DERS KATALOG FORMU
COURSE CATALOG FORM
Dersin Adı: Mühendislik Matematiği Course Name: Engineering Mathematics
Bölüm / Program: Makina Mühendisliği / Makina Mühendisliği
Department / Program: Mechanical Engineering / Mechanical Engineering 		Dersin Dili (Course Language): English/Türkçe
Kod
(Code)		 Kredi
(Local Credits)		 AKTS Kredi
(ECTS Credits) 		Ders Uygulaması, Saat/Hafta
(Course Implementation, Hours/Week)
Ders
(Theoretical)		 Uygulama
(Tutorial)		 Laboratuar
(Laboratory)
MAK201E-MAK201 3 5 2 2 0
Önşartlar
(Prerequisites) 		Ders önşartı (Course prerequisite) ( MAT 102 MIN. DD or MAT 102E MIN. DD ) or ( MAT 104 MIN. DD or MAT 104E MIN. DD )
Sınıf önşartı (Class prerequisite): Yok (None)
Dersin Tanımı
(Course Description) 		-Bu ders, diferansiyel denklemlerin mühendislikteki önemini ve uygulama alanlarını kapsamaktadır. Ders kapsamında diferansiyel denklemler sınıflandırılarak, birinci mertebeden diferansiyel denklemler ile ikinci ve daha yüksek mertebeden lineer ve değişken katsayılı diferansiyel denklemler incelenmektedir. Ayrıca Laplace dönüşümleri, birinci mertebeden lineer denklem sistemleri ve kısmi diferansiyel denklemler konularına yer verilmektedir. Dersin sonunda öğrenciler, diferansiyel denklemleri mühendislik problemlerinin modellenmesi ve çözümünde etkin biçimde kullanma becerisi kazanırlar.
-This course covers the importance and applications of differential equations in engineering. It includes the classification of differential equations, first-order differential equations, and second- and higher-order linear and variable-coefficient differential equations. The topics also include Laplace transforms, first-order linear systems of equations, and an introduction to partial differential equations. By the end of the course, students will be able to effectively use differential equations to model and solve engineering problems.
Dersin Amacı
(Course Objectives)
  1. Diferensiyel denklemleri anlamak, kurmak, çözmek ve yorumlamak için gereken temel kavramları tanıtmak.
  2. Çeşitli tiplerdeki diferansiyel denklemlerin çözüm yöntemlerini öğretmek.
  3. Matematik bilgilerini mühendislik problemlerine uygulama becerisi kazandırmak.
  1. To introduce the basic concepts required to understand, construct, solve and interpret differential equations.
  2. To teach methods to solve differential equations of various types.
  3. To give an ability to apply knowledge of mathematics to engineering problems.
Dersin Öğrenme Çıktıları
(Course Learning Outcomes)
  1. Diferansiyel denklemleri belli özelliklerine göre sınıflandırır.
  2. Birinci mertebeden lineer ve belirli tipte lineer olmayan diferansiyel denklemleri çözer ve çözümleri yorumlar.
  3. Lineer denklem çözümleri için varlık ve teklik koşullarını anlar.
  4. İkinci ve daha yüksek mertebeden sabit katsayılı lineer denklemler için çözüm bulur ve lineer bağımsız çözümlerden tüm çözümleri türetir.
  5. Cauchy-Euler denklemi gibi değişken katsayılı özel diferansiyel denklem türlerini çözer.
  6. Laplace dönüşümü kullanarak başlangıç değer problemlerini çözer.
  7. Değişkenlere ayırma yöntemini kullanarak temel kısmi diferansiyel denklemler için çözüm üretir.
  8. Lineer denklem sistemlerini çözer.
  1. Classify differential equations according to certain features.
  2. Solve first order linear equations and nonlinear equations of certain types and interpret the solutions.
  3. Understand the conditions for the existence and uniqueness of solutions for linear differential equations.
  4. Solve second and higher order linear differential equations with constant coefficients and construct all solutions from the linearly independent solutions.
