| CODE | MAT3815 | ||||||||
| TITLE | Mathematics for Engineers 3 | ||||||||
| UM LEVEL | 03 - Years 2, 3, 4 in Modular Undergraduate Course | ||||||||
| MQF LEVEL | 6 | ||||||||
| ECTS CREDITS | 4 | ||||||||
| DEPARTMENT | Mathematics | ||||||||
| DESCRIPTION | Study-Unit Aims: This study-unit continues to equip engineering students with the necessary mathematical tools needed to address and handle a variety of mathematical problems involving vector calculus and optimization, which may have direct applications in different areas of mechanical and electrical engineering. The topics covered include: • The gradient, streamlines and contours • Divergence and curl • Vector Identities • Triple Integrals • Change of variables in Multiple Integrals • Jacobian • Space Curves – parametrization, tangent • Curvature and Torsion of a space curve • Frenet Frame along space curves • Line Integrals • Green’s Theorem • Surfaces – parametrization, tangents and normal • Quadrics • Surface Integrals for surfaces defined parametrically • Optimization: Global and local extrema of functions of several variables; Lagrange’s method for constrained problems; Lagrange’s method with two constraints. Learning Outcomes: 1. Knowledge & Understanding: By the end of the study-unit the student will be able to: - Recognise and interpret the main terminology associated with vector calculus; - Understand the meaning and applications of the gradient, divergence and curl operators; - Visualise and solve problems involving multiple integrals, line integrals and surface integrals; - Obtain a basic knowledge of the geometry of curves; - Learn about the parametrization of surfaces and different types of quadrics; - Solve Optimization problems with one or two constraints. 2. Skills: By the end of the study-unit the student will be able to: - Visualize and analyse mathematical problems relevant to Engineering; - Formulate solutions to such problems by using appropriate mathematical techniques; - Evaluate the applicability of different theorems to simplify problems. Main Text/s and any supplementary readings: Main Texts: - Larson R., Edwards B.H. and O' Neil P., Mathematics for Engineers, Custom Edition for the University of Malta, Cengage, 2015. - Roe J., Elementary Geometry, Oxford Science Publications, Clarendon Press, 1997. Supplementary Readings: - Zill D.G. and Wright W.S., Advanced Engineering Mathematics, Jones and Bartlett Publishers, 5th Edition, 2012. - Hass J.R. and Weir M.D., Thomas’ Calculus, Pearson, 13th Edition, 2014. |
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| ADDITIONAL NOTES | Follows from: MAT1801, MAT1802 | ||||||||
| STUDY-UNIT TYPE | Lecture | ||||||||
| METHOD OF ASSESSMENT |
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| LECTURER/S | Joseph Sultana |
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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 2024/5. It may be subject to change in subsequent years. |
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