Ders Planı

Lesson Information

Course Credit	4.0
Course ECTS Credit	5.0
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	Compulsory
Mode of Delivery	Face-to-face
Does the course require compulsory or optional work experience?	Z
Course Coordinator	Assist. Prof. Dr. AYŞEGÜL KIVILCIM JENSEN
Instructor (s)	Assist. Prof. Dr. LÜTFİYE DAHİL
Course Assistant

Purpose and Content

The aim of the course	To introduce the basic concepts required to understand, establish, solve and interpret differential equations. To give an ability to apply knowledge of differential equations in engineering problems.
Course Content	Differential equations and related basic concepts, initial and boundary value problems, existence and uniqueness theorems, homogeneous differential equations, linearity of P and Q, exact differential equations, integration factor and the integral factor of equations, linear, Bernoulli and Riccati differential equations, equations systems, variable transformation, graphical methods, steep and oblique orbits, first order and higher order differential equations, Lagrange and Clairaut equations, contradictory solutions, adverbs, nth order linear fixed coefficient linear equations, indeterminate coefficient methods, , method of changing parameters, differential equation of Euler equation, linear differential equations with varying coefficients, Laplace Transformations, Solutions with Laplace Transform.

The aim of the course

To introduce the basic concepts required to understand, establish, solve and interpret differential equations. To give an ability to apply knowledge of differential equations in engineering problems.

Course Content

Differential equations and related basic concepts, initial and boundary value problems, existence and uniqueness theorems, homogeneous differential equations, linearity of P and Q, exact differential equations, integration factor and the integral factor of equations, linear, Bernoulli and Riccati differential equations, equations systems, variable transformation, graphical methods, steep and oblique orbits, first order and higher order differential equations, Lagrange and Clairaut equations, contradictory solutions, adverbs, nth order linear fixed coefficient linear equations, indeterminate coefficient methods, , method of changing parameters, differential equation of Euler equation, linear differential equations with varying coefficients, Laplace Transformations, Solutions with Laplace Transform.

Learning Outcomes

Sufficient knowledge in mathematics, science and related engineering disciplines; The theoretical and practical knowledge in these areas, the ability to use in complex engineering problems
Ability to identify, define, formulate and solve complex engineering problems; Selecting and implementing appropriate analysis and modeling methods for this purpose
Ability to develop, select and use modern techniques and tools for analyzing and solving complex problems in engineering applications ; The ability to use information technologies effectively
Ability to design experiments, conduct experiments, collect data, analyze and interpret results for observing complex engineering problems or discipline-specific research topics
The ability to design a complex system, process, device or product under realistic constraints and conditions to meet specific requirements; The ability to apply modern design methods for this purpose
Information on the effects of engineering applications on health, environment and safety in universal and social dimensions, and on the problems of the modern era reflected in the field of engineering; Awareness of the legal consequences of engineering solutions
Effective communication skills in Turkish verbal and written communication; At least one foreign language knowledge; Ability to write effective reports and understand written reports, to prepare design and production reports, to make effective presentations, to give clear and clear instructions
Conducting ethical principles, professional and ethical responsibility; Information about the standards used in engineering applications
The ability to work effectively in disciplinary and multidisciplinary teams; Individual work skill
Information on practices in business, such as project management, risk management and change management; Awareness about entrepreneurship, innovation; Information on sustainable development
Awareness of the necessity of life-long learning; Ability to access knowledge, follow developments in science and technology, and constant self-renewal skills
Physics knowledge based on mathematics and chemistry knowledge
Advanced mathematical knowledge, including multivariable mathematical and differential equations; Familiarity with statistics and linear algebra
The ability to work in both thermal and mechanical systems, including design and realization of such systems.
Ability to develop, select and use modern techniques and tools for analyzing and solving complex problems in engineering applications ; The ability to use information technologies effectively
Develop self professionalism by having adequate background for the related engineering area.
Awareness of the necessity of life-long learning; Ability to access knowledge, follow developments in science and technology, and constant self-renewal skills
Effective communication skills in Turkish verbal and written communication; At least one foreign language knowledge; Ability to write effective reports and understand written reports, to prepare design and production reports, to make effective presentations, to give clear and clear instructions
Conducting ethical principles, professional and ethical responsibility; Information about the standards used in engineering applications
Physics knowledge based on mathematics and chemistry knowledge
Advanced mathematical knowledge, including multivariable mathematical and differential equations; Familiarity with statistics and linear algebra
The ability to work in both thermal and mechanical systems, including design and realization of such systems.

Weekly Course Subjects

1	Differential equation and related basic concepts, initial and boundary value problems.
2	Existence and Uniqueness theorems, Homogeneous differential equations which can be separated into variables.
3	Exact differential equations
4	The concept of integral multiplier and finding the integral multiplication of equations.
5	Linear differential equations, Bernoulli differential equations.
6	Riccati differential equation, solution with variable change
7	Systems, steep and oblique orbits.
8	First order differential and higher order differential equations.
9	Lagrange and Clairaut equations, singular solutions, envelopes.
10	Base 'n' digits than the fixed coefficient linear equations.
11	Indefinite coefficient methods, short methods.
12	Method of changing parameters.
13	Euler differential equation. Linear differential equations with variable coefficients.
14	Laplace Transformations, 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.

CLASS 1

CLASS 2

CLASS 3

CLASS 4

Lesson Information

Purpose and Content

Learning Outcomes

Weekly Course Subjects

Resources

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