Ders Planı

Lesson Information

Course Credit
Course ECTS Credit
Teaching Language of Instruction	Türkçe
Level of Course	Bachelor's Degree, TYYÇ: Level 6, EQF-LLL: Level 6, QF-EHEA: First Cycle
Type of Course
Mode of Delivery	Face-to-face
Does the course require compulsory or optional work experience?
Course Coordinator
Instructor (s)
Course Assistant

Purpose and Content

The aim of the course	To provide students with introductory level information on the theory of Differential Equations.
Course Content	Differential equations and related basic concepts, initial and boundary value problems, existence and uniqueness theorems, separable and homogeneous differential equations, the linearity of P and Q, complete differential equations, the concept of integral factor and finding the integral factor of equations, linear, Bernoulli and Riccati differential equations, systems of equations, changing variables, graphical methods, steep and inclined orbits, first-order and higher-order differential equations, Lagrange and Clairaut equations, paradoxical solutions, envelopes, nth-order linear equations with constant coefficients, method of indefinite coefficients, short methods , parameter variation method, Euler equation differential equation, linear differential equations with varying coefficients, Laplace Transforms, Solutions with Laplace Transform.

The aim of the course

To provide students with introductory level information on the theory of Differential Equations.

Course Content

Differential equations and related basic concepts, initial and boundary value problems, existence and uniqueness theorems, separable and homogeneous differential equations, the linearity of P and Q, complete differential equations, the concept of integral factor and finding the integral factor of equations, linear, Bernoulli and Riccati differential equations, systems of equations, changing variables, graphical methods, steep and inclined orbits, first-order and higher-order differential equations, Lagrange and Clairaut equations, paradoxical solutions, envelopes, nth-order linear equations with constant coefficients, method of indefinite coefficients, short methods , parameter variation method, Euler equation differential equation, linear differential equations with varying coefficients, Laplace Transforms, Solutions with Laplace Transform.

Learning Outcomes

PO1. Adequate knowledge of mathematics, science and engineering subjects related to Food Engineering; Ability to apply theoretical and applied knowledge in these fields to model and solve complex engineering problems.
PO2. Ability to identify, define, formulate and solve complex engineering problems; Ability to select and apply appropriate analysis and modeling methods for this purpose.
PO3. The ability to design a complex system, process, device or product to meet specific requirements, under realistic constraints and conditions; Ability to apply modern design methods for this purpose.
PO4. Ability to develop, select and use modern techniques and tools necessary for the analysis and solution of complex problems encountered in engineering applications; Ability to use information technologies effectively.
PO5. Ability to design, conduct experiments, collect data, analyze and interpret results for the study of complex engineering problems or discipline-specific research issues.
PO6. Ability to work effectively in intradisciplinary and multidisciplinary teams; individual work ability.
PO7. Ability to communicate effectively verbally and in written Turkish; knowledge of at least one foreign language; Ability to write effective reports and understand written reports, prepare design and production reports, make effective presentations, give and receive clear and understandable instructions.
PO8. Awareness of the necessity of lifelong learning; The ability to access information, follow developments in science and technology and constantly renew oneself.
PO9. Acting in accordance with ethical principles, awareness of professional and ethical responsibility; Information about the standards used in Food Engineering applications.
PO10. Knowledge of project management and business practices such as risk management and change management; awareness about entrepreneurship and innovation; Information about sustainable development.
PO11. Information about the effects of engineering applications on health, environment and security at universal and social dimensions and the problems of the age; Awareness of the legal consequences of engineering solutions.

Weekly Course Subjects

1	Differential equations and related basic concepts, initial and boundary value problems.
2	Existence and Uniqueness theorems, separable and homogeneous differential equations.
3	If P and Q are linear, complete differential equations.
4	The concept of integral factor and finding the integral factor of equations.
5	Linear differential equations, Bernoulli differential equation.
6	Riccati differential equation, solution with variable replacement.
7	Systems, vertical and inclined orbits.
8	First-order and Higher-order differential equations. Lagrange and Clairaut equations, Singular solutions, envelopes.
9	Midterm.
10	Linear equations with constant coefficients from the nth digit.
11	Uncertain coefficients method, short methods.
12	Method of variation of parameters, Euler differential equation.
13	Linear differential equations with variable coefficients.
14	Laplace Transforms, Solutions with Laplace Transform

Resources

1.William E. Boyce, Richard C.DiPrima, Elementary Differential Equations and Boundary Value Problems : International Student Version, Boyce & Dprima, John Wiley & Sons, 2010.

2. Richard Bronson, Erin J. Bredensteiner , Differential Equations,Schaum’s Outlines, McGraw-Hill, 2003.

3. Shepley L. Ross, Differential Equations, 3. Edition

4 Edward B. Saff and Arthur David Snider, Fundementals of Differential Equations and Boundary Value Problems, R. Kent Nagle, Addison,New York, 2004.
5-Yunus A. Çengel, William J. Palm. Mühendislik ve Temel Bilimler için Diferansiyel Denklemler.İzmir Güven Kitabevi. (2013) (Tahsin Engin, Cevdet Cerit, Fatma Ayaz)

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Lesson Information

Purpose and Content

Learning Outcomes

Weekly Course Subjects

Resources

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