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ME 361

Numerical Methods for Engineers

ME 361 is about turning the calculus and linear algebra you already know into algorithms a computer can actually execute, so you can attack engineering problems that have no clean closed-form answer. You'll spend the semester implementing root-finders, linear solvers, interpolation schemes, quadrature rules, and ODE integrators, then judging their accuracy and stability through quizzes, a project, and two exams. It sits right where your math background meets real engineering practice, and the habits you build here, discretization, error analysis, picking the right method for the problem, show up again in heat transfer, fluids, vibrations, and any later course where you'll lean on MATLAB or a solver instead of pencil and paper.

Kredi3ECTS5FakülteFaculty of EngineeringBölümMechanical EngineeringKoordinatörAli Javili

Ön koşul(CS 114 veya CS 115) ve (MATH 220 veya MATH 241 veya MATH 224) ve (MATH 240 veya MATH 242)

→ STARS müfredatı (resmi syllabus)

Haftalık müfredat 14 hafta

Hafta 114–20 Eyl

Taylor series, yaklaşım ve hata

Taylor Series, Approximations and Errors

Taylor seriesapproximationerror

Hafta 221–27 Eyl

Denklem köklerinde bisection ve false position

Roots of Equations: Bisection, False Position, and Iteration Methods

bisectionfalse positioniteration methodsroots of equations

Hafta 328 Eyl – 4 Eki

Newton-Raphson ve Secant yöntemleri

Newton-Raphson and Secant Methods, System of Non-linear Equations

Newton-RaphsonSecant methodnon-linear equations

Hafta 45–11 Eki

Lineer denklem sistemleri için sayısal yöntemler

System of Linear Algebraic Equations: Gauss Elimination, Matrix Inversion, Gauss-Seidel Iteration

Gauss eliminationmatrix inversionGauss-Seidel iteration

Hafta 512–18 Eki

Tek boyutlu kısıtsız optimizasyon

One-dimensional Unconstrained Optimization

one-dimensional optimizationunconstrained optimization

Hafta 619–25 Eki

Curve fitting ve least squares regression

Curve Fitting, Least Squares Regression

curve fittingleast squares regression

Hafta 726 Eki – 1 Kas

Polynomial Interpolation

Hafta 82–8 Kas

Spline interpolation yöntemi

Spline Interpolation

splineinterpolation

Hafta 99–15 Kas

Numerical differentiation

Hafta 1016–22 Kas

Numerical integration ve Newton-Cotes formülleri

Numerical Integration, Newton-Cotes Formulae

numerical integrationNewton-Cotes formulae

Hafta 1123–29 Kas

Romberg ve Gauss-Quadrature integrasyonu

Romberg’s and Gauss-Quadrature Integration

Romberg integrationGauss-Quadraturenumerical integration

Hafta 1230 Kas – 6 Ara

Ordinary differential equations'ın çözümü

Solution of Ordinary Differential Equations

ordinary differential equations

Hafta 137–13 Ara

Euler, Runge-Kutta ve multi-step yöntemleri

Euler, Runge-Kutta, Multi-Step Methods

Euler methodRunge-Kuttamulti-step methods

Hafta 1414–20 Ara

ODE sistemleri ve sınır-değer problemleri

System of ODE’s, Initial-Value Problems, Boundary-Value Problems

ODE sistemleriinitial-value problemboundary-value problem

Değerlendirme 100% · 4 adım

48%

22%

Project 1 Project x 8% = 8% 8%

Quiz 6 Lab Assignments x 8% = 48% 48%

Midterm 1 Exam x 22% = 22% 22%

Final 1 Exam x 22% = 22% 22%

en büyük tek kalem %48 · sınav ağırlığı %92 · 13 dönem ortalaması 2.30 (421 öğrenci) nasıl hesaplanıyor

