Mathematical Analysis I

All the math knowledge transmitted to students in the 10th, 11th and 12th years.

Theoretical classes are expository on the subjects listed in the program of the course. While the practical classes aim to discussion and problem solving by students on the subjects taught in the theoretical classes, with teacher guidance. In laboratory classes the topics of Chapter 6, component of numeric methods, are discussed using graphing calculators and MuPAD (symbolic calculus toolbox in Matlab). The evaluation can be done by exam worth 20 points in examination periods in the regulation or by distributed evaluation. Distributed evaluation consists of making three frequencies during the semester. A student is excluded from the distributed evaluation, if it is not obtain the minimum required in the frequencies and is approved when the sum of the marks obtained in the three frequencies is greater or equal than 10 points.

The main goal of the course unit of Mathematics Analysis I is to offer knowledge in differential and integral calculus in IR that will be essential to understand the topics taught in the other curricular units, in particular, the students have to acquire and interpret the notion of derivative and integral and apply these competences for understanding, solving and analyzing results of problems in engineering.

Real valued functions in IR – Elementary functions: inverse trigonometric; hyperbolic. Differential calculus in IR – Derivatives. Theorems of Rolle, Lagrange and Cauchy. Indeterminate forms and Cauchy rule. Increment and differential. Taylor polynomial and error of Lagrange. Primitives – Definition of primitive and properties. Techniques of calculus of primitives. Integral calculus in IR – Definition of Riemannian integral, and properties. Fundamental theorems of integral calculus in IR. Applications to the calculus of areas, curves length and volumes. Undefined integral. Improper integral. Introduction to the study of differential equations – Definition of differential equation. Cauchy problem. Ordinary differential equations of 1st order. Component of numeric methods – Introduction to the theory of errors. Numeric methods of computing of a nonlinear equation solution. Polynomial interpolation. Numeric integration. Numeric methods to solve ordinary differential equations of 1st order.

NAO