

Course Information
Course Unit Title 
: 
Engineering Mathematics ll 
Course Unit Code 
: 
INS210 
Type of Course Unit 
: 
Compulsory 
Level of Course Unit

: 
First Cycle 
Year of Study

: 
2 
Semester

: 
4.Semester 
Number of ECTS Credits Allocated

: 
4,00 
Name of Lecturer(s) 
: 

Course Assistants 
: 

Learning Outcomes of The Course Unit 
: 
1. Understanding the multivariable functions, the fundamental concepts and definitions 2. Understanding limit and derivates of multivariable functions and applications 3. Understanding double integral and applications 4. Understanding triple integral and applications 5. Understanding curvilinear integrals and applications 6. Understanding surface integrals and applications

Mode of Delivery 
: 
FaceToFace

Prerequisities and Corequisities Courses 
: 
Unavailable

Recommended Optional Programme Components 
: 
Unavailable

Course Contents 
: 
Introduction, Functions with multivariate, Limit, Particular and exact derivates, Extremum problems, Multiple integral, Curvilinear integrals, Surface integrals and their applications

Languages of Instruction 
: 

Course Goals 
: 

Course Aims 
: 
Studies of the theory of multivariate function; Double, Triple, Curvilinear, Surface integrals and their applications, which are necessary for civil engineering tasks.

WorkPlacement 

Not Available


Recommended or Required Reading
Textbook

: 
Course Notes of Engineering Mathematics II/ Prof. Dr. Abdullah AVEY

Additional Resources

: 
1. Basic and General Mathematics/ Hilmi Hacısalihoglu in Turkish
2. High Mathematics2 / Halilov H, Hasanoğlu A., Can M, 2001 in Turkish
3. Calculus and Analytic Geometry / G.B Thomas and R. L. Finney

Material Sharing
Documents

: 

Assignments

: 

Exams

: 

Additional Material

: 


Planned Learning Activities and Teaching Methods
Lectures, Practical Courses, Presentation, Seminar, Project, Laboratory Applications (if necessary)


ECTS / Table Of Workload (Number of ECTS credits allocated)
Student workload surveys utilized to determine ECTS credits.

Activity

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Course Duration (Excluding Exam Week)

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Time Of Studying Out Of Class

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Homeworks

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Presentation

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Project

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Lab Study

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Field Study

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Visas

:


Finals

:


Workload Hour (30)

:


Total Work Charge / Hour

:


Course's ECTS Credit

:



Assessment Methods and Criteria
Studies During Halfterm

: 

Visa

: 

Quiz

: 

Homework

: 

Attendance

: 

Application

: 

Lab

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Project

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Workshop

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Seminary

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Field study

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TOTAL

: 

The ratio of the term to success

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The ratio of final to success

: 

TOTAL

: 


Weekly Detailed Course Content
Week

Topics

1

Introduction, Functions with multivariate: Fundamental concepts and definitions, Limit, Continuity, Regular continuity, Review problems


Study Materials: Course Notes of Engineering Mathematics II/ Prof. Dr. Abdullah AVEY

2

Double limits, Derivates, First and Second order exact differentials of the functions with two variable, Review problems


Study Materials: Course Notes of Engineering Mathematics II / Prof. Dr. Abdullah AVEY

3

Resultant function, Generalized Chain rule, Closed function, Maximum and minimum of functions with multivariate, Necessary conditions for local extremum of functions with two variables, Review problems


Study Materials: Course Notes of Engineering Mathematics II/ Prof. Dr. Abdullah AVEY

4

Rules for extremum of functions with multivariate: Slyvestre rule (two and three variable), Lagrange multiplier rule, Review problems


Study Materials: Course Notes of Engineering Mathematics II / Prof. Dr. Abdullah AVEY

5

Basic definitions of analytical geometry


Study Materials: Course Notes of Engineering Mathematics II / Prof. Dr. Abdullah AVEY

6

Double integral: Calculation of the double integral, Zone transformation at double integral, Calculation of area by using double integral, Review problems


Study Materials: Course Notes of Engineering Mathematics II / Prof. Dr. Abdullah AVEY

7

Applying double integrals: Calculations of center of volume, gravity, mass, moment of inertia and surface area by using double integral, Review problems


Study Materials: Course Notes of Engineering Mathematics II / Prof. Dr. Abdullah AVEY

8

Triple integrals: Zone transformation at triple integrals, Triple integrals at cylindrical and spherical coordinates, Review problems


Study Materials: Course Notes of Engineering Mathematics II / Prof. Dr. Abdullah AVEY

9

Applying triple integrals: Calculation of volume, center of gravity and inertial moment by using triple integral by using triple integral, Review problems


Study Materials: Course Notes of Engineering Mathematics II / Prof. Dr. Abdullah AVEY

10

First order curvilinear integrals: Definitions, Property, Calculations, Applying first order curvilinear integrals, Review problems. Second order curvilinear integrals: Definitions, Property and Calculations.


Study Materials: Course Notes of Engineering Mathematics II / Prof. Dr. Abdullah AVEY

11

Applying second order curvilinear integrals: Vector area, Gradient, Divergent, Rotation, Work of vector area, Fundamental theorem of curvilinear integral (Green theorem), Review problems


Study Materials: Course Notes of Engineering Mathematics II / Prof. Dr. Abdullah AVEY

12

First type of surface integral: Definitions, Property, Calculations, Review problems. Second type of surface integral: Definition


Study Materials: Course Notes of Engineering Mathematics II / Prof. Dr. Abdullah AVEY

13

Second type of surface integral: Property, Calculations, Stokes theorem, Divergens theorem, Review problems


Study Materials: Course Notes of Engineering Mathematics II / Prof. Dr. Abdullah AVEY

14

General Assessment


Study Materials: Course Notes of Engineering Mathematics II / Prof. Dr. Abdullah AVEY

























































































