Code: | EC0001 | Acronym: | AMAT1 |
Keywords | |
---|---|
Classification | Keyword |
OFICIAL | Mathematics |
Active? | Yes |
Web Page: | https://moodle.up.pt/course/view.php?id=562 |
Responsible unit: | Mathematics Division |
Course/CS Responsible: | Master in Civil Engineering |
Acronym | No. of Students | Study Plan | Curricular Years | Credits UCN | Credits ECTS | Contact hours | Total Time |
---|---|---|---|---|---|---|---|
MIEC | 12 | Syllabus since 2006/2007 | 1 | - | 7 | 75 | 187 |
OBJECTIVES:
Lead the students to processes of reformulation of their working methods from the 1st. semester, with empowerment of knowledge acquired during that period. Understand, handle and apply the concepts of integration of real variable functions and series. Provide a base set of math skills required for the proper functioning of other course curriculum units. Develop scientific-mathematician reasoning and the ability of being receptive to the application of mathematical concepts.
EXPECTED SKILLS:
At the end of the term, students should, in each of the following strands, be able to:
Knowledge: describe the main achievements in the area of basic training of mathematical analysis, notably in the field of differential and integral calculus, numerical series and polynomial approximation of real variable functions by Taylor Polynomials. Identify the techniques to use in solving proposed problems.
Understanding: build suitable attitude and thought for solving engineering problems. Application: develop a solid foundation for subsequent course units, enabling the proper use of the techniques and the rigorous formulation of problems.
0. Revision of essential concepts: 0.1. Calculation of functions limits 0.2. Rational functions and inequalities 0.3 Graphics of elementary functions, their association and elementary operations: translations, reflections, enlargements, reductions, etc.
1. Differential calculus of real functions of real variables:
1.1. Methodology of mathematics, Fundamentals of mathematical logic, axiomatic of real numbers, brief topological notions. Bolzano-Weierstrass theorem.
1.2. Trigonometric, inver trigonometric and hyperbolic functions
1.3. Real functions of real variables: limits and continuity. Intermediate values and Weierstrass theorems
1.4. Differential calculus of functions of one variable: definitions and geometric interpretation. Rolle, Lagrange and Cauchy theorems. Derivative of inverse and composed functions. Practical rules and applications of derivation.
2. Integral calculus of real functions of real variable:
2.1. Riemann integral, operations with integrals, indefinite integrals. Fundamental theorem of calculus, Barrow’s formula and mean value theorem.
2.2. Integration of rational functions. Integration by parts and substitution.
2.3. Improper integrals
2.4. Calculation of areas in the plan.
3. Numerical sequences and series:
3.1. Cauchy sequence, convergence analysis and sum of a series, simple convergence and absolute convergence.
3.2. Series of positive terms: criteria of comparison, d’ Alembert, Cauchy and the integral.
3.3. Series of alternating terms: Leibniz’s criterion
4. Sequences and series of functions:
4.1. one point convergence and uniform convergence
4.2. power series: radius and convergence range
4.3. polynomial approximation: Taylor’s polynomial and series.
DISTRIBUTION:
The estimated percentage distribution of scientific and technological content conforms to the following table:
Program item estimated %
1 25
2 40
3 20
4 15
DEMONSTRATION OF THE SYLLABUS COHERENCE WITH THE CURRICULAR UNIT'S OBJECTIVES:
This curricular unit is within the group of curricular units in the scientific area of mathematics, mainly focusing on providing students a solid education in the concepts of integration and the calculation of real functions of real variable and numerical and function series. The syllabus includes the differential calculus, integral calculus, numerical sequences and series of functions. These materials are the basis of mathematical calculation, and the concepts presented in class and the results using clear examples with possible use of appropriate software.
In lectures (theoretical and practical), concepts and results are presented resorting to geometrical interpretation (when possible) and illustrative examples. Some constructive demonstrations are presented. Strong appeal is made to the understanding of the concepts and calculation capacity. Throughout the course unit, students are reminded of the available computational tools, its capabilities and limitations. Classes are held with some demonstrations of the use of appropriate software and the student is guided along the selected problem solving.
DEMONSTRATION OF THE COHERENCE BETWEEN THE TEACHING METHODOLOGIES AND THE LEARNING OUTCOMES:
The presentation of the concepts and results using the geometric interpretation of illustrative examples aims to develop scientific and mathematical logical thinking and the ability to be aware for the application of mathematical concepts. In this way a proper attitude and thinking is developed to solve engineering problems and a solid basis for the subsequent curricular units is acquired, allowing the use of correct techniques and rigorous problems formulation.
Designation | Weight (%) |
---|---|
Exame | 75,00 |
Teste | 25,00 |
Total: | 100,00 |
Designation | Time (hours) |
---|---|
Frequência das aulas | 100,00 |
Total: | 100,00 |
Achieving final classification requires compliance with attendance at the course unit, according to the MIEC memorandum of 26th November 2013. It is considered that students meet the attendance requirements if, being regularly enrolled, the number of absences of 33% for classes is not exceeded.
Components of the evaluation:
One final exam (EF)
Two practical exercises performed during lectures time (EP1 e EP2)
The final marks (CF) are determined as follows:
EP1_2 – result of 2 exercises carried out during lectures
EF - classification of the final exam
CF = 0.25 max {EP12, Group I of EF} + 0.75 (Group II of EF)
Students who, having frequency, do not get approval on the course unit, have access to the examination of appeal with groups I e II as in the final exam.
SPECIAL RULES FOR MOBILITY STUDENTS: Proficiency in Portuguese; attendance to secondary disciplines that underpin this course unit; evaluation components as determined for ordinary students.
Students approved according to CF classification, may apply to an improving exam.
Estimated weekly working time outside lectures: 5 hours.
Calculators are not allowed at any of the various components of evaluation. Fraud in the realization of an examination - in any of the several modes -implies the respective cancellation (article 13 of Normas Gerais de Avaliação da FEUP).