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

Course Introduction and Application Information

Course Code:

MATH109

Course Name:

Calculus 1

Semester:

Fall

Course Credits:

ECTS

Language of instruction:

English

Course Condition:

Does the Course Require Work Experience?:

Type of course:

Compulsory Courses

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:

Prof. Dr. SELÇUK DEMİR

Course Lecturer(s):

Assist. Prof. Dr. FUNDA ÖZDEMIR

Course Assistants:

Course Objective and Content

Course Objectives:	To teach the concepts of limit, continuity, derivative and integral in functions of one variable and to gain the ability to use these concepts in solving engineering problems.
Course Content:	Functions, graphs, limit, continuity, derivative definition, differentiation rules, chain rule, derivatives of implicit functions, applications of derivatives, definite integral, indefinite integral, applications of integral, transcendental functions.

Learning Outcomes

The students who have succeeded in this course;
1) Understands the concept of functions, the main types of functions and their properties.
2) Understands the concepts of limit and continuity analytically and graphically, and makes limit calculations.
3) Comprehends the concept of derivative together with its geometric meaning, calculates the derivative by using the main differentiation rules and applies the derivative on various problems.
4) Learns the concept of integral together with its geometric meaning, calculates definite and indefinite integrals by using main integral calculation techniques and uses integral in solving various problems.

Course Flow Plan

Week	Subject	Related Preparation
1)	Functions and their graphs , combining functions, shifting and scaling graphs
2)	Trigonometric functions, exponential functions, inverse functions and logarithms
3)	Rates of change and tangent line to curves, limit of a function and limit laws, one-sided limits, continuity
4)	Limits involving infinity, asymptotes of graphs
5)	Tangent lines and derivative at a point, the derivative as a function, differentiation rules, the derivative as a rate of change, derivatives of trigonometric functions
6)	Chain rule, implicit differentiation
7)	Derivatives of inverse functions, derivatives of logaritms and exponential functions, erivatives of inverse trigonometric functions
8)	Midterm Exam
9)	Extreme values of functions, mean value theorem, monotonic functions and the first derivative test, concavity and curve sketching
10)	Concavity and curve sketching, indeterminate forms and L'hopital's rule, applied optimization, antiderivatives
11)	Area and estimating with finite sums, sigma notation and limits of finite sums, definite integral, fundamental theorem of calculus
12)	Indefinite integrals and substitution method, change of variable, area between curves, integrals of natural logarithm and exponential functions
13)	Volumes using cross-sections, volumes using cylindrical shells
14)	Using basic integration formulas, integration by parts, trigonometric integrals, trigonometric substitutions, integration of rational functions by partial fractions

Sources

Course Notes / Textbooks:	Thomas, G.B. et al., Thomas’ Calculus, Pearson
References:	Lecture Notes

Course - Program Learning Outcome Relationship

Course Learning Outcomes	1	2	3	4
Program Outcomes
1) Build up a body of knowledge in mathematics, science and Mechanical Engineering subjects; use theoretical and applied information in these areas to model and solve complex engineering problems.	3	3	3	3
2) Identify, formulate, and solve complex Mechanical Engineering problems; select and apply proper modeling and analysis methods for this purpose.
3) Design complex Mechanical systems, processes, devices or products under realistic constraints and conditions, in such a way as to meet the desired result; apply modern design methods for this purpose.
4) Devise, select, and use modern techniques and tools needed for solving complex problems in Mechanical Engineering practice; employ information technologies effectively.
5) Design and conduct numerical or pysical experiments, collect data, analyze and interpret results for investigating the complex problems specific to Mechanical Engineering.
6) Cooperate efficiently in intra-disciplinary and multi-disciplinary teams; and show self-reliance when working on Mechanical-related problems.
7) Ability to communicate effectively in English and Turkish (if he/she is a Turkish citizen), both orally and in writing. Write and understand reports, prepare design and production reports, deliver effective presentations, give and receive clear and understandable instructions.
8) Recognize the need for life-long learning; show ability to access information, to follow developments in science and technology, and to continuously educate oneself.
9) Develop an awareness of professional and ethical responsibility, and behave accordingly. Be informed about the standards used in Mechanical Engineering applications.
10) Learn about business life practices such as project management, risk management, and change management; develop an awareness of entrepreneurship, innovation, and sustainable development.
11) Acquire knowledge about the effects of practices of Mechanical Engineering on health, environment, security in universal and social scope, and the contemporary problems of Mechatronics engineering; is aware of the legal consequences of Mechanical engineering solutions.

Course - Learning Outcome Relationship

No Effect	1 Lowest	2 Average	3 Highest

	Program Outcomes	Level of Contribution
1)	Build up a body of knowledge in mathematics, science and Mechanical Engineering subjects; use theoretical and applied information in these areas to model and solve complex engineering problems.	3
2)	Identify, formulate, and solve complex Mechanical Engineering problems; select and apply proper modeling and analysis methods for this purpose.
3)	Design complex Mechanical systems, processes, devices or products under realistic constraints and conditions, in such a way as to meet the desired result; apply modern design methods for this purpose.
4)	Devise, select, and use modern techniques and tools needed for solving complex problems in Mechanical Engineering practice; employ information technologies effectively.
5)	Design and conduct numerical or pysical experiments, collect data, analyze and interpret results for investigating the complex problems specific to Mechanical Engineering.
6)	Cooperate efficiently in intra-disciplinary and multi-disciplinary teams; and show self-reliance when working on Mechanical-related problems.
7)	Ability to communicate effectively in English and Turkish (if he/she is a Turkish citizen), both orally and in writing. Write and understand reports, prepare design and production reports, deliver effective presentations, give and receive clear and understandable instructions.
8)	Recognize the need for life-long learning; show ability to access information, to follow developments in science and technology, and to continuously educate oneself.
9)	Develop an awareness of professional and ethical responsibility, and behave accordingly. Be informed about the standards used in Mechanical Engineering applications.
10)	Learn about business life practices such as project management, risk management, and change management; develop an awareness of entrepreneurship, innovation, and sustainable development.
11)	Acquire knowledge about the effects of practices of Mechanical Engineering on health, environment, security in universal and social scope, and the contemporary problems of Mechatronics engineering; is aware of the legal consequences of Mechanical engineering solutions.

Assessment & Grading

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

Workload and ECTS Credit Calculation

Activities	Number of Activities	Preparation for the Activity	Spent for the Activity Itself	Completing the Activity Requirements	Workload
Course Hours	13	0	3		39
Application	13	0	2		26
Study Hours Out of Class	13	0	3		39
Midterms	1	13	2		15
Final	1	23	2		25
Total Workload					144