Week	Sections in Text	Suggested Homework	Comments
05/01 to 08/01	Review of Chapter 4. Sections 18.1, 18.2, 18.3	4.3   ## 17  4.4   ## 19 4.5   ##  3, 4, 7, 8, 9, 10 4.6   ##  7, 8, 9, 10 18.1 ##  8, 9, 20 18.2 ##  5, 6, 7, 8, 9, 11, 12	After a brief review of some basic facts about complex numbers, as contained in Chapter 4, I will teach you how to differentiate complex functions and derive the Cauchy-Riemann equations that analytic (holomorphic) functions have to satisfy.  I will then teach you how to integrate complex functions, or better one forms f(z)dz, along curves.
11/01 to 15/01	Sections 18.3, 18.4, 18.5	18.2 ##  16, 17, 22 18.3 ##   do all of them 18.4 ##   1 to 24	This week we will prove a version of the CAUCHY INTEGRAL THEOREM (the mother of all theorems in complex analysis) based on Green's Theorem. We will also derive the CAUCHY INTEGRAL FORMULA and use it to derive TAYLOR SERIES and LAURENT  SERIES I will then discuss zeros and poles of complex functions
18/01 to 22/01	Sections 18.6, 19.2, 19.3	18.5 ##  do all of them 18.6 ##   do all of them 19.2 ##  do all of them	This week we will do the RESIDUE THEOREM (which is the key technique used to integrate in  complex analysis) We will learn how to evaluate a lot of real-valued definite integrals using the residue theorem Assignment #1 is due this week on Friday during the lecture period. Please hand it to me (Min-Oo)
25/01 to 29/01	Sections 19.2, 19.3, 19.4	19.3 ##   do all of them 19.4 ## 4 to 20	This week we will evaluate a lot of real-valued definite integrals, such as the Fresnel integral, and also sum interesting series, such as  Riemann zeta function at even numbers, by using contour integration techniques. We will discuss the Maximum Modulus Principle the Argument Principle and Rouche's Theorem which can be used to count the number of zeros and poles inside a contour
01/02 to 05/02	Sections 17.1&17.2 (review) 19.1,  19.5	17.1 ##  10, 11, 12, 13, 17, 18, 19, 20, 21 17.2 ##   5, 8, 9, 10, 11 19.1 ##   7, 8, 9, 10, 11, 12, 13, 14, 18, 20 19.5 ##   6, 7, 10, 12, 16, 17, 18, 19, 20, 21, 22, 23	We will look at Laplace transforms from the complex point of view and derive a formula for the inverse transform using contour integrals (Bromwich) WE will then study conformal mappings Assignment #2  is due on Friday during the lecture period
08/02 to 12/02	Sections 19.6, 19.7	19.6 ##  do all of them 19.7 ##   3, 4, 5, 6, 7, 8, 9	This week will be about conformal mappings and how to use them to solve the Dirichlet problem and fluid flow problems in the plane. TEST #1  will be held on FRIDAY, February 10th (tentative date) during the lecture period HH/302 The test will cover material from Chapters 18 and 19.1, 19.2, 19.3 and 19.4. Next week is Mid-term Recess
22/02 to 26/02	Sections 21.1, 21.2, 21.3, 17.5(revision)	21.1 ##  7, 8, 9, 10, 11, 12, 13, 15 21.2 ##   2, 3, 5, 6, 9, 11, 12, 13, 14, 15, 16, 17, 18	This week it's about RANDOM VARIABLES I will introduce a number of important probability distributions, both discrete and continuous. Bernoulli, binomial, negative binomial, multinomial, hypergeometric, Poisson, Uniform, Normal (Gaussian).
29/02 to 04/03	Sections  21.3, 21.4, 21.5	21.3 ##   8, 11, 12, 13, 14, 15, 16 21.4 ##  2, 3, 5, 8, 9, 14, 15, 16, 17, 18, 19, 20,  21	I will define the moment generating function and the characteristic function of a random variable and  prove the Central Limit Theorem. I will also explain Chebyschev's The rest of the week is an introduction to stochastic processes and about the Gamma distribution as waiting time for Poisson.
07/03 to 11/03	Sections 21.5, 22.1, 22.2	21.5 ##  1, 4, 9, 10, 11, 12, 13, 14, 15 22.1 ##  3, 4, 5, 7, 8, 10, 11, 12, 15 22.2 ##  4, 5, 9	I will explain how to find estimators in parametric statistics, the maximum likelihood estimator and more about the multivariate normal distribution and its important descendants: chi-squared, student-t, gamma, beta and the F-distribution. Assignment #3   is due this week on Friday in class.
14/03 to 18/03	Sections 22.3, 22.4	22.2 ##  14, 15, 16, 17, 18, 20 22.3 ##  4, 5, 7, 8 9, 10, 11, 16, 17, 22	We will study Confidence Intervals and the chi-squared test for Goodness of Fit.
21/03 to 25/03	Sections 22.4, 22.5	22.4 ##  do all of them 22.5 ##  4, 5, 6, 7, 8, 9, 10	TEST #2 will be held in class on WEDNESDAY, March 23rd  The test will cover the material from Chapter 21 and 22.1, 22.2 On Friday we will do Regression and Correlation
28/03 to 01/04	Extra material and REVIEW	22.5 ## 12, 13, 14, 15, 16, 17, 18, 23, 25	Assignment #4  (the last one) is due this week on Friday, April 1st,  in class
04/04 to 08/04	Extra material and REVIEW