  5. Solve special types of differential equations with variable coefficients, such as the Cauchy-Euler equation.
  6. Solve initial value problems using the Laplace transform.
  7. Find solutions for basic partial differential equations using the method of separation of variables.
  8. Solve systems of linear differential equations.
DERS PLANI
Hafta Konular Dersin Öğrenme Çıktıları
1 Giriş ve Temel Kavramlar 1-7
2 Birinci Mertebeden Diferansiyel Denklemler – I 1-6-7
3 Birinci Mertebeden Diferansiyel Denklemler – II 1-6-7
4 İkinci Mertebeden Lineer Diferansiyel Denklemler – I 1-6-7
5 İkinci Mertebeden Lineer Diferansiyel Denklemler – II 1-6-7
6 Yüksek Mertebeden Lineer Diferansiyel Denklemler 1-6-7
7 Değişken Katsayılı Diferansiyel Denklemler – I 1-6-7
8 Değişken Katsayılı Diferansiyel Denklemler – II 1-6-7
9 Laplace Dönüşümüne Giriş 1-6-7
10 Laplace Dönüşümü ile Diferansiyel Denklem Çözümü 1-2-6-7
11 Lineer Denklem Sistemleri – I 1-2-6-7
12 Lineer Denklem Sistemleri – II 1-2-5-6-7
13 Kısmi Diferansiyel Denklemler 1-2-5-6-7
14 Bilgisayar Destekli Mühendislik Uygulamaları 1-2-3-4-5-6-7
COURSE PLAN
Weeks Topics Course Learning Outcomes
1 Introduction and Basic Concepts 1-7
2 First-Order Differential Equations – I 1-6-7
3 First-Order Differential Equations – II 1-6-7
4 Second-Order Linear Differential Equations – I 1-6-7
5 Second-Order Linear Differential Equations – II 1-6-7
6 Higher-Order Linear Differential Equations 1-6-7
7 Variable-Coefficient Differential Equations – I 1-6-7
8 Variable-Coefficient Differential Equations – II 1-6-7
9 Introduction to Laplace Transform 1-6-7
10 Solving Differential Equations Using Laplace Transform 1-2-6-7
11 Systems of Linear Differential Equations – I 1-2-6-7
12 Systems of Linear Differential Equations – II 1-2-5-6-7
13 Introduction to Partial Differential Equations 1-2-5-6-7
14 Computer Aided Engineering Applications 1-2-3-4-5-6-7
Ders Kitabı Cengel, Y. A., & Palm, W. J. (2013). Differential Equations for Engineers and Scientists. New York: McGraw-Hill Education.
Textbook Cengel, Y. A., & Palm, W. J. (2013). Differential Equations for Engineers and Scientists. New York: McGraw-Hill Education.
Diğer Kaynaklar Zill, D. G., & Zill, D. G. (2001). A first course in differential equations with modeling applications. Pacific Grove, CA: Brooks/Cole Thomson Learning.
Kreyszig, E. (2006). Advanced Engineering Mathematics. John Wiley & Sons, Inc. New York, 9th Edition.
Xie, W. (2010). Differential equations for engineers. New York: Cambridge University Press.
Boyce, William E & DiPrima, Richard C (2005). Elementary differential equations and boundary value problems (7th ed). Wiley, Hoboken, NJ.
Bronson, R., & Bronson, R. (1993). Schaum's outline of theory and problems of differential equations. New York: McGraw-Hill.
Other References Zill, D. G., & Zill, D. G. (2001). A first course in differential equations with modeling applications. Pacific Grove, CA: Brooks/Cole Thomson Learning.
Kreyszig, E. (2006). Advanced Engineering Mathematics. John Wiley & Sons, Inc. New York, 9th Edition.
Xie, W. (2010). Differential equations for engineers. New York: Cambridge University Press.
Boyce, William E & DiPrima, Richard C (2005). Elementary differential equations and boundary value problems (7th ed). Wiley, Hoboken, NJ.
Bronson, R., & Bronson, R. (1993). Schaum's outline of theory and problems of differential equations. New York: McGraw-Hill.
Ödevler ve Projeler
(Homework & Projects)
Laboratuar Uygulamaları
(Laboratory Work)
Bilgisayar Kullanımı
(Computer Usage)		 Matlab, Python ve/veya MS Excel
Matlab, Python and/or MS Excel
Diğer Uygulamalar
(Other Activities)

