Civil Engineering (English)
Bachelor TR-NQF-HE: Level 6 QF-EHEA: First Cycle EQF-LLL: Level 6

General course introduction information

Course Code: MATH113
Course Name: Mathematics I
Course Semester: Spring
Course Credits:
Theoretical Practical Credit ECTS
3 2 4 6
Language of instruction: EN
Course Requisites:
Does the Course Require Work Experience?: No
Type of course:
Course Level:
Bachelor TR-NQF-HE:6. Master`s Degree QF-EHEA:First Cycle EQF-LLL:6. Master`s Degree
Mode of Delivery: Face to face
Course Coordinator : Dr.Öğr.Üyesi MESERET TUBA GÜLPINAR
Course Lecturer(s): Prof. Dr. HASAN ÖZEKES
Course Assistants:

Course Objective and Content

Course Objectives: The aim of this course is to teach the basic definitions and theorems of the limits, limit rules, continuity, derivatives, differentiation rules, chain rule, closed derivatives, maximum-minimum problems, curve drawing, applied optimization problems, integrals, Riemann sums, definite integrals, curves, transcendental functions and to gain the ability to solve the related problems.
Course Content: This course will investigate limits, rules of limits, continuity, derivatives, differentiation rules, chain rule, implicit differentiation, maximum-minimum problems, curve sketching, applied optimization problems, integration, Riemann sums, definite integrals, area between curves, volumes of revolution, transcendental functions.

Learning Outcomes

The students who have succeeded in this course;
Learning Outcomes
1 - Knowledge
Theoretical - Conceptual
1) Able to give a mathematical proof for the existence of limits and continuity of functions at specified points and calculate the limits of functions and determine their asymptotes using the limit laws and determine the points where a function is continuous.
2) Able to use the mathematical definition of the derivative to derive the rules of differentiation, apply these basic rules, chain rule and implicit differentiation to calculate the derivatives of varies functions.
3) Able to determine the intervals where the function is decreasing and increasing, determine the points where it has local extremum values, and inflection points and then sketch graphs of functions. Calculate the linear estimates of functions.
4) Able to calculate indefinite integrals by using basic rules of integration and substitution. Write the expression of the fundamental theorem of calculus and apply it for evaluating definite integrals and derivatives of integrals with variable limits of integration and calculate the area between curves.
5) Able to calculate the volumes of solid objects by using cross sections, volumes of objects obtained by revolving the areas between curves about varies axes, the arc length of curves and the surface areas of surfaces obtained by revolving the curves around varies axes.
6) Able to find the analytical expressions for inverse functions where it is possible or use graphical methods to determine the behavior of inverse functions. Calculate the derivatives of inverse functions and transcendental functions and use them in evaluating definite and indefinite integrals.
2 - Skills
Cognitive - Practical
3 - Competences
Communication and Social Competence
Learning Competence
Field Specific Competence
Competence to Work Independently and Take Responsibility

Lesson Plan

Week Subject Related Preparation
1) Functions Lecture Notes
2) Limits and Continuity Lecture Notes
3) Limits and Continuity Lecture Notes
4) Differentiation Lecture Notes
5) Differentiation Lecture Notes
6) Differentiation Lecture Notes
7) Applications of Derivatives Lecture Notes
8) Applications of Derivatives Lecture Notes
9)
10) Integration Lecture Notes
11) Integration Lecture notes
12) Applications of Definite Integrals Lecture Notes
13) Transcendental Functions Lecture Notes
14) Transcendental Functions Lecture Notes

Sources

Course Notes / Textbooks: Thomas’ Calculus, 13th Edition in SI Units
George B. Thomas, Maurice D. Weir, Joel R. Hass
Pearson Education Inc.
References: A Complete Course Calculus, 8th Edition.
Robert A. Adams, Christopher Essex
Pearson Canada Inc.
ISBN 978: 0321781079

