratios; - An introductory overview to trigonometric and hyperbolic functions, equations, and identities, and to their use and applications; - An outline of the applications of numerical methods to find valid approximations. Learning Outcomes: 1. Knowledge & Understanding By the end of the study-unit the student will be able to: - 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; - Describe the relationship between Cartesian and polar coordinates; - Explain the use of the trapezium rule and of Simpson's rule and appreciate the use of numerical techniques to obtain an approximate but useful solution. 2. Skills By the end of the study-unit the student will be able to: - 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; - Differentiate and integrate trigonometric and hyperbolic functions and their inverses, and make use of these functions in problems of integration; - Derive the series expansions of the major trigonometric and hyperbolic functions; - Convert between polar and Cartesian coordinates; - Sketch polar curves, find the points of intersection of two such curves, and determine the area enclosed by a polar curve or between two polar curves; - Locate the roots of an equation by considering changes of sign and find an approximation to such root by the Newton-Raphson method; - Use the logarithmic, exponential and Maclaurin series for approximations; - Use the trapezium rule and Simpson’s rule as approximations in definite 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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