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# Calculus III

 Code 15758 Year 2 Semester S1 ECTS Credits 6 Workload TP(60H) Scientific area Mathematics Entry requirements Knowledge of real functions with several variables, derivation and integration. Learning outcomes This curricular unit is an introduction to the study of differential equations, Laplace transforms and Fourier series. At the end of the course unit the student should be able to: - distinguish and solve the different types of differential equations - solve initial value problems - calculate direct and inverse Laplace transforms of usual functions. Solve differential and integral equations using Laplace transforms - determine Fourier series of periodic functions and functions defined in bounded intervals - use the method of separation of variables in obtaining solutions to partial derivative problems Syllabus 1 - Introduction to Complex Analysis. 2 - Ordinary differential equations of first order. 3 - Ordinary linear differential equations of higher order than the first. 4 - Systems of linear ordinary differential equations of first order. 5 - Laplace transforms and application to the resolution of ordinary differential equations and systems of ordinary differential equations. 6 - Fourier series and application to solving partial derivatives equations. 7 - Fourier Transforms. Main Bibliography R. Churchill, Operational Mathematics, McGraw-Hill R. Churchill and J. Brown, Complex Variables and Applications, McGraw-Hill W. Boyce and R. Di Prima, Elementary Differential Equations and Boundary Value Problems, Fourth Edition, John Wiley & Sons, 1986 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.

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Electromechanical Engineering
Last updated on: 2023-10-10

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