Önerilen kaynaklar 1 kitap

📕

Zorunlu

Numerical Methods for Engineers

S.C. Chapra and R.P. Canale

7th edition / 2014 · McGraw Hill

Bu dersi alınca · 5 öğrenme çıktısı

Enhancing problem solving skills: Numerical methods are extremely powerful problem-solving tools. They are capable of handling large system of equations, non-linearities, and complicated geometries that are not uncommon in engineering practice, and that are often impossible to solve analytically.6 Lab Assignments x 8% = 48%, 1 Exam x 22% = 22%, 1 Exam x 22% = 22%
Giving knowledge of the basic theory: the intelligent use of “pre-packaged” or “canned” computer programs that involve Numerical methods is often predicated on the knowledge of the basic theory underlying these methods.6 Lab Assignments x 8% = 48%, 1 Exam x 22% = 22%, 1 Exam x 22% = 22%
Designing computer programs: Many engineering problems cannot be approached using “canned programs”. Being conversant with numerical methods and being adept at computer programming, gives the capability of solving problems without having to buy or commission expensive software.and global climate change, and will be able to assess the validity of energy conversion claims made in popular media.6 Lab Assignments x 8% = 48%, 1 Exam x 22% = 22%, 1 Exam x 22% = 22%
Exhibit power and limitations of computers: Successfully implementation of numerical methods on a computer and then their application to solve otherwise intractable problems, provides a dramatic demonstration of how computers can serve one’s professional development, and helps acknowledge and control the errors of approximation that are part and parcel of all large-scale numerical calculations.6 Lab Assignments x 8% = 48%, 1 Exam x 22% = 22%, 1 Exam x 22% = 22%
Reinforce understanding of mathematics: Because one function of numerical methods is to reduce higher mathematics to basic arithmetic operations, they get at the 'nuts and bolts' of some otherwise obscure topics. Enhanced understanding and insight can result from this alternative perspective.6 Lab Assignments x 8% = 48%, 1 Exam x 22% = 22%, 1 Exam x 22% = 22%

Bilkent'in resmî syllabus'ünden. Sağdaki etiket o çıktının hangi değerlendirmeyle ölçüldüğünü söylüyor.

🤖 GenAI politikası

Students are advised to consult their instructor regarding the use of Generative AI tools and their appropriateness. Responsible use of GenAI is encouraged in accordance with Bilkent University's GenAI Guidelines (https://w3.bilkent.edu.tr/bilkent/generative-artificial-intelligence-genai-guideline).

Ders notları · henüz yok

ME 361 için defter ekibi henüz not yazmadı.

İlk dosyayı sen atarsan: not, slayt, geçmiş sınav, çözüm, cheat-sheet, ne varsa. defter ekibi öğrenci paylaşımlarından bu dersin notlarını yazar. Drive linki / PDF / ZIP, hepsi olur.

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Geçmiş GPA dağılımı 13 dönem · ort. 2.30

Dönem	Course CPA
2024-2025 Spring	2.97	1 sec · 28 öğr
2023-2024 Spring	3.28	1 sec · 55 öğr
2021-2022 Fall	1.36	1 sec · 14 öğr
2020-2021 Fall	1.83	1 sec · 29 öğr
2019-2020 Spring	2.30	1 sec · 11 öğr
2018-2019 Fall	1.27	1 sec · 42 öğr
2017-2018 Fall	2.13	1 sec · 47 öğr
2016-2017 Fall	2.44	1 sec · 53 öğr
2015-2016 Fall	2.27	1 sec · 41 öğr
2014-2015 Fall	1.81	1 sec · 21 öğr

Aggregate course GPA · Bilkent STARS'tan public data. Hoca-bazlı per-section detayı için STARS evaluation report →. Öğrenci anket cevapları KVKK kapsamında defter'de tutulmaz. Tüm derslerin ortalamaları →

2026-2027 Güz için şubesi henüz görünmüyor. Kayıt sistemi bu dersi bu dönem listelemiyor, ama şube girişi sürüyor: ders kaydı 15 Eylül, bölümler o güne kadar şube ekleyebiliyor. Son 4 güz döneminde açılmamış; en son 2021-2022 güz döneminde açılmış. Ön kayıt müfredat üzerinden yapılıyor, açılan şube listesi üzerinden değil; o yüzden ön kayıtta seçebildiğin bir dersin şubesi burada henüz görünmeyebilir. Kesin sonuç ders kaydında belli oluyor. kayıt tarihleri → · açık dersler

⚠️ FZ engelleyen şartlar

Course Learning Outcomes: Course Learning Outcome Assessment Enhancing problem solving skills: Numerical methods are extremely powerful problem-solving tools. They are capable of handling large system of equations, non-linearities, and complicated geometries that are not uncommon in engineering practice, and that are often impossible to solve analytically. 6 Lab Assignments x 8% = 48% 1 Exam x 22% = 22% 1 Exam x 22% = 22% Giving knowledge of the basic theory: the intelligent use of “pre-packaged

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