EP208 Computational Methods in Physics INTRODUCTION TO COURSE Department of Engineering Physics University of Gaziantep Feb 2014

Content Introduction The Course Example Numerical Problems

Introduction This is an introductory level course in numerical and computational methods with emphasis on applied computing. Solving problems in engineering often relies on a numerical method when an analytical method is complex or not available. In such cases computers are employed to perform the numerical calculations with speed and accuracy. Numerical analysis is very large discipline; see the list of topics given in wikipedia.

By the end of the course, the student will be able to approach some problems from a computational point of view and be able to implement solutions in the form of dedicated computer programs. We will use C++ Programming Language for the implementation of the numerical methods on the computer. gnuplot for plotting data Processing for plotting data

Course Web Page http://www.gantep.edu.tr/~bingul/ep208 Also search Google and Wikipedia for any of the expressions used in this course.

Course Content Sources of Errors Numerical Differentiation Roots of Equations Optimization Numerical Integration Solutions of Differential Equations Least Square Fitting Monte Carlo Methods

Lectures, Labs, Attendance, Exams Mondays – 08:30-10:20 (17:00-18:40) two-hour lecture Thursdays – 13:30-15:20 (19:45-21:30) two-hour lab Attendance You must attend at least 70% of the course Exams Mid-term 30% 22 Mar 2014 Quiz 30% Weekly Final 40% ?? May 2014

Grading FIRST & SECOND EDUCATION Independent from the arithmetic mean of the class, the following rules will be applied for each student: 00-19 -> FF 20-29 -> FD 30-39 -> DD 40-49 -> DC 50-59 -> CC 60-66 -> CB 67-75 -> BB 75-84 -> BA 85-99 -> AA

YOUR LAPTOP or FLASH DISK WITH YOU Computer Labs We’ll use Windows and/or Linux operating systems Every week, there will be a QUIZ You may need to save them on a flash drive or on the internet. DO NOT FORGET TO BRING YOUR LAPTOP or FLASH DISK WITH YOU

Example Numerical Problems Find the root of the equation: Evaluate the integral: Solve the differential equation:

Example Numerical Problems Aerospace engineers sometimes compute the trajectories (path) of projectiles like rockets. A trajectory of a rocket is defined by a (x, y) coordinates and is modelled by Find the appropriate initial angle θ if v0 = 200 m/s and x = 1950 m (a) For y0 = 0 and y1 = 0 (a) For y0 = 28 m and y1 = 123 m.

Solution: (a) We have analytical solution (b) It is not easy to find the analytical solution of the last equation. We can use a numerical method which gives We’ll see later…