| CODE | MAT1954 | ||||||
| TITLE | Calculus 2 | ||||||
| UM LEVEL | 01 - Year 1 in Modular Undergraduate Course | ||||||
| EQF/MQF LEVEL | 5 | ||||||
| ECTS CREDITS | 2 | ||||||
| DEPARTMENT | Mathematics | ||||||
| DESCRIPTION | • Matrices and Determinants     * Evaluating determinants     * Rules for manipulating determinants     * Inverse of 3x3 matrices     * Simple applications • Systems of equations     * The augmented matrix     * Gaussian elimination method     * Cramer's Rule • Partial Differentiation     * First partial derivatives of simple functions of more than one variable     * The chain rule     * Small increments     * Higher partial derivatives Study-unit Aims: In their course of studies, students have had limited opportunity to deal with functions of more than one variable and the aim of this unit is to formalize the techniques involved when working with such functions from two perspectives – algebra and calculus. From an algebraic perspective, the work involved in solving systems of linear equations involving two or more variables is considerably simplified if matrices are availed of. Matrices are used for a large number of different reasons by various people, starting from simple “recipes” to more advanced uses in electronics, genetics and optimisation problems. This unit aims at consolidating the students’ knowledge on the algebra of matrices and considering some applications of matrix algebra to problems arising from practical situations. Partial differentiation involves finding the rate of change of functions with respect to one variable, whilst keeping all the other variables constant. The methods how such functions can be differentiated will be explored and some applications of partial differentiation would be also considered. Learning Outcomes: 1. Knowledge & Understanding: By the end of the study-unit the student will be able to: • Evaluate and manipulate determinants. • Perform algebraic operations on matrices (including finding the inverse). • Solve systems of linear equations by using different methods. • Find the partial derivatives of functions of more than one variable. 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., Chandler, S., and Rourke, C. (1982) Further Pure Mathematics, Stanley Thornes. • Larson, R., and Hodgkins, A.V. (2012) College Algebra and Calculus: An Applied Approach (2nd Ed.), Brooks/Cole Cengage Learning. Supplementary Readings: • 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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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 2026/7. It may be subject to change in subsequent years. |
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