1. The Islamic University of Gaza Faculty of Engineering Civil Engineering Department Numerical Analysis ECIV 3306 Introduction Course Outline

2. Introduction Solve

3. Numerical Methods - Definition Numerical Methods Numerical methods are techniques by which mathematical problems are formulated so that they can be solved with arithmetic operations. Numerical methods involve large numbers of tedious arithmetic calculations. These methods have gained popularity due to the advancements in efficient computational tools such as digital computers and calculators.

4. Numerical Methods Noncomputer methods Analytical or exact methods Graphical solutions used to solve complex problems but the results are not very precise. They are extremely tedious without computers  limited problems. Calculators

5. Numerical vs. Analytical Methods Analytical Methods Solution have been derived for some engineering problems using analytical (or exact) methods. In general there are few closed-form engineering or exact solutions including problems that can be approximated with linear models or that have simple geometry and low dimensionality. These solutions are often useful and provide excellent insight into the behavior of an engineering system.

6. Numerical vs. Analytical Methods Examples: Analytical Methods

7. Numerical vs. Analytical Methods Need for Numerical Methods In general, there are few analytical (closed-form) solutions for many practical engineering problems. Numerical methods can handle: Large systems of equations Non-linearity Complicated geometries that are common in engineering practice and that are often impossible to solve analytically. Examples:

8. Mathematician and Engineer The thinking of engineers toward mathematics has always been different from that of mathematicians. Mathematician may be interested in finding out whether a solution to a differential equation exists. An engineer simply assumes that the existence of a physical system is proof enough of the existence of a solution and focuses instead on finding it.

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10. Course Content (continued)

12. Exams and Grading Policy Homework, Quizzes and Programming Assignment25 points Midterm Exam25 points Final Exam50 points Total100 points Text Book: Numerical Methods for Engineers, S. C. Chapra & R. P. Canale, Fourth Edition, McGraw-Hill Inc. UK, 2002 Course Outline

13. WeekTopics 1.Introduction (Approximation and Errors) Chapter 1Mathematical Modeling Chapter 3Approximation and Round-off Errors Chapter 4Truncation Errors and Taylor Series 2-4 Roots of Equations Chapter 5Bracketing Methods Chapter 6Open Methods Chapter 7Roots of Polynomials Chapter 8Engineering Applications 5-8 System of Linear Algebraic Equations Chapter 9Gauss Elimination Chapter 10LU Decomposition and Matrix Inversion Chapter 11Special Matrices and Gauss-Seidel Chapter 12Engineering Applications Midterm Exam Course Outline

14. Week Topics 9-10Curve Fitting Chapter 17Least–Square Regression Chapter 18Interpolation Chapter 20Engineering Applications 11-12Numerical Differentiation and Integration Chapter 21Newton–Cotes Integration Formulas Chapter 22Integration of Equations Chapter 23Numerical Differentiation Chapter 24Engineering Applications 13Ordinary Differential Equations Chapter 25Runge-Kutta Methods 14Partial Diffrential Equations Chapter 29Finite Difference Method: Elliptic Equations Chapter 30Finite Difference Method: Parabolic Equations Course Outline