| CODE | ENR0013 | ||||||||||||
| TITLE | Matrices, Numerical Methods and Probability | ||||||||||||
| UM LEVEL | 00 - Mod Pre-Tert, Foundation, Proficiency & DegreePlus | ||||||||||||
| ECTS CREDITS | 6 | ||||||||||||
| DEPARTMENT | Faculty of Engineering | ||||||||||||
| DESCRIPTION | This study-unit aims to introduce matrix algebra and the use of matrices for linear transformations and for solving a system of linear equations. The method of mathematical induction is introduced with its application to simple problems involving summation of series, inequalities, expressions with a multiplicity or divisibility property and De Moivre's theorem. Students will also be introduced to numerical methods such as the Newton-Raphson method for finding the approximate roots of equations, the Trapezium and Simpson's rule for approximate integration and numerical methods for series expansion. The study-unit will also cover simple counting problems involving permutations and combinations, and introduce the students to the probability of events. Study-Unit Aims: This study-unit aims to introduce matrix algebra, presents the method of mathematical induction and its application to simple problems, gives an introduction to numerical methods to determine approximate values and presents the theory of probability. Learning Outcomes: 1. Knowledge & Understanding: By the end of the study-unit the student will be able to: a. describe the rules and properties governing matrix algebra, including the definition of the identity, square, diagonal and singular matrices; b. express systems of linear equations in matrix form; c. express linear transformations in a plane or in three dimensions using matrices; d. explain the use of numerical methods such as the Newton-Raphson method, the trapezium rule and Simpson's rule; e. understand the principles for counting probabilities, permutations and combinations and describe these through the use of probability trees and Venn diagrams; f. distinguish between mutually exclusive, independent events and understand the concept of conditional probability. 2. Skills: By the end of the study-unit the student will be able to: a. perform addition, subtraction and multiplication of matrices; b. calculate the determinant of a matrix; c. calculate the inverse of a matrix using both elementary row operations and the adjoint method; d. use matrix operations to solve systems of up to three linear equations; e. use matrix operations find and perform linear transformations; f. apply the method of mathematical induction to simple problems involving summation of series, inequalities, expressions with a multiplicity or divisibility property and De Moivre's theorem; g. apply the Newton-Raphson method to determine approximate roots of an equation, limited to up to two iterations; h. apply the trapezium rule and Simpson's rule to determine approximations for definite integrals; i. use logarithmic, exponential, binomial and trigonometric series to find approximate values; j. solve simple counting problems involving permutations and combinations; k. calculate the probabilities of an event, the complement of an event, the union and the intersection of two events, use Venn diagrams and tree diagrams to solve problems in probability. Main Text/s and any supplementary readings: Main Texts: - 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 | ||||||||||||
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| LECTURER/S | Anthea Agius Anastasi Nathaniel Barbara |
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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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