Fundamental Mathematics

20

CM-0125L

2015/6

Semester 1

A

FHEQ Level 4

Linked 10+10

Computer Science

School of Electrical Engineering & Computer Science

Dr C Lei

Prof A Vourdas

None

None

To develop geometric skills and knowledge of basic matrix methods. To present an introduction to the concepts of complex number theory.

Formative assessment assignments encourage the ongoing digestion of the material, with the extent of the cumulative

Study Hours: | ||||||

Lectures: | 24.00 | Directed Study: | 149.50 | |||

Seminars/Tutorials: | 24.00 | Other: | 0.00 | |||

Laboratory/Practical: | 0.00 | Formal Exams: | 2.50 | Total: 200.00 |

On successful completion of this module you will be able to...

show a breadth of knowledge of, and the utility of, algebraic manipulation and calculus, geometry, matrices, sequences, series and complex number theory.

On successful completion of this module you will be able to...

manipulate with and apply the fundamental properties of geometry, matrices, sequences, series and complex number theory.

On successful completion of this module you will be able to...

show a breadth of knowledge of, and the utility of, geometry, matrices, sequences, series and complex number theory.

001. | Assessment Type | Duration | Percentage |

Coursework | 25% | ||

Description | |||

2 assignments consisting of questions taking approximately 2 hours to answer per assignment | |||

002. | Assessment Type | Duration | Percentage |

Examination - closed book | 2.50 | 75% | |

Description | |||

Examination | |||

900. | Assessment Type | Duration | Percentage |

Examination - closed book | 3.00 | 100% | |

Description | |||

Supplementary examination |

GEOMETRY: line, circle, ellipse, parabola; polar forms; parametric forms. VECTORS: preliminaries; vector addition; geometrical applications; components; vector multiplication; triple products; lines and planes. MATRIX METHODS: notation; matrix algebra; transpose; rank; inverse; simultaneous linear equations in matrix form and solution by Gaussian elimination; inversion by Gauss-Jordan reduction; determinants and their manipulation; adjoints and cofactors.

PROOF BY INDUCTION. SEQUENCES AND SERIES: monotonicity of sequences; convergence; recurrence relations; partial sums; positive series; comparison test; ratio test; alternating series; absolute and conditional convergence; re-ordering; power series; radius of convergence. COMPLEX NUMBERS: algebraic rules; modulus; geometrical applications; Argand diagram; polar forms, multiplication, division; De Moivre`s theorem; Euler`s formula; exponential form; multiple angles; roots of complex numbers.

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