This course is a programming course; students need to implement all discussed topics by any programming language in class per class fashion.This course include these topics: Introduction to error analysis, root finding methods for non-linear equations (interval halving, false position), Newton’s method, definition of interpolation, Newton’s-Gregory interpolation, central interpolation (Gauss forward and backward, Bessel, Stirling), Least square approximation, Spline curves, Numerical differentiation, Numerical integration (Trapezoidal method, Simpson's), Numerical solution of ordinary differential equations (Taylor’s series method), Euler method, Runge-Kutta method.
Intended learning outcomes
Knowledge and understanding
That the student recognize the errors in the numerical solution and measure the error
To familiarize the student with series and how to use them in numerical methods
That the student remember the appropriate formulation of the law for solving a problem and how to formulate the solution in the form of an algorithm
That the student draws a function curve and knows the limits, periods, and operations that are based on functions
mental skills
That the student recognize the errors in the numerical solution and measure the error
To familiarize the student with series and how to use them in numerical methods
That the student remember the appropriate formulation of the law for solving a problem and how to formulate the solution in the form of an algorithm
That the student draws a function curve and knows the limits, periods, and operations that are based on functions
Practical and professional skills
The ability to solve mathematical problems in: calculus, integration, differential equations, systems of linear equations, find approximate solutions to nonlinear equations using numerical methods and study their accuracy and the possibility of improvement.
The ability to write an algorithm for the numerical method to solve a given problem
The ability to write a program for the numerical method to solve a specific problem
The student should use ready-made software such as a programming language or Math Lab to solve numerical problems
Work independently to complete weekly assignments and exercises
General and transferable skills
The ability to solve mathematical problems in: calculus, integration, differential equations, systems of linear equations, finding approximate solutions to nonlinear equations using numerical methods and studying their accuracy and the possibility of improving them using ready-made software.
Solve examples and problems on the topic in question
The ability to use the computer and the Internet to search for a solution to a specific problem or a similar previous study
Editorial communication through presentations and assignments on a specific topic assigned to the student.
Teaching and learning methods
Lectures
Tutorials
Problem-based learning
Mini-projects
Methods of assessments
Written test (midterm) = 25
Written test (final) = 25
Scientific activities = 15
Discussions = 10
Course contents
Introduction
Introduction to error analysis and sources of error
