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Calculus III

Code 8546
Year 2
Semester S1
ECTS Credits 6
Workload TP(60H)
Scientific area Mathematics
Entry requirements Knowledge of real functions with several variables, differentiation and integration.
Mode of delivery Face-to-face.
Work placements Non applicable.
Learning outcomes This Curricular Unit aims to give an introduction to the study of differential equations, Laplace transforms and Fourier series.
In the end of this Curricular Unit the student should be able to:
-classify and solve diferent types of differential equations
-solve initial value problems
-compute direct and inverse Laplace transforms. Solve differential and integral equations using Laplace transforms
-compute Fourier series of periodic functions and of functions defined in bounded intervals
-use the method of separations of variables to solve partial diferential equations
Syllabus 1 - Introduction to complex analisys.
2 - First order ordinary differential equations.
3 - Higher order linear ordinary differential equations.
4 - Systems of first order linear ordinary differential equations.
5 - Laplace transforms and application to the resolution of ordinary differential equations and systems of equations.
6 - Fourier series and application to the resolution of partial differential equations.
7 - Fourier transforms.
Main Bibliography -An introduction to Laplace Transforms and Fourier Series, P.P.G. Dyke, Springer.
-Operational Mathematics, R. Churchill, McGraw-Hill.
-Complex Variables and Applications, R. Churchill and J. Brown, McGraw-Hill.
-Elementary Differential Equations and Boundary Value Problems, W. Boyce and R. DiPrima, Fourth Edition, John Wiley & Sons, 1986.
-Teoria Elementar de Equações Diferenciais Ordinárias, F. Pestana da Costa, IST Press, 1998.
Teaching Methodologies and Assessment Criteria Three tests rated at 6,7,7 (test scores rounded to tenth).
To pass the course in continuous assessment, the student must meet the following conditions: (a) obtain a grade greater than or equal to 3 in the sum of the frequencies; (b) arithmetic mean (rounded to the unit) of the marks obtained in the written tests greater than or equal to 10 in the continuous assessment process. In this case, the final grade is precisely the arithmetic sum (rounded to the unit) of the rankings obtained in the three written tests if that mean is in the interval [10,17]. If that mean is in the interval ]17,20] the student must take a supplementary test (oral/work to be agreed with the student) to maintain the obtained grade (if not interested in defending the grade, his final grade will be 17).
Any attempt at fraud, made at any time of assessment, implies failure in the course.
Language Portuguese. Tutorial support is available in English.
Last updated on: 2021-11-11

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