Mathematical Analysis I

Code:

L.AERO02

Acronym:

AMI

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2024/2025 - 1S (of 23-09-2024 to 10-01-2025)

Active?	Yes
Responsible unit:	Department of Electrical and Computer Engineering
Course/CS Responsible:	Bachelor in Aerospace Engineering

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L.AERO	31	Syllabus	1	-	6	58,5	162

Teaching language

Portuguese

Objectives

1. Know the rules of derivatives and differentials of functions of a variable.


2. Know the fundamental concepts about indefinite integrals


3. Use the Fundamental Theorems of Calculus as the link between definite integral, indefinite integral and primitive.


4. Calculate integrals by substitution and by parts.


5. Calculate primitives of rational algebraic fractions and rational trigonometric expressions.


6. Calculate primitives of rational algebraic fractions and rational trigonometric expressions.


7. Calculate areas in Cartesian and polar coordinates.


8. Calculate volumes by integration.


9. Calculate improper integrals.


10. Analyze the convergence of the numerical series.


11. Obtain the polynomial approximation of real functions with a variable by Taylor Polynomials with the notion of the error.


12. Construct the Taylor series from the respective polynomial.


13. Solve first order ordinary differential equations.

Learning outcomes and competences

1) Correctly apply the mathematical techniques included in the programme of the CU.
2) Select appropriate mathematical tools for the solution of the proposed problems.
3) Clearly show the rationale and techniques used to solve the proposed problems.
4) Analyse and assess the results obtained in the solution of the problems. CDIO: 1.1, 2.4

Working method

Presencial

Program

Integral Calculus in R: Riemann sums and the integral: Definition and properties. Mean-value theorem for integrals. Fundamental theorems of calculus. Primitive functions and integration by substitution and by parts. Areas of plane regions by integrals calculation. Polar coordinates and area calculation. Volume calculations by the method of cross sections. Integration by rational partial fractions. Rational trigonometric integrals.

Mandatory literature

Maria do Rosário de Pinho e Maria Margarida Ferreira; ; Análise Matemática 1, Apontamentos das Aulas Teóricas
Conceição António, C.A.; Análise Matemática I - Conteúdo Teórico e Aplicações (edição aumentada). (edição em português), 2017

Teaching methods and learning activities

Lectures supported by slides on the content of the course (UC). The presentation of each chapter includes examples of application. In practical classes, exercises are solved.

Lessons p/ week- 4,5h TP; Scheduled total:58,5h; Study:65h; Exam preparation:38,5h; Class hours.

Evaluation Type

Distributed evaluation without final exam

Assessment Components

Designation	Weight (%)
Exame	100,00
Total:	100,00

Amount of time allocated to each course unit

Designation	Time (hours)
Estudo autónomo	103,50
Frequência das aulas	58,50
Total:	162,00

Eligibility for exams

1st test (T1), mandatory and weighting 50% final grade and UC content; 2nd test (T2) only for students with grade T1>=6 (20), weighting 50%;
Final Exam (FE) on whole content, simultaneously with T2, mandatory for students with T1<6 (20); Recursive Exam (ER) on whole content, for students without minimum grade in T1 or T2, or without averaging 10 values in both tests or in EF.

Calculation formula of final grade

Final grade (CF): (Tl+T2)/2 if T1>=6 and T2>=6 or CF=EF or CF=ER

Examinations or Special Assignments

Internship work/project

Special assessment (TE, DA, ...)

Classification improvement

Observations