Class Calculus I

Provides a wide range of basic mathematical knowledge, skills and tools essential for Engineering studies: describe and solve static and dynamic problems and optimize solutions on the plane; calculate lengths, areas and volumes.

1.- Real numbers. Properties of the operations with real numbers. Elements of topology. Number e.

2.- Functions. Algebra and composition of functions. Inverse function. Monotony. Trigonometric and inverse trigonometric functions. Implicit function.

3.- Limits and continuity of functions. Asymptotes. Theorems of Bolzano and Weierstrass.

4.- Derivative and differencials. Geometric interpretation. Techniques of differentiation. The chain rule. Derivative of the inverse. Implicit and parametric differentiation. Cauchy´s rule. Complete study of a function.

5.- Integral calculus in IR. The indefinite integral. Techniques of integration. Riemann´s integral. Properties. Fundamental theorem of calculus. Mean value theorem. Applications of the definite integral: lengths, areas, and volumes.

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

Sarrico, C. - Análise Matemática, 8ª ed. Lisboa: Gradiva, 2017