Analysis IV

MATH-207(d) / 4 credits

Teacher: Braun Mathias Viktor Joachim

Language: English

Summary

The course studies the fundamental concepts of complex analysis and Laplace analysis with a view to their use to solve multidisciplinary scientific engineering problems.

Content

Complex analysis.

  • Definitions and examples of complex functions.
  • Holomorphic functions.
  • Cauchy-Riemann equations.
  • Complex integrals and Cauchy formulas.
  • Laurent series.
  • Residue theorem.

Laplace analysis.

  • Laplace transforms.
  • Applications to ordinary differential equations.
  • Applications to partial differential equations.

Learning Prerequisites

Required courses

Linear algebra, Analysis I, Analysis II, Analysis III

Learning Outcomes

By the end of the course, the student must be able to:

  • Formulate the definitions and results of the lectures.
  • Apply the concepts learned in class to concrete problems.
  • Analyze problems related to the topics treated in the course.
  • Choose to solve a given problem.
  • Prove some elementary statements about the topics of the course.
  • Solve exercises on the topics.

Teaching methods

Weekly lectures with instructor and weekly exercise sessions with assistants.

Expected student activities

Attending the lectures and solving the exercises.

Assessment methods

Written exam.

Resources

Moodle Link

In the programs

  • Semester: Spring
  • Exam form: Written (summer session)
  • Subject examined: Analysis IV
  • Courses: 2 Hour(s) per week x 14 weeks
  • Exercises: 2 Hour(s) per week x 14 weeks
  • Type: mandatory
  • Semester: Spring
  • Exam form: Written (summer session)
  • Subject examined: Analysis IV
  • Courses: 2 Hour(s) per week x 14 weeks
  • Exercises: 2 Hour(s) per week x 14 weeks
  • Type: optional
  • Semester: Spring
  • Exam form: Written (summer session)
  • Subject examined: Analysis IV
  • Courses: 2 Hour(s) per week x 14 weeks
  • Exercises: 2 Hour(s) per week x 14 weeks
  • Type: optional
  • Semester: Spring
  • Exam form: Written (summer session)
  • Subject examined: Analysis IV
  • Courses: 2 Hour(s) per week x 14 weeks
  • Exercises: 2 Hour(s) per week x 14 weeks
  • Type: mandatory
  • Semester: Spring
  • Exam form: Written (summer session)
  • Subject examined: Analysis IV
  • Courses: 2 Hour(s) per week x 14 weeks
  • Exercises: 2 Hour(s) per week x 14 weeks
  • Type: mandatory
  • Semester: Spring
  • Exam form: Written (summer session)
  • Subject examined: Analysis IV
  • Courses: 2 Hour(s) per week x 14 weeks
  • Exercises: 2 Hour(s) per week x 14 weeks
  • Type: optional

Reference week

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