Course Schedule

Mathematics A3 in English

For Civil Engineering Students

Fall, Academic Year 2006-2007

Ordinary differential equations

Date:
09.11 Announcements, etc. Separable differential equations. Modelling with differential equations.

09.18 First-order linear differential equations. Existence and uniqueness theorems for first order equations. Numerical methods. Ljapunov- and asymptotic stability.

09.25 Constant coefficient homogeneous linear differential equations.

10.02 Constant coefficient inhomogeneous linear differential equations.

10.09 Incomplete second order differential equations. Exact differential equations.

10.16 First midterm

10.30 First part: Systems of differential equations.

Probability theory

10.30 Second part: Basic properties and combinatorial methods of probability.

11.06 Conditional probability, Multiplication Rule, Law of Total Probability, Bayes Theorem.

11.13 Independence, random variables. Expectation and variance of discrete and continuous random variables.

11.20 Discrete distributions: the Binomial, Poisson and Geometric distribution.

11.27 Second midterm

12.04 Density and distribution functions. Continuous distributions: the Uniform, Exponential, Normal and Gamma distributions.

12.11 Properties of expectation and variance. Approximating the Binomial distribution by Normal. The Central Limit Theorem.

Recommended text:

Erwin Kreyszig, Advanced Engineering Mathematics, Wiley. The course will not follow this book, but it contains some of our topics with lots of problems.

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