Class Calculus III

Provides a wide range of basic mathematical knowledge, skills and tools essential for Engineering studies.

Sequences. Series. Convergence. Geometric and Mengoli series. Non Negative Terms.  Simple and absolute convergence. Leibniz criterion.

Power Series. Domain of convergence. Power series development. Taylor series.

Ordinary Differential Equations (ODE). Fields of directions. Templates that contain first order ODE. Growth models. Logistic models. Mixing and heating problems.

Algebraic methods for first order ODE resolution. Separation of variables, variation of parameters. Applications of first order ODE to engineering problems.

Second Order ODE. Algebraic and numerical methods for second order ODE resolution. Second-order ODE applications to engineering problems. Vibratory models.

Escalar and Vector fields. Conservative vector fields. Line Integrals. Independence of path. Green´s Theorem. Work done by a force. Independence of path.

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., Cálculo, vol. 1, 2ª ed.; Reverté, 2004.

STRANG, G., Calculus, MA: Wellesley-Cambridge Press, 1991.

WYLIE, C. R., Advanced engineering mathematics, 6th ed. NY: McGraw-Hill, 1995.