DisCont mathematics 2
Learning advanced and modern techniques of evaluation of the values of some functions and various forms of its approximations.
- Understand the principles of numerical calculation of some elementary functions.
- Understand the principles of varyous types of approximations.
- Use the technique of approximatrion of a function by orthogonal polynomials.
- Use the technique of fast summing algorithms.
- Use the technique of acceleration of the convergence of some numerical series.
- Understzand the asymptotical convergence and its application in calculations of values of some special functions.
- Learn how to use modern mathematical literature
- Lear how to use mathematical software in solving of complex problems.
Forms of Teaching
Lectures are organized through two cycles. The first cycle consists of 7 weeks of classes and mid-term exam, a second cycle of 6 weeks of classes and final exam. Classes are conducted through a total of 15 weeks with a weekly load of 4 hours.Exams
Mid-term exam in the 8th week of classes and final exam in the 15th week of classes.Consultations
Consultations are held one hour weekly according to arrangement with students.Other
|Type||Threshold||Percent of Grade||Comment:||Percent of Grade|
|Homeworks||0 %||20 %||0 %||20 %|
|Seminar/Project||0 %||10 %||0 %||10 %|
|Mid Term Exam: Written||0 %||30 %||0 %|
|Final Exam: Written||0 %||40 %|
|Exam: Written||0 %||60 %|
Week by Week Schedule
- Evaluation of values of functions. Horner's algorithm. Fast summation algorithm. identities.
- Solving algebraic equations
- Acceleration of convergence. Manipulation with series.
- The connection between integrals and sums. Complex techniques of summing.
- Continued fractions. Basic properties and formulas.
- Representation of numbers and functions by continued fractions. Rational approximations.
- Orthogonal polynomials. Polynomials given by reccursive relations. Applications of fast summing algorithms
- Čebyšev's polynomials and problem of approximations. Fast calculations of Fourier series.
- Series of functions. Generating functions of functional series. Z-transformation
- Factorial and gamma functions. Stirling formula. Approximations of binomial coefficients.
- Asympthotic behaviour. Asymptotic series.
- Harmonic series and related problems. Euler constant.
- Student seminar. Solution of advanced problems