| CODE | MAT1956 | ||||||
| TITLE | Introductory Calculus 2 | ||||||
| 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: - Complex numbers - The imaginary coefficient - Types of roots of quadratic equations - First order ordinary differential equations - Solving by separable variables and integrating factor - Second order linear ordinary differential equations - Homogeneous equations and non-homogeneous equations - Auxiliary equation and method of undetermined coefficients - Matrices and Determinants - Evaluating determinants and rules for manipulating determinants - Inverse of 3x3 matrices - Systems of equations - The augmented matrix - Gaussian elimination method and 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: This study-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. It also aims to extending the number system, namely by introducing complex numbers. The first main aim of this unit is to give the opportunity to students to start experiencing functions of more than one variable and to formalize the techniques involved when working with such functions from two perspectives – algebra and calculus. Another aim is to introduce matrices and determinants to the students, and to apply these when solving systems of equations. A final aim is to explore methods how these functions can be differentiated and to consider some applications of partial differentiation. Learning Outcomes: 1. Knowledge & Understanding: By the end of the study-unit the student will be able to: - Solve first order ordinary differential equations by using an appropriate method; - Solve second order ordinary differential equations with constant coefficients; - 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., 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. Larson, R., and Hodgkins, A.V. (2012) College Algebra and Calculus: An Applied Approach (2nd Ed.), Brooks/Cole Cengage Learning. 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 Qualification: 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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