Mathematical Analysis I

Instance: 2023/2024 - 1S

Cycles of Study/Courses

Last updated on 2023-09-18.

Fields changed: Components of Evaluation and Contact Hours

Teaching language

Objectives

This course aims to acquaint students with the differential and integral calculus, in order to make them able to apply basic tools of mathematical analysis in problem solving related with subjects of Informatics and Computing Engineering. This course also aims to expand students’ knowledge, so that they can address new methodologies applied to engineering problems. At the end of the course, the learning outcomes are: 1. To solve derivatives of functions, draw graphics and study functions in general; 2. To solve integrals and use them in various engineering applications; 3. To use different integration techniques and differential equations; 4. To use and understand approximation concepts based on series and polynomials.

Learning outcomes and competences

As a result of this course, students should be aquainted with the following matters:
1. To study functions, solve derivatives and draw graphics
2. To solve integrals and use them in various engineering applications
3. To use differential equations and Laplace Transform
4. To understand approximation concepts using series and polynomials.

Working method

Pre-requirements (prior knowledge) and co-requirements (common knowledge)

Knowledge of pre-calculus at the level of the high school program of Math A.

Program

1-      Differenciation
   a.      Applications to engineering problems
   b.      Limits
   c.       Theorems on continuous functions and derivatives
   d.       Taylor series
2-      Integration
   a.   Indefinite integral
   b.   Definite integral
   c.   Fundamental Theorem
   d.  Integration Techniques
   e.  Applications of integration
3-      Differential Equations
             a.       First Order Differential Equations
             b.      Second Order Differential Equations
4-      Laplace Transform and their use to solve Differential Equations
5-      Series
   a.       Convergence criteria
   b.      Trigonometric series, power series ...
6-      Function approximation: Fourier series

Mandatory literature

Complementary Bibliography

Teaching methods and learning activities

Theoretical classes will be based on the presentation of the themes of the course unit. These classes are aimed to motivate students, where examples of application will be showed. Theoretical-practical classes will be based on the analysis and on problem solving by students, where they have to apply tools and mathematical concepts taught in theoretical classes. These classes are aimed to assess students’ understanding and dexterity of the themes of the course unit.

Attendance in practical courses is controlled and the student may not exceed the designated number of absences (25% of the scheduled hours) indicated by the professor for each practical course. If the student exceeds the specified number of absences, he/she will not be able to attend the course or take any exam in that course unless he/she has a special statute (see FEUP's pedagogical and evaluation rules).

keywords

Evaluation Type

Assessment Components

Amount of time allocated to each course unit

Eligibility for exams

Participation in 75% of the practical lessons (solving exercises)

Calculation formula of final grade

Grade (rounded to the nearest units) obtained by: 

20% of the grade of test 1 plus 80% of the grade of test 2

- Test 1 will exclusively consist of multiple-choice questions.
- Test 2 will encompass both multiple-choice questions and essay questions.

Classification improvement

The student that has already obtained approval can attend the “appeal exam”.