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Presentation
Presentation
Provides knowledge, skills and mathematical tools essential for the description of models useful in the resolution of engineering problems, based on differential equations and methods of solving them.
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Class from course
Class from course
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Degree | Semesters | ECTS
Degree | Semesters | ECTS
Bachelor | Semestral | 6
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Year | Nature | Language
Year | Nature | Language
2 | Mandatory | Português
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Code
Code
ULHT1706-14628
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Prerequisites and corequisites
Prerequisites and corequisites
Not applicable
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Professional Internship
Professional Internship
Não
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Syllabus
Syllabus
Elements of complex analysis. Analytical functions. Cauchy-Riemann equations. Laplace equation. Harmonic functions. 1st order linear ordinary differential equations: separable variables, exact, Bernoulli, and Ricatti equations. Applications: population growth / decrease; mixtures; radioactive disintegration. Existence and uniqueness of solutions. 2nd order linear differential equations. Homogeneous and non-homogeneous constant coefficient equations. Applications: free mass-spring damped/undamped system; forced mass-spring system. Fourier series. Heat equation and wave equation.
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Objectives
Objectives
Solve linear ordinary differential equations. Use graphical and numerical methods in addition to algebraic techniques to find solutions to differential equations. Describe models of applications to various sciences and engineering solved by building appropriate differential equations and solving them. Understand the development in Fourie series and its application to the resolution of differential equations to partial derivatives.
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Teaching methodologies and assessment
Teaching methodologies and assessment
Series of exercises will be proposed with the aim of consolidating knowledge and stimulating problem-solving skills. The evaluation of the discipline, expressed on a scale from 0 to 20 points, will be made at different times, including 2 midterms (40% + 50%) and individual work to be developed outside the classroom (10%). If the weighted average of these evaluations is equal to or greater than 9.5, the student will be successful in the subject, otherwise the student will be able to attend a global frequency. In the final exam, the student can improve the grade. The minimum passing grade for these assessments is also 9.5. Assessment criteria are explained at the beginning of the semester.
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References
References
ANTON, H., Calculus. 10ª ed. EUA: John Wiley & Sons, 2012
APOSTOL, T.M., Calculus, vols. I, II, Wiley, 1975
SANTOS, R. J., Introdução às equações diferenciais ordinárias, MG, ISBN 978-85-7470-021-2, 2011.
WYLIE, C. R., Advanced engineering mathematics, 6th ed. NY: McGraw-Hill, 1995.
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Office Hours
Office Hours
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Mobility
Mobility
No