Subject: Diferential Equations

Scientific Area:

Mathematics

80 Hours

Number of ECTS:

7,5 ECTS

Language:

Portuguese

# Overall objectives:

1 - Equip students with techniques of calculation related to the integration of differential equations, and analyzing solutions.
2 - Complementary techniques of calculation and to address specific problems in the field of applications of differentilals equations.

# Syllabus:

1 - First Order Differential Equations. Exercises
1.1 - General Considerations. Exercises
1.2 - Separable Equations. Exercises
1.3 - Exact Equations and Integrating Factors. Exercises
1.4 - Linear Equations and Variation of Parameters. Exercises
1.5 - The Existence and Uniqueness Theorem. Exercises
2 - Second Order Linear Equations
2.1 - Definition and Examples
2.2 - Homogeneous Equations with Constant Coefficients. Exercises
2.3 - Nonhomogeneous Equations with Constant Coefficients. Exercises
2.4 - The Existence and Uniqueness Theorem. The Wronskian. Exercises
2.5 - Applications
3 - Higher Order Linear Equations
3.1 - Homogeneous Equations of Order n. Exercises
3.2 - Homogeneous Equations of Order n with Constant Coefficients. Exercises
3.3 - Nonhomogeneous Equations of Order n. Exercises
3.4 - The Laplace Transform Method. Exercises
4 - Systems of First Order Linear Equations
4.1 - Basic Theory of Systems of First Order Linear Equations
4.2 - Homogeneous Linear Systems with Constant Coefficients. Exercises
4.3 - Nonhomogeneous Linear Systems with Constant Coefficients. Exercises
5 - Partial Differential Equations
5.1 - Definitions and Examples. Exercises
5.2 - First Order Partial Differential Equations. Exercises
5.3 - The Wave Equation and Separation of Variables. Exercises
5.4 - The Heat Equation. Exercises
5.5 - Fourier Transform and Convolution. Exercises

# Literature/Sources:

C.R.Wylie, L.C.Barrett , 1985 , Advanced Engineering Mathematics , MacGraw-Hill Int. Ed.
W.E.Boece, R.C.DiPrima , 1992 , Elementary differential equations and boundary value problems , John Wiley& Sons, Inc.
E. Kreyszig. , 2011 , Advanced Engineering Mathematics. , John Wiley & Sons

# Assesssment methods and criteria:

Classification Type: Quantitativa (0-20)

Evaluation Methodology:
2 Several tests (50% +50%): So we can measure how much knowledge, both theoretical and practical, the student has acquired and his ability to solve problems. It also aims to analyze the student's ability to relate the different concepts and results that have been taught throughout the course.