| CODE | MAT3711 | ||||||||
| TITLE | Differential Equations | ||||||||
| UM LEVEL | 03 - Years 2, 3, 4 in Modular Undergraduate Course | ||||||||
| MQF LEVEL | 6 | ||||||||
| ECTS CREDITS | 4 | ||||||||
| DEPARTMENT | Mathematics | ||||||||
| DESCRIPTION | - Fundamental theorem of differential equations; - Linear differential equations; - Green’s function; - Power series and Frobenius’ method; - Simple dynamical systems. Study-Unit Aims: Differential equations are ubiquitous in applications, especially in mathematical physics and numerical mathematics. This study unit provides both a theoretical introduction to the topic as well as methods to solve simultaneous differential equations. The fundamental theorem gives criteria for when a solution exists. For a linear equation, such a solution can be given in terms of a Green’s function. For non-linear equation, one often has to resort to qualitative descriptions using the phase diagram. Learning Outcomes: By the end of the study-unit, the student will be able to: - Decide whether a given differential equation has unique solutions; - Solve fully a linear system of equations; - Solve a higher order equation with variable coefficients using the power series and Frobenius’ methods; - Sketch a phase diagram of an equation in two variables, determine its equilibrium points, and bifurcation values of parameters. Suggested Reading: - Derrick W., Grossman S., Elementary Differential Equations with boundary value problems, 4th edition, Addison-Wesley, 1996. - Braun M., Differential Equations and Their Applications, 4th edition, Springer, 1993. - Hirsch M. and Smale S., Differential Equations, Dynamical Systems and Linear Algebra, Academic Press, 1997. - Ayres F., Differential Equations, Schaum’s Outline Series, McGraw-Hill, 1972. - Tenebaum M. and Pollard H., Ordinary Differential Equations, Dover Publications, 1985. |
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| ADDITIONAL NOTES | Follows from: MAT1211, MAT1091 Leads to: MAT3712 |
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| STUDY-UNIT TYPE | Lecture and Tutorial | ||||||||
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| LECTURER/S | Joseph Muscat |
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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 Units not attracting a sufficient number of registrations may be withdrawn without notice.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 2024/5. It may be subject to change in subsequent years. |
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