| CODE | MAT1955 | ||||||
| TITLE | Introductory Calculus 1 | ||||||
| UM LEVEL | 01 - Year 1 in Modular Undergraduate Course | ||||||
| MQF LEVEL | 5 | ||||||
| ECTS CREDITS | 4 | ||||||
| DEPARTMENT | Mathematics | ||||||
| DESCRIPTION | This study-unit addresses the topics and sub-topics listed hereunder: - Algebraic techniques - Equations, identities, remainder theorem and factor theorem - Partial fractions - Indices and logarithms - Coordinate geometry - Cartesian equations and gradients of lines - Differentiation - Derivatives of simple functions -The chain rule, the product rule and the quotient rule - Higher order derivatives - Parametric functions and implicit functions - Stationary points and simple curve sketching - Maxima, minima, small percentage increments and rates of change - Integration - Integration of standard functions - Integrating products: by change of variables, by parts - Integrating quotients: by change of variables, using partial fractions - Evaluating the constant of integration - Definite integration Study-Unit Aims: The study-unit aims at introducing calculus to the students. In order to do this efficiently and effectively, the algebraic tools and the geometric techniques that turn out to be essential in this area are sharpened and enhanced. These concepts are then used in synergy to generate an understanding of the basics of calculus, namely differentiation and integration of functions of one variable. The knowledge and skills acquired are applied to address problems involving, but not limited to, establishing maxima/minima, determining the effect of small percentage increments, working with rates of change, and finding areas enclosed by curves. Learning Outcomes: 1. Knowledge & Understanding: By the end of the study-unit the student will be able to: - Express algebraic fractions into partial fractions; - Handle indices and logarithms; - Find gradients of lines and curves; - Sketch straight lines and simple curves; - Use the chain rule to differentiate functions of functions; - Differentiate and integrate products and quotients of functions; - Find derivatives of implicit and parametric functions; - Solve problems involving maxima, minima, percentage increments, rates of change, and areas enclosed by curves. 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: Main Texts: 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. |
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| ADDITIONAL NOTES | Pre-requisite Qualifications: Ordinary Level Mathematics | ||||||
| STUDY-UNIT TYPE | Lecture | ||||||
| METHOD OF ASSESSMENT |
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| LECTURER/S | Kirstie Alice Asciak |
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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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