Mathematics A3 SYLLABUS (2017/2018 first semester)

Topic I. Differential equations:

Sept. 5. Classification and application of differential equations. Separable equations. Homogeneous (in the variable) equations. The existence and uniqueness theorem for first order equations.

Sept. 12. First order linear differential equations. Autonomous equations, stability.

Sept. 19. Exact equations. Second order linear equations. Homogeneous equations: fundamental solutions, linear independence and Wronskian, linear equations with constant coefficients.

Sept.26. Inhomogeneous second order linear equations : with constant coefficients (Method of Undetermined Coefficients), Variation of Parameters Method.

Oct. 3. Will be a practical lesson. Applications, e.g., oscillations..

Oct. 10. First midterm, continue with systems of linear differential equations, special types of nonlinear second order equations (missing terms)

Topic II. Probability theory:

Oct. 17. Combinatorial analysis. Permutations, variations, combinations, binomial theorem. Sample space and events.

Oct. 24. Axioms of probability. Sample spaces having equally likely outcomes, geometric probability. Conditional probability, multiplication rule.

Oct. 31. Law of total probability, Bayes’ Formula, independence of events. Random variables. Distribution functions, expectation, and variance. Independence of random variables.

Nov. 7. Discrete random variables: Bernoulli, Binomial, Geometric, Negative Binomial (Pascal), Hypergeometric, Zeta (Zipf) distributions.

Nov. 14. NO class.

Nov. 21. Absolutely continuous random variables, density and distribution functions. Uniform, Exponential, Normal (Gaussian) distributions.

Nov. 28. Second midterm, continue with Chebysev’s inequality and the weak law of large numbers. The Central Limit Theorem, Moivre–Laplace Theorem.

Dec. 5. Linear regression, basic statistics.

Lecturer: István Kolossváry
homepage: www.mat.bme.hu/~istvanko/CivilA3English
e-mail: istvanko@math.bme.hu