複變函數

To study elementary theory of functions of a complex variable and its applications to science and engineering

Calculus

無備註

Lecture: three hours per week Web: E3 platform

Homework and Quiz 30% Midterm Exam 30% Final Exam 40%

• Functions of a complex variable

  limits, continuity, derivatives, Cauchy-Riemann equations, analytic functions, harmonic functions

• Elementary functions

  exponential and logarithmic functions, and trigonometric and hyperbolic functions

• Integrals

  contour integrals, upper bounds for moduli of contour integrals, antiderivatives, Cauchy-Goursat theroem, Cauchy integral formula, Liouville's theorem and fundamental theorem of algebra, and maximum modulus principle.

• Series representaions of functions

  Taylor series, Laurent series, and power series

• Theory of residues and its applications

  isolated singular points, Cauchy's residue theorem, residue at poles, zeros of analytic functions, argument principle, Rouche's theorem, and inverse Laplace transform

• Mapping by elementary functions

  Linear transformations, linear fractional transformations, mappings by 1/z, z^2,and z^(1/2), etc.

• Conformal mapping

  Preservation of angles, scale factors, local inverse, harmonic conjugates, transformation of harmonic functions, and transformation of boundry conditions

Text: J. W. Brown and R. V. Churchill, Complex variables and applications, 9th Ed., McGraw Hill, 2014. Reference: D. G. Zill and P. D. Shanahan, Complex analysis: a first course with applications, 3rd Ed., Jones & Bartlett Learning, 2015.

地點

EE768

時間

Office hours: 15:30-17:00 Tuesday

聯絡方式

ywliang@cn.nctu.edu.tw ext. 31669