Ders Planı

CLASS 4

Lesson plan / ENGINEERING MATHEMATICS-II

Lesson Information

Course Credit	2.0
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
Instructor (s)
Course Assistant

Purpose and Content

The aim of the course	The objective of the course is to expose the students to an elementary level treatment of differential equations methods to obtain closed form solutions when available and to the concepts existance and uniqness of soltuions.
Course Content	Differential equations and their derivations, definition of the solutions, first order general differential equations, separable equations, linear equations, homogeneous equations, exact differential equations and integrating factor, higher order differential equations and their applications, homogeneous equations with constant coefficients, non-homogeneous equations, change of the constant or the Lagrange method, higher order differential equations with constant coefficients, linear differential equations with variable coefficients, Cauchy Euler equations, Lagrance transform, solution of boundary value problems, systems of linear differential equations, the operator method for systems with constant coefficients.

The aim of the course

The objective of the course is to expose the students to an elementary level treatment of differential equations methods to obtain closed form solutions when available and to the concepts existance and uniqness of soltuions.

Course Content

Differential equations and their derivations, definition of the solutions, first order general differential equations, separable equations, linear equations, homogeneous equations, exact differential equations and integrating factor, higher order differential equations and their applications, homogeneous equations with constant coefficients, non-homogeneous equations, change of the constant or the Lagrange method, higher order differential equations with constant coefficients, linear differential equations with variable coefficients, Cauchy Euler equations, Lagrance transform, solution of boundary value problems, systems of linear differential equations, the operator method for systems with constant coefficients.

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	Derivation of differential equations
2	First order differential equation
3	High order linear differential equations
4	Homogeneous equations
5	Exact differential equations and the integrating factor
6	Non-homogeneous equations and solution methods
7	Lagrange method of variation of the constant
8	Midterm exam
9	High order differential equaitons with constant coefficients, second order equations with constant coefficients
10	Linear equations with variable coefficients
11	Cauchy Euler equations
12	Laplace transform, solution of boundary value problems
13	Operator method for systems with constants coefficients
14	Overall assesment

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, Fundamentals of Differential Equations and Boundary Value Problems, R. Kent Nagle, Addison,New York, 2004.

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Lesson Information

Purpose and Content

Learning Outcomes

Weekly Course Subjects

Resources

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