Syllabus Information

5.1. Methodological overview

• Theoretical and problem sessions on the blackboard.
• Use of Moodle for communicating and displaying learning material.
• Mentoring.

5.2. Learning tasks

• Master classes on theoretical results and key problems.
• Problem sessions to understand and apply the theoretical results.
• Problem assignments for individual work.
• Individual tutoring.

See http://www.unizar.es/analisis_matematico/docencia.html and https://moodle2.unizar.es/add/ for more information and material.

5.3. Syllabus

1. Holomorphic functions. Cauchy-Riemann conditions. Harmonic functions.
2. Analytic functions. Power series. Elementary functions.
3. Complex integration. Cauchy local theory.
4. Cauchy global theory. Cycles and homology. Simple connection.
5. Zeroes and singularities. Meromophic functions. Laurent expansions.
6. Residue theorem and applications.
7. Conformal mappings.

5.4. Course planning and calendar

• Three hours weekly of master classes all year long.
• Lessons 1,2,3 correspond to the first semester. Lessons 4 to 7 to the second semester.
• Exam period and dates and the academic calendar is available at the Faculty of Science web page, http://ciencias.unizar.es/.

5.5. Bibliography and recommended resources

• Conway, John B.. Functions of one complex variable. 2nd ed., New York, Springer, 1978.
• Palka, Bruce P. An introduction to complex function theory. New York, Springer, 1991.
• Ponnusamy, S.. Complex variables with applications. Herb Silverman, Boston, Birkhauser, 2006.
• Rudin, Walter. Análisis real y complejo; traducción José María Martinez Ansemil. 3a. ed., Madrid, McGraw-Hill, 1987.

See also http://www.unizar.es/analisis_matematico/docencia.html and https://moodle2.unizar.es/add/.