| CODE | MAT1953 | ||||||
| TITLE | Calculus 1 | ||||||
| UM LEVEL | 01 - Year 1 in Modular Undergraduate Course | ||||||
| MQF LEVEL | 5 | ||||||
| ECTS CREDITS | 2 | ||||||
| DEPARTMENT | Mathematics | ||||||
| DESCRIPTION | • Differentiation * Products and quotients of functions * Implicit functions * Parametric functions * Second order derivatives • Integration * Using substitution * By parts • First order ordinary differential equations * Separable variables * Integrating factor • Second order linear ordinary differential equations * Homogeneous equations * Non-homogeneous equations * Auxiliary equation and method of undetermined coefficients Study-unit Aims: This unit aims at enhancing the students' skills in calculus by presenting them with a number of techniques which are useful in this area. Calculus is the study of any phenomenon involving change, whether it is the change of a quantity with respect to time or the change between quantities. Change can be observed all around us, be it temperature with energy, density with depth, displacement with time, and so on. The mathematical tools used to address change are differentiation and integration, and thus the need to be able to work with calculus is important at different extents for practically everyone. This unit is intended to help students gain confidence in handling simple relationships which involve derivatives (and hence differential equations), and thus enabling them to understand better the world around them. Learning Outcomes: 1. Knowledge & Understanding: By the end of the study-unit the student will be able to: • Differentiate and integrate products and quotients of functions. • Find second order derivatives of implicit and parametric functions. • Solve first order ordinary differential equations by using an appropriate method. • Solve second order ordinary differential equations with constant coefficients. 2. Skills: By the end of the study-unit the student will be able to: • Use calculus to solve problems related to change. • Interpret the results obtained and judge their validity. • Address questions requiring mathematical reasoning. • Demonstrate the abilities of logical and analytical thinking. Main Text/s and any supplementary readings: • Bostock, L., and Chandler, S. (2000) Core Maths for Advanced Level (3rd Ed.), Nelson Thornes. • Bostock, L., and Chandler, S. (1981) Mathematics: The Core Course for A-level, Stanley Thornes. • Bostock, L., Chandler, S., and Rourke, C. (1982) Further Pure Mathematics, Stanley Thornes. Supplementary Readings: • Smedley, R., and Wiseman, G. (2001) Introducing Pure Mathematics (2nd Ed.), Oxford University Press. • Gaulter, B., and Gaulter, M. (2001) Further Pure Mathematics, Oxford University Press. |
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| ADDITIONAL NOTES | Pre-requisite Qualifications: Intermediate Level Pure Mathematics | ||||||
| STUDY-UNIT TYPE | Lecture and Independent Study | ||||||
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| LECTURER/S | John B. Gauci |
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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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