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### Mathematical methods in chemistry 2

 Code: 41013 ECTS: 5.0 Lecturers in charge: prof. dr. sc. Branimir Bertoša Lecturers: prof. dr. sc. Branimir Bertoša - Seminar Take exam: Studomat

### 1. komponenta

Lecture typeTotal
Lectures 30
Seminar 15
Description:
COURSE CONTENT:
Approximate numbers: sources of errors, significant figures, rounding numbers, errors of arithmetic operations and functions, error progression. Nonlinear equations: root isolation, bisection method, Newton-Raphson method, secant method, method of successive approximations. Interpolation: interpolation problem, finite differences, Newton's method, Lagrange's method, spline method. Numerical differentiation and integration: numerical differentiation of continuous and discrete functions, numerical integration, trapezoidal formula, Simpson's formula. Ordinary differential equations: Euler's method, Runge-Kutta methods, finite difference method. Optimization: non-derivative and derivative minimisation methods, simplex, steepest descents algorithm, conjugate gradients algorithm, Newton-Raphson method, global search, Monte Carlo method, genetic algorithm. Probability theory: classical definition of probability, axiomatic definition of probability, conditional probability, total probability, Bayes formula, basics of combinatorics, fundamental theorem of counting, variations, permutations, combinations. Basic statistics: descriptive statistics, measures of central tendency and dispersion, sampling and graphical representation of data. Discrete randrom variables: random variables, probability function, cumulative distribution function, moments of distribution, uniform distribution, Bernoulli trials, binomial distribution, Poisson distribution, hypergeometric distribution, estimate of distribution parameters. Continuous distribution function: probabiltiy density function, cumulative distribution function, moments of distribution, continuous uniform distribution, Gauss distribution, exponential distribution, estimate of distribution parameters. Statistical hypothesis testing: null-hypothesis, statistical model checking, location and dispersion tests. Regression: linear regression and correlation, confidence intervals, nonlinear regression.

LEARNING OUTCOMES:
- to discriminate the exact and the approximate numbers
- to calculate the relative and the absolute error
- to solve nonlinear equations using adequate numerical methods
- to use numerical methods for interpolation
- to use numerical methods for differentiation and integration
- to discriminate numerical methods for optimisation of functions
- to explain basic principles of probability theory
- to explain basic principles of statistics
- to discriminate discrete and continuous variables
- to explain probability density function and cumulative distribution function
- to use binomial, Poisson, and hypergeometric distributions
- to use normal (Gaussian) distribution and uniform distribution
- to define statistical tests and hypothesis
- to use regression analysis
Literature:
1. 1. T. Hrenar: Matematičke metode u kemiji, rkp. u pripremi i dijelom dostupan putem Sveučilišnog centra za e učenje Merlin (http://merlin.srce.hr, za pristup je potreban AAI korisnički račun).
2. N. Sarapa Teorija vjerojatnosti, drugo izdanje, Školska knjiga, Zagreb 1992.
3. P. Atkins and J. de Paula: Physical Chemistry, 8th Ed., Oxford University Press, Oxford, 2007.
4. P. Atkins and R. Friedman: Molecular Quantum Mechanics, 4th Ed., Oxford University Press, Oxford, 2005.
5. Numerical Recipes in Fortran 77 http://www.nrbook.com/nr3/
2. L. Klasinc, Z. Maksić, N. Trinajstić: Simetrija molekula, Školska knjiga, Zagreb 1979.
3. D. C. Montgomery, G. C. Runger: Applied Statistics and Probability for Engineers, Wiley, New York 2003.
4. K. F. Riley, M. P. Hobson, S. J. Bence: Mathematical Methods for Physics and Engineering, Cambridge University Press, Cambridge
1998.
5. D. B. Chesnut: Finite Groups and Quantum Theory, Wiley, New York 1974.
6. D. S. Moore: The Basic Practice of Statistics, Freeman, New York 2003.
Prerequisit for:
Enrollment :
Attended : Mathematical methods in chemistry 1

Examination :
Passed : Mathematics 2
 4. semester Mandatory course - Regular study - Chemistry
Consultations schedule: