Mathematical Analysis III
Keywords |
Classification |
Keyword |
OFICIAL |
Mathematics |
Instance: 2008/2009 - 1S
Cycles of Study/Courses
Acronym |
No. of Students |
Study Plan |
Curricular Years |
Credits UCN |
Credits ECTS |
Contact hours |
Total Time |
MIEC |
273 |
Syllabus since 2006/2007 |
2 |
- |
5,5 |
60 |
145 |
Teaching language
Portuguese
Objectives
Introduction of the fundamental concepts for the study of behaviour of ordinary differential equations, using analytical, qualitative and numerical methods. Preparation of formulation engineering problems using ordinary differential equations.
Program
1. First Order Differential Equations.
Differential Equations and Mathematical Models. Integrals as General and Particular Solutions. Slope Fields and Solution Curves. Separable Equations and Applications. Linear First Order Equations. Substitution Methods and Exact Equations.
2. Mathematical Models and Numerical Methods.
Numerical Approximation: Euler's Method. The Runge-Kutta Method.
3. Linear Equations of Higher Order.
Introduction. General Solutions of Linear Equations. Homogeneous Equations with Constant Coefficients. Mechanical Vibrations. Nonhomogeneous Equations and Undetermined Coefficients. Forced Oscillations and Resonance.
4. Introduction to Systems of Differential Equations.
First-Order Systems and Applications. Linear Systems and Matrices. The Eigenvalue Method for Homogeneous Systems. Second Order Systems and Mechanical Applications. Multiple Eigenvalue Solutions. Matrix Exponentials and Linear Systems. Nonhomogeneous Linear Systems.
5. Qualitative Techeniques
Stability and the Phase Plane. Linear and Almost Linear Systems.
Mandatory literature
Maria do Carmo Coimbra; Equações Diferenciais, Uma Primeira Abordagem, 2008
Complementary Bibliography
Edwards, Charles Henry;
Differential Equations. ISBN: 0-13-067337-4
Zill, Dennis G.;
Equações diferenciais com aplicações em modelagem. ISBN: 85-221-0314-3
Madureira, Luísa;
Problemas de equações diferenciais ordinárias de Laplace. ISBN: 972-752-065-0
Teaching methods and learning activities
Formative with special care to mathematical formulation of engineering problems. Fundamental theoretical knowledge coordinated with subjects placed ahead in the course. Enhancement of intuitive knowledge, as well as computational capacities. Frequent use of physical and geometrical examples. Encouragement of the use of software.
keywords
Physical sciences > Mathematics > Mathematical analysis > Differential equations
Evaluation Type
Distributed evaluation with final exam
Assessment Components
Description |
Type |
Time (hours) |
Weight (%) |
End date |
Subject Classes |
Participação presencial |
56,00 |
|
|
|
Total: |
- |
0,00 |
|
Eligibility for exams
Limitations are as fixed by the school regulations (Artº 4-nº1).
Calculation formula of final grade
E: classification in the final exam
P: classification in the coursework
Final classification = max(E, 0.80*E + 0.20*P)
Special assessment (TE, DA, ...)
Final Exam
SPECIAL RULES FOR MOBILITY STUDENTS:
Proficiency in Portuguese; Previous attendance of introductory graduate courses in the scientific field addressed in this module; Evaluation by exam and/or coursework(s) defined in accordance with student profile.
Classification improvement
Final Exam
Observations
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Working time estimated out of classes: 3 hours