Calculus III

Recommended Prerequisites

Calculus I, Calculus II, Linear Algebra and Analytic Geometry.    

Teaching Methods

The teaching in this course assumes two formats: theoretical and example classes. During a theoretical class teaching is mostly expository. During an example class teaching consists of problem solving by the students under the guidance of the lecturer. A strong interaction between notions and their practical application is emphasized. In this task, the visualization and the analysis of concrete examples takes on a central role and prepares the way for the abstract definitions. Tutorial support is available to students to help them on the tasks assigned by the lecturers.

Learning Outcomes

Provide knowledge about ordinary differential equations, systems of linear differential equations, and partial differential equations, as well as the fundamental concepts and ways to compute Laplace transforms. The student who successfully completes this course will be able to:

1. Solve a separable differential equation;

2. Solve diferencial linear equations;

3. Solve systems of linear differential equations with constant parameters;

4. Use Laplace transform to solve a differential equation;

5. Identify and solve the heat, wave and Laplace equations;

6. Solve problems with applications of differential equations to mathematical modelling.    

Work Placement(s)

No

Syllabus

I. Ordinary Differential Equations

I.1 First order linear differential equations: the separable and linear cases 

I.2 Higher order linear differential equations: annihilator, reduction of order, variation of parameters methods

I.3 Systems of linear differential equations with constant parameters

I.4 Laplace transform and applications to solving differential equations

 

II. Partial Differential Equations

II.1 Separation of variables and Superposition methods

II.2 Heat equation, wave equation and Laplace equation.    

Head Lecturer(s)

Paulo dos Santos Antunes

Assessment Methods

Final assessment
Exam: 100.0%

Continuous assessment
2 or more midterm exams: 100.0%

Bibliography

Dennis G. Zill: Equações Diferenciais com aplicações em modelagem. Cengage Learning (tradução da 10ª edição norte-americana), 2016 

Figueiredo, D.; Neves, A.. Equações Diferenciais Aplicadas. Coleção Matemática Universitária, IMPA, R. Janeiro, 2018.

Spiegel, M. Análise de Fourier, Colecção Schaum, 1977.

Dennis G. Zill: Differential Equations with Boundary-Value Problems. Cengage Learning (9ª edição), 2018.

Erwin Kreiszig: Advanced Engineering Mathematics. Willey (10ª edição), 2014.