Course-Program Learning Outcome Relationship

Learning Outcomes

1

2

3

4

5

6

Program Outcomes
1) Adequate knowledge in mathematics, science and engineering subjects pertaining to the relevant discipline; ability to use theoretical and applied information in these areas to model and solve engineering problems.
2) Ability to identify, formulate, and solve complex engineering problems; ability to select and apply proper analysis and modelling methods for this purpose.
3) Ability to design a complex system, process, device or product under realistic constraints and conditions, in such a way so as to meet the desired result; ability to apply modern design methods for this purpose. (Realistic constraints and conditions may include factors such as economic and environmental issues, sustainability, manufacturability, ethics, health, safety issues, and social and political issues according to the nature of the design.)
4) Ability to select and use modern techniques and tools needed for analyzing and solving complex problems encountered in engineering practice; ability to employ information technologies effectively.
5) Ability to design and conduct experiments, gather data, analyze and interpret results for investigating complex engineering problems or discipline specific research questions.
6) Ability to work efficiently in intra-disciplinary and multi-disciplinary teams; ability to work individually.
7) Ability to communicate effectively, both orally and in writing; knowledge of a minimum of one foreign language; ability to write effective reports and comprehend written reports, prepare design and production reports, make effective presentations, and give and receive clear and intelligible instructions.
8) Recognition of the need for lifelong learning; ability to access information, to follow developments in science and technology, and to continue to educate him/herself.
9) Knowledge on behavior according ethical principles, professional and ethical responsibility and standards used in engineering practices.
10) Knowledge about business life practices such as project management, risk management, and change management; awareness in entrepreneurship, innovation; knowledge about sustainable development.
11) Knowledge about contemporary issues and the global and societal effects of engineering practices on health, environment, and safety; awareness of the legal consequences of engineering solutions.

Course - Learning Outcome Relationship

No Effect 1 Lowest 2 Low 3 Average 4 High 5 Highest
           
Program Outcomes Level of Contribution
1) Adequate knowledge in mathematics, science and engineering subjects pertaining to the relevant discipline; ability to use theoretical and applied information in these areas to model and solve engineering problems. 5
2) Ability to identify, formulate, and solve complex engineering problems; ability to select and apply proper analysis and modelling methods for this purpose.
3) Ability to design a complex system, process, device or product under realistic constraints and conditions, in such a way so as to meet the desired result; ability to apply modern design methods for this purpose. (Realistic constraints and conditions may include factors such as economic and environmental issues, sustainability, manufacturability, ethics, health, safety issues, and social and political issues according to the nature of the design.)
4) Ability to select and use modern techniques and tools needed for analyzing and solving complex problems encountered in engineering practice; ability to employ information technologies effectively.
5) Ability to design and conduct experiments, gather data, analyze and interpret results for investigating complex engineering problems or discipline specific research questions.
6) Ability to work efficiently in intra-disciplinary and multi-disciplinary teams; ability to work individually.
7) Ability to communicate effectively, both orally and in writing; knowledge of a minimum of one foreign language; ability to write effective reports and comprehend written reports, prepare design and production reports, make effective presentations, and give and receive clear and intelligible instructions.
8) Recognition of the need for lifelong learning; ability to access information, to follow developments in science and technology, and to continue to educate him/herself.
9) Knowledge on behavior according ethical principles, professional and ethical responsibility and standards used in engineering practices.
10) Knowledge about business life practices such as project management, risk management, and change management; awareness in entrepreneurship, innovation; knowledge about sustainable development.
11) Knowledge about contemporary issues and the global and societal effects of engineering practices on health, environment, and safety; awareness of the legal consequences of engineering solutions.

Learning Activity and Teaching Methods

Lesson
Reading
Homework
Problem Solving
Q&A / Discussion

Assessment & Grading Methods and Criteria

Written Exam (Open-ended questions, multiple choice, true-false, matching, fill in the blanks, sequencing)
Homework

Assessment & Grading

Semester Requirements Number of Activities Level of Contribution
Homework Assignments 6 % 20
Midterms 2 % 40
Final 1 % 40
total % 100
PERCENTAGE OF SEMESTER WORK % 60
PERCENTAGE OF FINAL WORK % 40
total % 100

Workload and ECTS Credit Grading

Activities Number of Activities Duration (Hours) Workload
Course Hours 15 5 75
Study Hours Out of Class 12 1 12
Homework Assignments 7 7 49
Midterms 2 11 22
Final 1 22 22
Total Workload 180