| CODE | IFS0013 | ||||||||||||
| TITLE | Complex Numbers, Functions and Series | ||||||||||||
| 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 complex numbers, functions, series and the method of induction. Study-unit Aims: To provide: - An outline of the applications of finite and infinite series, the induction method, functions and complex numbers. Learning Outcomes: 1. Knowledge & Understanding: By the end of the study-unit the student will be able to: - Recognise arithmetic series, finite and infinite geometric series; - Describe the effect of simple transformations on the graphs of functions; - Explain what are the domain and the range of a function, and recognise one 鈥� one and onto functions; - Describe complex numbers, their modulus and argument, and illustrate these on an Argand diagram; - Describe De Moivre's Theorem for any rational index; - Explain what odd and even functions are, and about the role of symmetry asymptotes (including oblique asymptotes). 2. Skills: By the end of the study-unit the student will be able to: - Apply the method of differences and the sum of the squares and cubes of the first natural numbers to problems involving finite series; - Summate the terms of a simple infinite series; - Find the Maclaurin series of a function, including the general term in simple cases; - Use the method of induction in problems involving series, sequences, divisibility, and inequalities, and to prove De Moivre鈥檚 theorem; - Derive the polar and exponential forms of a complex number, and use them together with De Moivre鈥檚 Theorem to find the complex roots of a complex number and to derive trigonometric identities; - Solve equations and inequalities involving the modulus of complex numbers and sketch the corresponding loci and regions on an Argand diagram; - Use a graph to determine the range of a function and to obtain the graph of the reciprocal of the function. 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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| 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 2025/6. It may be subject to change in subsequent years. |
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