Differential Equations
Keywords |
Classification |
Keyword |
OFICIAL |
Mathematics |
Instance: 2024/2025 - 2S ![Requerida a integração com o Moodle Ícone do Moodle](/fcup/pt/imagens/MoodleIcon)
Cycles of Study/Courses
Teaching Staff - Responsibilities
Teaching language
Portuguese
Objectives
Acquisition of basic knowledge of the theory of Differential Equations and Fourier Analysis.
Learning outcomes and competences
The students should acquire techniques which enable them:
a. to solve both classical ordinary differential equations of 1st and 2nd order and linear systems of ordinary differential equations;
b. to solve classical partial differential equations (heat, wave and Laplace's equations) using separation of variables and Fourier series.
Working method
Presencial
Pre-requirements (prior knowledge) and co-requirements (common knowledge)
Real Analysis I, II and III and Linear Algebra and Analytic Geometry I and II.
Program
1. First order ordinary differential equationsLinear, separable and exact differential equations. Applications: dating through radioactive decay, population growth, mixtures, among others.
2. Theorem of existence and uniqueness of solutions 3. Systems of first order ordinary differential equationsLinear homogeneous systems with constant coefficients.
4. Second order linear differential equationsHomogeneous linear equations. Phase portrait and graph of the solutions in the case of constant coefficientes.
Method of variation of parameters and method of reduction of order for nonhomogeneous equations.
Solutions obtained through power series expansion. Applications: motion of an object under the influence of an elastic spring, with or without friction, with or without external forces.
5. Partial differential equations
Boundary value problems. Separation of variables. Fourier series.
Heat, wave and Laplace's equations and their resolution.
Mandatory literature
Braun Martin;
Differential equations and their applications. ISBN: 0-387-90266-X
Complementary Bibliography
Hirsch Morris W.;
Differential equations, dynamical systems, and linear algebra. ISBN: 0-12-349550
Teaching methods and learning activities
Theoretical classes with exposition of the theory and illustration by examples.
Practical classes with resolution by the students of concrete problems.
keywords
Physical sciences > Mathematics > Mathematical analysis > Differential equations
Evaluation Type
Distributed evaluation with final exam
Assessment Components
designation |
Weight (%) |
Exame |
60,00 |
Teste |
40,00 |
Total: |
100,00 |
Amount of time allocated to each course unit
designation |
Time (hours) |
Estudo autónomo |
171,00 |
Frequência das aulas |
72,00 |
Total: |
243,00 |
Eligibility for exams
Not applicable.
Calculation formula of final grade
With the final exam of 20 points.