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Calculus III

Code 10279
Year 2
Semester S1
ECTS Credits 6
Workload TP(60H)
Scientific area Mathematics
Entry requirements None
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, Fourier series and Complex Analysis.
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
-solve integrals in the complex plane.
Syllabus 1- First order ordinary differential equations.
2- Higher order linear ordinary differential equations.
3- Systems of first order linear ordinary differential equations.
4- Laplace transforms and application to the resolution of ordinary differential equations and systems of equations.
5- Fourier series and application to the resolution of partial differential equations.
6- Fourier transforms.
7- Introduction to complex analisys.
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 Classes are theoretical-practical, where after presenting the main results, they are illustrated with examples and exercises.
Students are provided with support sheets and exercises to work at home.

The Teaching-Learning Assessment consists of three tests, T1, T2 and T3, rated for 20 values.
The Teaching-Learning classification is calculated as follows EA=0.3*T1+0.35*T2+0.35*T3.

Students with EA greater than or equal to 9.5 and less than 17 are exempt from the exam and with a final grade EA; and those with an EA greater than or equal to 17 are invited to a supplementary test.

Students with EA less than 3 values are not admitted. Finalist students and student workers are Admitted to the Exam.
Language Portuguese. Tutorial support is available in English.
Last updated on: 2023-10-10

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