| CODE | FST0012 | ||||||||||||
| TITLE | Coordinate Geometry, Vectors and Matrices | ||||||||||||
| 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 two and three dimensional Cartesian coordinate geometry, vectors in two and three dimensions, matrices and transformations. The tools and techniques developed in this study-unit will enable the students to formulate a mathematical representation of a real life situation and to solve it by using rigorous methods and procedures. Study-unit Aims: To provide: - A review of the Cartesian coordinate system and an extension of this through an elementary treatment of lines,circles and curves; - An introductory overview to vector algebra and matrix algebra; - An outline of the applications of coordinate geometry, vectors and matrices. Learning Outcomes: 1. Knowledge & Understanding: By the end of the study-unit the student will be able to: - Describe the terms distances, angles, direction ratios, lines, and curves used in two and three dimensional Cartesian coordinate systems; - Explain the use of vectors in two and three dimensions, and represent vectors using different notations, with particular reference to their applications to mechanics and electricity problems; - Recognise skew lines and intersecting lines in three dimensions; - Describe the rules underlyingthe algebra of matrices; - Define what singular and non-singular matrices are; - Recognise the matrices associated with standard linear transformations; - Identify the relationship between composition of transformations and matrix multiplication; - Describe the possible solution sets of a system of up to three linear equations in three unknowns and give their geometrical interpretation. 2. Skills: By the end of the study-unit the student will be able to: - Construct the Cartesian and parametric equations of lines, circles and curves; - Find the vector equation of a line and of a plane; - Find the scalar product and the vector product of two vectors, and the triple scalar product of three vectors; - Use vectors in two and three dimensional geometry to find the area of a parallelogram and triangle, and the volume of parallelepiped and tetrahedron; - Add, subtract, and multiply matrices and find the determinants of matrices; - Find the inverse of a and a matrix both by elementary row operations and by the adjoint method; - Find the matrix associated with a linear transformation and vice-versa; - Solve a system of up to three linear equations in three unknowns by using matrices; - Use the method of induction in problems involving matrices. 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 | ||||||||||||
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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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