Calculus III

Recommended Prerequisites

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

Teaching Methods

Theoretical classes are expository, in practical classes the students solve exercises  under the instructor’s guidance. The students are encouraged to solve  problems autonomously. A strong interaction between concepts and their practical application will prevail,  giving a central role to visualization and analysis of particular situations before making a progressive approach to more abstract notions. The transformation of concepts into working tools will be achieved by encouraging personal work. The formal lectures will be complemented by periods of individual attendance.

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. Throughout the course, students must develop computational skills and acquire competence in applying theoretical knowledge to solve problems. Students must also acquire an understanding of the concepts that will enable them to evaluate the scope and limitations of the studied materials, as well as their applications in engineering and other sciences.

Work Placement(s)

No

Syllabus

First order differential equations (separable variables and linear) and applications

Linear differential equations of order higher than one

- Solving homogeneous linear equations

- Method of the annihilator polynomial

- Reduction of order

- Method of variation of parameters

Systems of linear differential equations with constant coefficients

Laplace transforms and applications in solving differential equations

Partial differential equations

- Heat equation

- Wave equation

- Laplace equation.

Head Lecturer(s)

Paulo dos Santos Antunes

Assessment Methods

Continuous assessment
Mini Tests: 20.0%
Frequency: 80.0%

Final assessment
Exam: 100.0%

Bibliography

Zill, D.G.. A first course in differential equations with applications. Brooks/Cole, 2005.

Marcus,  D.. Differential equations. McGraw-Hill College, 1991.

Figueiredo, D.; Neves, A.. Equações Diferenciais Aplicadas. Coleção Matemática Universitária, IMPA, R. Janeiro, 2010.