Numerical Method
- 1. Course Details Numerical analysis Course code: 235 Course credit: 3.00 Presented By Zannatul Mawa Koli Designation: lecturer Contact number: 01878045829 E-mail: zannatulmawa.cse@diu.edu.bd Lecture One
- 2. • Course Content • Course Objective • Course Learning Outcome (CLO) • What is numerical analysis • Application of Numerical analysis Lecture outline
- 3. Course Content • Numbers and Errors: Introduction, Accuracy and errors, Significant digits, Absolute and relative error, Rounding error in functional evaluation, Propagation of error in arithmetic process and Truncation errors. • Solution of Non-linear Equation: Method of iteration, Bisection method, Newton– Raphson method, False position method, Secant method, Fixed point method. • Interpolation: Lagrange interpolation, Difference tables, Newton’s forward and backward interpolation formula, Spline interpolation. • Solution of Linear Equations: Gaussian elimination, Gaussian elimination by pivoting, LU decomposition, Cholesky method, Triangular systems and back substitution, Gauss-Jordan method, Iteration method of Jacob and Gauss-Seidel. • Curve fitting: Linear and polynomial regression, Fitting exponential and Trigonometric functions, Chebyshev polynomial. • Numerical Integration & Differentiation: Trapezoidal rule, Simpson’s 1/3 rule, Simpson’s 3/8 rule, Boole’s rule, Weddle method and Rhomberg rule with error, Min-Max values of tabulated functions. • Solution of Ordinary Differential Equations: Runge-kutta method, Euler and modified Euler’s method, Picard's method, Milne's method, Taylors series methods.
- 4. Course Objective Computing integrals and derivatives. Solving differential equations. Building models based on data, be it through interpolation, Least Square, or other methods. Root finding and numerical optimization. Estimating the solution to a set of linear and nonlinear equations. Computational geometry.
- 5. Course Learning Outcome (CLO) CLO1 Demonstrate an understanding of common numerical methods and how they are used to obtain approximate solutions to otherwise intractable mathematical problems. CLO2 Apply numerical methods to obtain approximate solutions to mathematical problems and estimate errors in the calculation of various methods. CLO3 Evaluate the accuracy of numerical methods for various mathematical operations and tasks, such as interpolation, differentiation, integration, the solution of linear and nonlinear equations, and the solution of differential equations.
- 6. What is numerical analysis Branch of mathematics that solves continuous problems using numeric approximation. Involves designing methods that give approximate but accurate numeric solutions, which is useful in cases where the exact solution is impossible or prohibitively expensive to calculate. The different types of numerical analysis are finite difference methods, propagation of errors, interpolation methods, and so on.
- 7. Application of Numerical analysis It investigates and provides accurate solutions to real-life problems from the field of science, engineering, biology, astrophysics and finance. Car safety enhancements, Airflow patterns in the Respiratory Tract, Financial industry, Weather predictions, Spacecraft Dynamics, Machine learning etc.