MCS 321 EXAM 1
- What: Exam on functions
- When: 12:30-1:20 Monday, March 15
- Where: Olin 319
This will be a closed-book exam focusing on chapters 2 and 3 of our text.
You may use one 4"-by-6" note card with anything you want written on both sides.
Many of the problems will be similar to problems you did for homework.
Special emphasis:
- The definition of the derivative
- Calculation of the derivative, f '(z), ...
- if f(z) is given as a function of z;
- if f(z) = u(x,y) + i v(x,y) is given;
- if f(z) = u + i v where u and v are given as
functions of the modulus r and argument theta.
- Necessary conditions for differentiability:
the Cauchy-Riemann equations
- Sufficient conditions for differentiability:
the Cauchy-Riemann equations plus regularity conditions
- Harmonic functions and harmonic conjugates
- Definitions and derivatives of elementary functions of a complex variable
- Calculation of values
- Solving equations
- Mappings of sets
- Verification of identities
- Calculation of derivatives
Some topics that should not be forgotten but will not be tested:
- The reflection principle
- Inverse trigonometric and hyperbolic functions