Class Differential Equations and Complex Analysis

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.

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.

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.

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.