Numerical Analysis - Civil Engineering
Caesar510
numerical_analysis_syllabus-3.pdf
NİŞANTAŞI ÜNİVERSİTESİ - Faculty of Engineering and Architecture
Description of Individual Course Units
2021-2022 Sprin g Semester
Course Unit code
Course Name Type of Course
Weekly Course Hours Credit ECTS Campus/ Weekly da y and date / Class
T U
ECVL208, ECVL220
Numerical Analysis Course 3 0 3,00 5,00 MASLAK 1453 NEOTECH KAMPÜSÜ, MASLAK 1453 BİNASI /Monday 10:00 – 12:20/ Online
Lectu rer Dr. Öğr. Üyesi Merve Temizer Ersoy Student Meeting Day and Time
Tuesday: 13:00-14:00
e-mail: [email protected]
Course Content
Error and Computer Arithmetic: floating-point numbers, error definitions and sources, propagation error, error in summation, loops and inner products. Root Finding: Bisection method and error analysis, Newton method and error analysis, Secant method and error analysis, fixed point iteration, ill -behaving root finding problems. Interpolation and Approximation: polynomial interpolation, error in polynomial interpolation, interpolation using spline functions, minimax approximation, Chebyshev poly nomials, least squares approximation. Numerical Integration and Differentiation: Trapezoidal and Simpson rules, error formulas, Gaussian numerical integration, numerical differentiation.
Learning Outcomes - Solves the analytical thinking ability for the solution of engineering problems with Numerical Methods
- Calculates the numerical differentiation and integration required in solving problems - Calculates numerical methods to be used in solving boundary value problems encountered in engineering.
- Applies numerical methods in solving differential equations
Reco mmendent or
Required Readin g
Numerical Analysis, J. Douglas Faires and Richard L. Burden, Thomson Press, 2004. Numerical Methods using MATLAB, J.H. Mathews & K.D. Fink, 4th Edt., Pearson, 2004.
WEEK Date Theori cal Reco mmendent or Required Readin g
1.Week BINARY NUMBERS 1.1 BINARY SHIFTING 1.2 MACHINE NUMBERS .
Numerical Analysis, J. Douglas Faires and Richard L. Burden, Thomson Press, 2004. Numerical Methods using MATLAB, J.H. Mathews
& K.D. Fink, 4th Edt., Pearson, 2004.
2. Week 2.ERROR ANALYSIS Numerical Analysis, J. Douglas Faires and Richard
L. Burden, Thomson Press, 2004. Numerical Methods using MATLAB, J.H. Mathews & K.D. Fink, 4th Edt., Pearson, 2004.
3. Week 3.1 FIXED-POINT ITERATION
3.2 BRACKETING METHODS 3.3 THE BISECTION METHOD OF BOLZANO 3.4 THE NEWTON-RAPHSON METHOD
Numerical Analysis, J. Douglas Faires and Richard L. Burden, Thomson Press, 2004. Numerical Methods using MATLAB, J.H. Mathews & K.D. Fink, 4th Edt., Pearson, 2004.
4. Week AITKEN’S PROCESS AND STEFFENSEN’S AND MULLER’S METHODS .
4.1 AITKEN’S PROCESS 4.2 STEFFENSEN’S ACCELERATION 4.3 MULLER’S METHOD
Numerical Analysis, J. Douglas Faires and Richard L. Burden, Thomson Press, 2004. Numerical Methods using MATLAB, J.H. Mathews & K.D. Fink, 4th Edt., Pearson, 2004.
5. Week ITERATION FOR NONLINEAR SYSTEMS
5.1 FIXED-POINT ITERATION 5.2 THE SEIDEL ITERATION 5.3 NEWTON’S ITERATION
Numerical Analysis, J. Douglas Faires and Richard L. Burden, Thomson Press, 2004. Numerical Methods using MATLAB, J.H. Mathews & K.D. Fink, 4th Edt., Pearson, 2004.
6. Week SOLUTIONS OF LINEAR SYSTEMS AX = B .
6.1 GAUSSIAN ELIMINATION METHOD 6.2 MODIFICATION GAUSSIAN ELIMINATION METHOD 6.3 L-U DECOMPOSITION
Numerical Analysis, J. Douglas Faires and Richard L. Burden, Thomson Press, 2004. Numerical Methods using MATLAB, J.H. Mathews & K.D. Fink, 4th Edt., Pearson, 2004.
7.Hafta PADE APPROXIMATION
7.1 INTERPOLATION 7.2 LAGRANGE’S METHOD 7.3 NEWTON’S METHOD
Numerical Analysis, J. Douglas Faires and Richard
L. Burden, Thomson Press, 2004. Numerical Methods using MATLAB, J.H. Mathews & K.D. Fink, 4th Edt., Pearson, 2004.
8. Week Midterm Exam Numerical Analysis, J. Douglas Faires and Richard
L. Burden, Thomson Press, 2004. Numerical Methods using MATLAB, J.H. Mathews & K.D. Fink, 4th Edt., Pearson, 2004.
9. Week 8 LEAST SQUARE LINES AND PARABOLAS. CURVE FITTING Numerical Analysis, J. Douglas Faires and Richard
L. Burden, Thomson Press, 2004. Numerical Methods using MATLAB, J.H. Mathews & K.D. Fink, 4th Edt., Pearson, 2004.
10. Week 9 NUMERICAL DIFFERENTIATION Numerical Analysis, J. Douglas Faires and Richard
L. Burden, Thomson Press, 2004. Numerical Methods using MATLAB, J.H. Mathews & K.D. Fink, 4th Edt., Pearson, 2004.
11. Week 10 NUMERICAL INTEGRATION
10.1 RECTANGLE RULE
10.2 TRAPEZOIDAL RULE 10.3 COMPOSITE TRAPEZOIDAL AND SIMPSON’S RULE
Numerical Analysis, J. Douglas Faires and Richard L. Burden, Thomson Press, 2004.
Numerical Methods using MATLAB, J.H. Mathews & K.D. Fink, 4th Edt., Pearson, 2004.
12. Week 11 NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS
11.1 ERROR OF DIFFERENCE SCHEME 11.2 STABILITY OF DIFFERENCE SCHEME 11.3 TAYLOR’S METHOD
Numerical Analysis, J. Douglas Faires and Richard L. Burden, Thomson Press, 2004. Numerical Methods using MATLAB, J.H. Mathews & K.D. Fink, 4th Edt., Pearson, 2004.
13. Week 11.4 RUNGE-KUTTA’S METHOD
11.5 HEUN’S METHOD 11.6 MODIFIED EULER-CAUCHY METHOD
Numerical Analysis, J. Douglas Faires and Richard L. Burden, Thomson Press, 2004. Numerical Methods using MATLAB, J.H. Mathews & K.D. Fink, 4th Edt., Pearson, 2004.
14. Week GENERAL REPETİTİON AND PRACTİCES Numerical Analysis, J. Douglas Faires and Richard
L. Burden, Thomson Press, 2004. Numerical Methods using MATLAB, J.H. Mathews & K.D. Fink, 4th Edt., Pearson, 2004.
Assessment
Activities Numb er Date Contribution to
Success Grade (%)
Final Examination 1 - 60,0
Midterm Examination 1
40,0
Workload Calculation
Activities Number Duration (Hours) Total Work Load (hours)
Midterm Examination 1 1 1
Final Examination 1 1 1
Attending Lectures 14 3 42
Self Study 14 3 42
Individual Study for Midterm
Examination
1 18 18
Individual Study for Final
Examination
1 18 18
Homework 1 14 14
Total Work Load (hours) 136
