Schedule of Mathematics A3

(for civil engineering students)

Fall (First) Semester of Academic Year 2010--11

Ordinary Differential Equations (ODE)

Sept 08 Requirements in the course. Separable ODE. Modelling with ODE.

Sept 15 First order linear ODE. Existence and uniqueness for first order ODE. Numerical methods. Stability.

Sept 22 Second order linear ODE: the homogenous case with constant coefficients.

Sept 29 Second order linear ODE: the inhomogenous case with constant coefficients.

Oct 06 Incomplete second order ODE. Exact DE.

Oct 13 Midterm 1.

Oct 20 Systems of linear differential equations.

Probability Theory

Oct 27 The concept of probability. Applications of the combinatorial methods.

Nov 03 Conditional probability, multiplication rule, conditioning, Bayes rule. Independence.

Nov 10 Discrete random variables, expectation and variance. Important discrete distributions: binomial, Poisson, geometric.

Nov 17 Open Day: no classes.

Nov 24 Probability density and distribution functions. Important continuous distributions: uniform and exponential.

Dec 01 Midterm 2.

Dec 08 Properties of expectation and variance. Normal distributions, central limit theorem.

Recommended textbooks:

• W E Boyce and R C DiPrima. Elementary Differential Equations, Wiley.
• S Ross. A First Course in Probability, Pearson.