Dersin Makina Mühendisliği Öğrenci Çıktılarıyla İlişkisi

Programın mezuna kazandıracağı bilgi ve beceriler (programa ait çıktılar) Katkı seviyesi
1 2 3
a Mühendislik, fen ve matematik ilkelerini uygulayarak karmaşık mühendislik problemlerini belirleme, formüle etme ve çözme becerisi. x
b Küresel, kültürel, sosyal, çevresel ve ekonomik etmenlerle birlikte özel gereksinimleri sağlık, güvenlik ve refahı göz önüne alarak çözüm üreten mühendislik tasarımı uygulama becerisi. x
c Farklı dinleyici gruplarıyla etkili iletişim kurabilme becerisi. x
d Mühendislik görevlerinde etik ve profesyonel sorumlulukların farkına varma ve mühendislik çözümlerinin küresel, ekonomik, çevresel ve toplumsal bağlamdaki etkilerini göz önünde bulundurarak bilinçli kararlar verme becerisi. x
e Üyeleri birlikte liderlik sağlayan, işbirlikçi ve kapsayıcı bir ortam yaratan, hedefler belirleyen, görevleri planlayan ve hedefleri karşılayan bir ekipte etkili bir şekilde çalışma yeteneği becerisi. x
f Uygun deney geliştirme, yürütme, verileri analiz etme ve yorumlama ve sonuç çıkarmak için mühendislik yargısını kullanma becerisi. x
g Uygun öğrenme stratejileri kullanarak ihtiyaç duyulduğunda yeni bilgi edinme ve uygulama becerisi. x
1: Az, 2: Kısmi, 3: Tam

Relationship of the Course to Mechanical Engineering Student Outcomes

Program Outcomes Level of Contribution
1 2 3
a An ability to identify, formulate, and solve complex engineering problems by applying principles of engineering, science, and mathematics. x
b An ability to apply engineering design to produce solutions that meet specified needs with consideration of public health, safety, and welfare, as well as global, cultural, social, environmental, and economic factors. x
c An ability to communicate effectively with a range of audiences. x
d An ability to recognize ethical and professional responsibilities in engineering situations and make informed judgments, which must consider the impact of engineering solutions in global, economic, environmental, and societal contexts. x
e An ability to function effectively on a team whose members together provide leadership, create a collaborative and inclusive environment, establish goals, plan tasks, and meet objectives. x
f An ability to develop and conduct appropriate experimentation, analyze and interpret data, and use engineering judgment to draw conclusions. x
g An ability to acquire and apply new knowledge as needed, using appropriate learning strategies. x
1: Low, 2: Medium, 3: High

Academic Calendar

  • Undergraduate Level Academic Calendar
  • Undergraduate Internal Transfer, Double Major, Minor Calendar
  • Pre-Registration Calendar
  • Graduate Level Academic Calendar
  • Graduate Level Evening Education Calendar
  • English Preparatory Class Calendar

    • Course Information

  • Course Plans
  • Course Equivalence
  • Prerequisites
  • Course Information
  • Course Schedules
  • Building Codes
  • Undergraduate Program Codes

    • Procedures

  • Application and Admission
  • Double Major, Minor, Internal Transfer Procedures
  • Graduation And Diploma Procedures

    • Institutes

  • Graduate School
  • Disaster Management Institute
  • Eurasia Institute of Earth Sciences
  • Informatics Institute
  • Energy Institute
  • Aviation Institute
  • Zero Waste Institute
  • Institute for the History of Engineering and Technology
  • Faculties
  • School of Foreign Languages
  • Turkish Music State Conservatory
    • Phone

    +90 212 365 78 00-99 (100 line)

    Fax

    +90 212 285 29 09

    İTÜ Ayazağa Campus

    Registrar's Office
    34469 Maslak - İstanbul

    Registrar's Office

    Create Help Ticket

    Registrar's Office

    Clarification Text

    Registrar's Office

    ogrenciisleri@itu.edu.tr

    İTÜ Information Technologies Department © 2024