- Book: J. W. Brown and R. Churchill, Complex Variables with Applications, 8-th Edition
- Material to be covered: Capters 1-7 and parts of Chapter 9 if time permits.

- Important results of the first Chapter:
- Basic properties of complex numbers, sum, product, ratio, algebraic and exponential form
- Conjugate and absolute value with their properties
- Geometrical interpretation of the sum, difference, and conjugate
- Principal argument and little argument
- Roots of unity

- Important result of the second Chapter, Sections 12 - 18:
- Computation of finite limits
- Definition of continuity
- Rules for limits at infinity and infinite limits

- Section 2: 1(a),2,11; Section 3: 1; Section 4: 1(a),3,4,5,6;
- Section 5: 1(b)(d), 7, 9, 10, 13, 14; Section 8: 1,2,6,10;
- Section 10: 6,7,8; Section 12: 1,2,3,4; Section 14: 1,3,7,8;
- Section 18: 3,5,10,11;

- Important results of the second Chapter, Sections 19-23:
- Definition of the complex derivative
- The derivative if the sum, difference, product, and quotient of two differentiable complex functions
- Fluid flow iknterpretation for the complex differential
- Cauchy-Riemann conditions for differentiability

- Section 20: 1,2,8
- Section 23: 1,3,5

- Important results of the second Chapter, Sections 24-27:
- Definition of analytic functions
- Operations with and properties of analytic functions
- Harmonic functions. The real and imaginary parts of an analytic function are harmonic
- Determination of the harmonic conjugate for a given harmonic function

- Important results for Chapter 3, Sections 29-36:
- The exponential function is entire. Opertions with the exponential function
- The logarithm is a multivalued function
- Principal value of logarithm and its properties. Different branch cuts of the logarithm
- Power function with complex exponents. Definition and properties
- Trigonometric functions. Definition and properties
- Hyperbolic functions. Definition and properties

- Important results in Chapter 4:
- The mathematical definition of the complex integral and its properties
- The physical interpretation of the complex integral
- Contour parametrization and the computation of integrals with the fundamental theorem of calculus
- Cauchy's theorem and its consequences
- Cauchy's integral theorem and its corollaries
- Liouville's theorem and the maximum modulus principle

- Section 25: 1,2,4
- Section 26: 1(c),3,8,9
- Section 29: 1,2,3,6,10,11,12,13
- Section 31: 1,3,5,8,9,11
- Section 32: 1,2
- Section 33: 1,2,3,8,9
- Section 34: 11,15
- Section 35: 16
- Section 42: 1,2,3
- Section 43: 1,2
- Section 45: 1,2,3

- In the begining offer the audiance the motivation behind your presentation. Why do you think it is important
- Also in the first part of your presentation try to offer a short outline of the whole presentation so that your colleagues will have a general idea about what to expect
- Clearly prepared slides. A good slide should not contain much information, just what is neccesary for you to convey your message. The main part of a presentation is oral. Oraly explain a lot your arguments!!!
- Fix among your team members a few (2 or 3) important ideas the audience should understand and build your presentation arround them.