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General numerical methods

General numerical methods

Course Materials - General Numerical Methods
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Course Information

CourseGeneral numerical methods CodeUSUM151
Directions70540202 – Mathematical Engineering (Master) Semester2
Type of subjectCompulsory Taught LanguageEnglish
Lectures30 Practical Lessons30
Subject TeacherUmid Karimov Independent Work90
Total Hours150 Credits5

Lectures

CodeTopicMaterial
L1Introduction. The errors and their sources. Methods of approximate computing. Significant figures (Digits).Download
L2Interpolation formulas. Lagrange interpolation formula. Newton interpolation formulas. Spline interpolation. The error of the interpolation formula. Least squares method. Download
L3Numerical solution of equations: Graphical solutions, Bisection method, Secant methods, Newtons methods, Fixed-point iteration method. Download
L4Numerical solution of system of linear equations: The Gauss-Seidel Method, The Jacobi Method.Download
L5Numerical integration. Quadrature formula for numerical integration. Trapezoidal rule. Simpsons formula. The error of the numerical integration formulas.Download
L6Numerical solution of ODEs. Euler’s rule. Modified Euler’s rule. Runge-Kutta methods.Download
L7The fourth-order Adams-Bashforth technique for solving IVPs for Ordinary Differential EquationsDownload
L8The fourth-order Adams-Moulton technique for solving IVPs for Ordinary Differential EquationsDownload
L9 Predictor-Corrector Methods for solving IVPs for Ordinary Differential EquationsDownload
L10 Numerical solution of the system of ODES.Download
L11 Boundary-Value Problems for Ordinary Differential Equations The Linear Shooting Method for solving Boundary-Value ProblemsDownload
L12 Numerical Solutions to Partial Differential Equations. Poisson Equation Finite-Difference. Parabolic Partial Differential Equations. Forward Difference Method for solving the Parabolic Partial Differential Equations.Download
L13 Backward-Difference Method for solving the Parabolic Partial Differential Equations. Heat Equation Backward-Difference. Wave Equation Finite-DifferenceDownload
L14 Numerical methods for integral equations: Quadrature methods. Numerical solution of Fredholm integral equation of the second kind. Download
L15 Numerical solution of Fredholm integral equation of the second kind.Download

Practical Lessons

CodeTopicMaterial
S1Round-off errors. Truncation Error. Absolute Error. Absolute relative error. Download
S2Lagrange interpolation formula. Newton’s first and second divided differences formula. Quadratic and Cubic spline interpolation. Least squares method.Download
S3Bisection method, Secant methods, Newtons methods, Fixed-point iteration method. Download
S4Numerical solution of system of linear equations: The Gauss-Seidel Method, The Jacobi Method.Download
S5Quadrature formula. Trapezoidal rule. Simpsons formula. Download
S6Euler’s rule. Modified Euler’s rule. Runge-Kutta methods.Download
S7The fourth-order Adams-Bashforth technique for solving IVPs for Ordinary Differential EquationsDownload
S8The fourth-order Adams-Moulton technique for solving IVPs for Ordinary Differential Equations Download
S9Predictor-Corrector Methods for solving IVPs for Ordinary Differential Equations Download
S10Numerical solution of the system of ODES: Adaptive Methods. Download
S11Boundary-Value Problems for Ordinary Differential Equations. The Linear Shooting Method for solving Boundary-Value Problems Download
S12Numerical solution of the Poisson Equation via Finite-Difference method. Forward Difference Method for solving the Parabolic Partial Differential Equations. Download
S13Numerical solution of the Wave Equation via Finite-Difference method. Numerical of the Heat Equation via Finite-Difference method.Download
S14Numerical methods for integral equations: Quadrature methods. Numerical solution of Fredholm integral equation of the second kind. Download
S15Numerical solution of Fredholm integral equation of the second kind.Download
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