Calculus III

Recommended Prerequisites

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

Teaching Methods

The theoretical lectures are predominantly expository. In practical classes the students will solve exercises under the guidance of the instructor. In the theoretical classes it will prevail a strong interaction between concepts and their practical application, giving, as much as possible, 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 integral calculus of real-valued functions of two and three variables, ordinary differential equations and systems of linear differential equations, as well as the fundamental concepts about special function transforms relevant to applications to engineering and other sciences. Throughout the course, students must develop computational skills and 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.

Work Placement(s)

No

Syllabus

Integral calculus in R2 and R3

• Double integrals and applications

• Triple integrals and applications

• Change of variables in double and triple integrals

• Line integrals. Green’s Theorem.

• Surface integrals. Stokes’ and Divergence Theorems.

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 transform and applications in solving differential equations

Fourier transform

Head Lecturer(s)

Raquel Susana Giraldes Caseiro

Assessment Methods

Final assessment
The final evaluation requires an exam : 100.0%

Continuous assessment
Continuous evaluation is done throughout the semester and may consist of tests, quizzes or homework.: 100.0%

Bibliography

• J. Stewart, Cálculo , 4ª ed., Vol.2, Pioneira, São Paulo, 2001.

• A. Breda e J. Costa, Cálculo com funções de várias variáveis, McGraw-Hill, Lisboa, 1996.

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