| CODE | MAT1511 | ||||||||
| TITLE | Analytical Geometry | ||||||||
| UM LEVEL | 01 - Year 1 in Modular Undergraduate Course | ||||||||
| MQF LEVEL | 5 | ||||||||
| ECTS CREDITS | 4 | ||||||||
| DEPARTMENT | Mathematics | ||||||||
| DESCRIPTION | - Vector geometry: - Affine spaces, - Position vectors; - Euclidean geometry: - The dot product; - Angles; - Isometries. - Coordinates and equations: - Cartesian coordinates; - Curves and equations; - Coordinate form of an isometry; - Change of coordinates. - Orientation and vector product: - Vector algebra; - Vector equations of lines and planes. - Conics: - The ellipse; - The parabola; - The hyperbola. Study-unit Aims: Analytical geometry is the unification of algebra and geometry. This study-unit gives a rigorous foundation for the study of geometry in two and three dimensions with the aim of developing the ability to analyse, interpret, and apply spatial information. This first course in geometry also provides a gentle introduction to theorems, proofs, and deductive reasoning. It forms the foundation for linear algebra, vector spaces, calculus of vector functions, and the geometry of curves, surfaces, and higher dimensional analogues, with applications in all science subjects, including physics, statistics, and computer science. Learning Outcomes: 1. Knowledge & Understanding By the end of the study-unit the student will be able to: - Appreciate the role and importance of definitions, theorems, and proofs in mathematics; - See the rigorous foundation of geometry through the basic concepts of addition, scalar multiplication, and dot product of vectors; - Make the connection between classical geometry and analytical geometry by proving classical theorems using vectors; - Translate geometrical problems into algebraic equations. 2. Skills By the end of the study-unit the student will be able to: - Prove classical Euclidean theorems using coordinate geometry; - Solve general three-dimensional problems involving straight lines, circles, and planes; - Analyse matrices in general and orthogonal matrices in particular, such as finding the axis and angle of rotation; - Analyse and classify conic equations in two variables using the method of rotation and translation of the axes. Textbooks: - Roe J., Elementary Geometry, Oxford Science Publications, Clarendon Press, 1997. Supplementary Reading: - Vaisman I., Analytical Geometry, World Scientific Publishing Company, 1998. - Camilleri C.J., Vector Analysis, Malta University Press, Malta, 1994. |
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| ADDITIONAL NOTES | Leads to: MAT2512 | ||||||||
| STUDY-UNIT TYPE | Lecture and Tutorial | ||||||||
| METHOD OF ASSESSMENT |
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| LECTURER/S | Joseph Muscat |
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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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