Calculus III

Code	8485
Year	2
Semester	S1
ECTS Credits	6
Workload	TP(60H)
Scientific area	Mathematics
Entry requirements	None
Mode of delivery	Presential classes
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.
Language	Portuguese. Tutorial support is available in English.