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	Assist. Prof. Dr. ELİF DEMİR
Instructor (s)
Course Assistant

Purpose and Content

The aim of the course	To give needed information about the structure and main classifications of the first order and high order Differential Equations and also the techniques for solving them that is used in engineering problems. Furthermore Laplace Transformation for solving Initial Value Problems
Course Content	Main Definitions and Fundamental concepts of the Differential Equations, First Order Differential Equations : Seperable DEs, Homogeneous DEs, Equations that can be transformed to seperable or homogeneous Equations, Exact DEs and Integrating Factors, Linear DEs, Bernoulli and Riccati Equations also First order but high degree Equations: Clairaut and Lagrange Equations, High Order Linear Equations, Existence and Structure of the solutions, Wronskian Determinant and the Concept of linear dependence and independence, Homogeneous Linear Equations with Constant Coefficents, Characteristic Equation and the roots, nonHomogeneous Linear Equations with Constant Coefficents,the method of undetermined coefficients and the Method of variation of Parameters, High order Linear Equations with Variable coefficients: Cauchy Euler Equation, Laplace Transformation for solving Initial Value Problems

The aim of the course

To give needed information about the structure and main classifications of the first order and high order Differential Equations and also the techniques for solving them that is used in engineering problems. Furthermore Laplace Transformation for solving Initial Value Problems

Course Content

Main Definitions and Fundamental concepts of the Differential Equations, First Order Differential Equations : Seperable DEs, Homogeneous DEs, Equations that can be transformed to seperable or homogeneous Equations, Exact DEs and Integrating Factors, Linear DEs, Bernoulli and Riccati Equations also First order but high degree Equations: Clairaut and Lagrange Equations, High Order Linear Equations, Existence and Structure of the solutions, Wronskian Determinant and the Concept of linear dependence and independence, Homogeneous Linear Equations with Constant Coefficents, Characteristic Equation and the roots, nonHomogeneous Linear Equations with Constant Coefficents,the method of undetermined coefficients and the Method of variation of Parameters, High order Linear Equations with Variable coefficients: Cauchy Euler Equation, Laplace Transformation for solving Initial Value Problems

Learning Outcomes

Competent knowledge of mathematics, science and technology, and civil engineering; ability to apply this knowledge to engineering solutions.
Skills to design and conduct experiments, collect data, analyze and interpret results.
Ability to design a system, a component or a process in a satisfactory manner considering realistic constraints and conditions such as economics, environmental issues, social, health, politics, ethics, security and sustainability; knowledge of project management and applications of risk management.
An ability to function within disciplinary and interdisciplinary teams as well as an individual.
Skills to determine, identify, formulate, and solve complex civil engineering problems; ability to select and apply apropriate analysis and modelling methods.
Determine, if available, the proper professional computer software to be used to analyze and design civil engineering structures.
An understanding of professional and ethical responsibilities.
An ability to effectively communicate in Turkish and in at least a foreign language; knowledge of a foreign language.
Knowledge of the impacts of civil engineering applications within a global and societal context; entrepreneurship, innovativeness, and awareness of sustainable development.
A recognition of the need for life-long learning; ability to reach knowledge, to follow advances in science and technology and to consistently renew oneself.
A knowledge of contemporary issues; an awareness of legal consequences of civil engineering solutions and implementations.
An ability to select, to improve and to utilize modern techniques and tools for civil engineering applications; an ability to efficiently utilize information and communication technologies.
Ability to work effectively in disciplinary and multidisciplinary teams; ability to work individually.
Awareness of the necessity of lifelong learning; the ability to access information, to follow developments in science and technology, and to constantly renew itself.
Ability to communicate effectively in Turkish, both orally and in writing; 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 understandable instructions.
Ability to design, conduct, collect, analyze, and interpret experiments for studying complex engineering problems or discipline-specific research topics

Weekly Course Subjects

1	Basic Definitions and Fundamental Concepts
2	First Order DES Seperable Equations and Homogeneous Equations
3	Equations that can be transformed to Sep. or Hom. Equations Exact DEs and Integrating Factors
4	Linear Equations Bernoulli and Riccati Equations
5	Lagrange and Clairaut Equations General and Singular solutions
6	High Order Linear equations, Existence theorems, Concept of Linear Dependence and Independence,Wronskian Determinant
7	High order Linear Equations with Constant coefficients The Method of Undetermined Coefficients
8	Midterm Exam
9	The Method of Undetermined Coefficients
10	The method of Variation of Parameters
11	High Order Linear Equation with variable Coefficients : Cauchy Euler Equation
12	Laplace Transformation
13	Inverse Laplace Transformation
14	Solutions of Initial Value Problems with Laplace transformation

Resources

1-Lecture Notes

CLASS 1

CLASS 2

CLASS 3

CLASS 4

Lesson Information

Purpose and Content

Learning Outcomes

Weekly Course Subjects

Resources

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