Course Details
Mathematics 5 (E)
Academic Year 2023/24
CA005 course is part of 1 study plan
N-P-C-SI (N) / N Winter Semester 1st year
Parametric and non-parametric problems with one and two random samples, analysis of relationships, regression analysis, introduction to time series. Use of the EXCEL program.
Errors in numeric calculation. Solving the f(x)=0 equation by graphic and bisection methods. Contraction theorem and solving an f(x)=0 equation by the simple iteration and Newton methods. Iteration methods used to solve systems of linear equations. Interpolating functions by polynomials and cubic splines. Numeric differentiation. Numeric integration.
Errors in numeric calculation. Solving the f(x)=0 equation by graphic and bisection methods. Contraction theorem and solving an f(x)=0 equation by the simple iteration and Newton methods. Iteration methods used to solve systems of linear equations. Interpolating functions by polynomials and cubic splines. Numeric differentiation. Numeric integration.
Course Guarantor
Institute
Objective
Students will learn how to use the EXCEL and STATISTICA programs to apply statistics, study the basic notions of regression, analysis of relationships, analysis of time series. Next they will acquaint themselves with the methods used to solve non-linear equations, iteration methods used to solve systems of linear and non-linear equations, to interpolate functions by polynomials and cubic splines, learning how to numerically differentiate, solve boundary problems in second order ordinary differential equations by the method of grids and by numeric integration.
Knowledge
Knowledge of using the statistical programs to apply statistics in regression, analysis of relationships and time series. Knowledge of numerical methods to solve non-linear equations, systems of linear equations, to interpolate functions by polynomials, to differentiate and integrate numerically.
Syllabus
1. Parametric problems with one random sample.
2. Parametric problems with two random samples.
3. Non-parametric tests. Goodness-of-fit tests.
4. Analysis of relationships.
5. Regression analysis.
6. Time series. Descriptive characteristics of a time series.
7. Estimating the trend and seasonal components of a time series.
8. Error in numeric calculation. Method of bisection. Contraction theorem.
9. Solving f(x)=0 by iteration methods. Norms of matrices and vectors.
10. Iteration methods used to solve systems of linear equations.
11. Interpolating functions by polynomials and cubic splines.
12. Numeric differentiating.
13. Numeric integration.
2. Parametric problems with two random samples.
3. Non-parametric tests. Goodness-of-fit tests.
4. Analysis of relationships.
5. Regression analysis.
6. Time series. Descriptive characteristics of a time series.
7. Estimating the trend and seasonal components of a time series.
8. Error in numeric calculation. Method of bisection. Contraction theorem.
9. Solving f(x)=0 by iteration methods. Norms of matrices and vectors.
10. Iteration methods used to solve systems of linear equations.
11. Interpolating functions by polynomials and cubic splines.
12. Numeric differentiating.
13. Numeric integration.
Prerequisites
Elementary notions of the theory of one- and more-functions (derivative, partial derivative, limit, continuity, graphs of functions). Calculating integrals of one-functions, knowing about their basic applications. The basics of the theory of probability and statistics.
Language of instruction
Czech
Credits
4 credits
Semester
winter
Forms and criteria of assessment
course-unit credit and examination
Specification of controlled instruction, the form of instruction, and the form of compensation of the absences
Extent and forms are specified by guarantor’s regulation updated for every academic year.
Offered to foreign students
Not to offer
Course on BUT site
Lecture
13 weeks, 2 hours/week, elective
Syllabus
1. Parametric problems with one random sample.
2. Parametric problems with two random samples.
3. Non-parametric tests. Goodness-of-fit tests.
4. Analysis of relationships.
5. Regression analysis.
6. Time series. Descriptive characteristics of a time series.
7. Estimating the trend and seasonal components of a time series.
8. Error in numeric calculation. Method of bisection. Contraction theorem.
9. Solving f(x)=0 by iteration methods. Norms of matrices and vectors.
10. Iteration methods used to solve systems of linear equations.
11. Interpolating functions by polynomials and cubic splines.
12. Numeric differentiating.
13. Numeric integration.
Exercise
13 weeks, 1 hours/week, compulsory
Syllabus
1. Graphical methods of data files representation I.
2. Graphical methods of data files representation II.
3. Computational methods of data processing I.
4. Computational methods of data processing II.
5. Summary of survey analysis of one-dimensional populations.
6. Two-dimensional data files.
7. Linear regression.
8. Nonlinear regression.
9. Linear forecasting.
10. Multiple correlation and regression.
11. Numerical solutions of nonlinear equations and systems of linear equations.
12. Interpolation. Numeric differentiating.
13. Numeric integration. Seminar evaluation.