Infinitesimal Analysis III

Recommended Prerequisites

Real Analysis I, II; Linear Algebra and Analytic Geometry I.

Teaching Methods

Active participation of the students in the theoretical and tutorial classes. This may include presentation in class of part of the homework assigments.

Students' work is closely observed and frequently evaluated by the instructor. The student has access to the results of each evaluation and is encouraged to meet individually with the instructor to discuss his/her performance.

Learning Outcomes

The main objective is the study of Differential Calculus of vectorial functions defined in Rn. The approach used in the presentation of the topics represents a compromise between rigorous foundations and an interdisciplinary point of view, addressing applications to Science and Engineering. Graphic software (as for example MATHEMATICA) will be used to illustrate theoretical concepts and to improve visualization. The skills to be developed include learning of the theoretical foundations of Vector Differential Calculus; capacity of generalization and abstraction; capacity to pose problems and to translate them in mathematical language; calculation capacity; development of oral and written expression.

Work Placement(s)

No

Syllabus

I.Elements of Topology in Rn.

 

II. Sequences in Rn

 

III- Vector functions

 

IV-Differential Calculus

 

V-Implicit Function Theorem

 

VI-Fourier Analysis.

Head Lecturer(s)

Susana Margarida Pereira da Silva Domingues de Moura

Assessment Methods

Assessment
Approval in this course unit requires to score at least 10 (out of 20). The students that perform, along the semester, the mid-term exams, the test, and/or the homework may be exempted from final examination. The sum of percentages corresponding to these three components is 100%. The other students are evaluated in a final exam which is worth 100%.: 100.0%

Bibliography

J. E. Marsden, Elementary Classical Analysis. Freeman, NY, 1974.

 

J. E. Marsden, Calculus III. 2nd edition. Springer, NY, 1991.

 

M. P.  Serra Oliveira, C. Oliveira, Análise Infinitesimal III, Notas de Curso, 2008