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| MATH0024-1 | Equations with partial derivatives
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| Duration : | 30h Th, 30h Pr |
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| Number of credits : |
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| Lecturer : | Maarten Arnst |
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Language(s) of instruction :
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| French language |
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Organisation and examination :
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| Teaching in the first semester, review in January |
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Course contents :
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| Partial differential equations (PDEs) arise as models of physical and mechanical behavior in many branches of modern science and engineering. PDEs model relationships between physical quantities and their rates of change as a function of space and time. Understanding and exploiting the implications of these relationships often requires solving PDEs. Although numerical methods are nowadays the dominant means for obtaining solutions, the successful application of numerical methods is always challenging and requires physical and mathematical insight into the special problems to which these numerical methods apply.
This course offers an introduction to computational modeling using PDEs. The course focuses on four fundamental types of PDE which often arise in applications in engineering: the Laplace, the heat, the wave, and the transport equation. For each PDE, the course describes the physical phenomena that can be modeled by the equation, provides an analytical study of its mathematical structure, and introduces effective numerical methods for the computational approximation of its solution. |
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Learning outcomes of the course :
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| This course offers an understanding of the physical basis, mathematical structure, and numerical solution of different types of PDE, as well as of the relationships between these physical, mathematical, and computational perspectives. |
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Prerequisites and co-requisites/ Recommended optional programme components :
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| This course assumes that students have a background in calculus (real and vector calculus, trigonometry, ordinary differential equations, Fourier analysis), linear algebra, mechanics and physics, and the use of scientific software (Matlab). The required background material will be recalled in class as needed. |
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Planned learning activities and teaching methods :
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| The course takes the form of a series of lectures. The lectures are complemented by discussion sessions and homeworks, which revolve around reading assignments, analytical exercises, numerical exercises, and combinations thereof. |
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Mode of delivery (face-to-face ; distance-learning) :
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| Face-to-face. |
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Recommended or required readings :
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| Each lecture is supported by slides prepared by the instructor. The slides are complemented by relevant chapters from selected books, which the ULg library provides online access to. For students wishing to consult additional material, comprehensive reference texts are recommended during the first lecture. |
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Assessment methods and criteria :
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| The assessment is based on regular homework and a final exam. The final grade is a weighted average of the grades obtained for the regular homework (25%) and for the final exam (75%). |
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Work placement(s) :
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Organizational remarks :
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| The course is offered in the Fall semester. |
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Contacts :
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| Maarten Arnst
Office: B52 - 0/419
Email: maarten.arnst@ulg.ac.be |
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