FACULTY OF ENGINEERING

Department of Software Engineering

MATH 153 | Course Introduction and Application Information

Course Name
Calculus I
Code
Semester
Theory
(hour/week)
Application/Lab
(hour/week)
Local Credits
ECTS
MATH 153
Fall
2
2
3
6

Prerequisites
None
Course Language
English
Course Type
Required
Course Level
First Cycle
Mode of Delivery -
Teaching Methods and Techniques of the Course Discussion
Problem Solving
Lecture / Presentation
Course Coordinator
Course Lecturer(s)
Assistant(s)
Course Objectives This course aims to built fundamentals of calculus and its applications for engineers
Learning Outcomes The students who succeeded in this course;
  • find limits of functions.
  • investigate continuity of functions.
  • compute derivatives of explicit and implicit functions.
  • solve related rates problems.
  • classify critical points of functions.
  • sketch graphs of functions.
  • solve extreme value problems.
  • compute areas of plane regions.
Course Description Calculus I provides important tools in understanding functions of one variable and has led to the development of new areas of mathematics.

 



Course Category

Core Courses
Major Area Courses
Supportive Courses
X
Media and Management Skills Courses
Transferable Skill Courses

 

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week Subjects Related Preparation
1 Graphs of quadratic functions, Polynomials and rational functions, the trigonometric functions, examples of velocity, growth rate and area Robert A. Adams, Christopher Essex, Calculus, "A complete course", 9th edition , (Pearson, 2018)Section P3, P6, P7, 1.1
2 Limits of Functions, limits at infinity and infinite limits Robert A. Adams, Christopher Essex, Calculus, "A complete course", 9th edition , (Pearson, 2018) Section 1.2, 1.3
3 Continuity, tangent lines and their slopes Robert A. Adams, Christopher Essex, Calculus, "A complete course", 9th edition , (Pearson, 2018) Section 1.4, 2.1.
4 The derivative, differentiation rules, the chain rule, derivatives of trigonometric functions Robert A. Adams, Christopher Essex, Calculus, "A complete course", 9th edition , (Pearson, 2018) Section 2.2, 2.3,2.4, 2.5.
5 Higher-order derivatives, the mean value theorem Robert A. Adams, Christopher Essex, Calculus, "A complete course", 9th edition , (Pearson, 2018) Section 2.6, 2.8.
6 Implicit differentiation, inverse functions, Exponential and logarithmic functions Robert A. Adams, Christopher Essex, Calculus, "A complete course", 9th edition , (Pearson, 2018)Section 2.9, 3.1, 3.2
7 Midterm Exam
8 The natural logarithm and exponential. The inverse trigonometric functions Robert A. Adams, Christopher Essex, Calculus, "A complete course", 9th edition , (Pearson, 2018) Section 3.3,3.5
9 Related rates, indeterminate forms Robert A. Adams, Christopher Essex, Calculus, "A complete course", 9th edition , (Pearson, 2018) Section 4.1, 4.3.
10 Extreme values, concavity and inflections Robert A. Adams, Christopher Essex, Calculus, "A complete course", 9th edition , (Pearson, 2018) Section 4.4, 4.5
11 Sketching the graph of a function, extreme value problems Robert A. Adams, Christopher Essex, Calculus, "A complete course", 9th edition , (Pearson, 2018) Section 4.6, 4.8
12 Extreme value problems properties of the definite integral.The fundamental theorem of calculus Robert A. Adams, Christopher Essex, Calculus, "A complete course", 9th edition , (Pearson, 2018) , Section 4.8, 5.4.5,5
13 The method of substitution Robert A. Adams, Christopher Essex, Calculus, "A complete course", 9th edition , (Pearson, 2018) Section 5.6
14 The method of substitution, areas of plane regions Robert A. Adams, Christopher Essex, Calculus, "A complete course", 9th edition , (Pearson, 2018)Section 5.6, 5.7
15 Semester review
16 Final exam

 

Course Notes/Textbooks

"Calculus, A complete course" by Robert A.Adams & Christopher Essex, Publisher: Prentice Hall, 9th edition,2013. ISBN-13: 978-0134154367.

 

Suggested Readings/Materials

''Calculus, Early Transcendentals'',James Stewart, Cengage Learning; 7th edition, 2010.ISBN-13:978-0538497909

 

EVALUATION SYSTEM

Semester Activities Number Weigthing
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques
6
24
Portfolio
Homework / Assignments
Presentation / Jury
Project
Seminar / Workshop
Oral Exams
Midterm
1
26
Final Exam
1
50
Total

Weighting of Semester Activities on the Final Grade
7
50
Weighting of End-of-Semester Activities on the Final Grade
1
50
Total

ECTS / WORKLOAD TABLE

Semester Activities Number Duration (Hours) Workload
Theoretical Course Hours
(Including exam week: 16 x total hours)
16
2
32
Laboratory / Application Hours
(Including exam week: '.16.' x total hours)
16
2
32
Study Hours Out of Class
14
3
42
Field Work
0
Quizzes / Studio Critiques
6
5
30
Portfolio
0
Homework / Assignments
0
Presentation / Jury
0
Project
0
Seminar / Workshop
0
Oral Exam
0
Midterms
1
14
14
Final Exam
1
30
30
    Total
180

 

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

#
Program Competencies/Outcomes
* Contribution Level
1
2
3
4
5
1

To have adequate knowledge in Mathematics, Science, Computer Science and Software Engineering; to be able to use theoretical and applied information in these areas on complex engineering problems.

X
2

To be able to identify, define, formulate, and solve complex Software Engineering problems; to be able to select and apply proper analysis and modeling methods for this purpose.

X
3

To be able to design, implement, verify, validate, document, measure and maintain a complex software system, process, or product under realistic constraints and conditions, in such a way as to meet the requirements; ability to apply modern methods for this purpose.

4

To be able to devise, select, and use modern techniques and tools needed for analysis and solution of complex problems in software engineering applications; to be able to use information technologies effectively.

X
5

To be able to design and conduct experiments, gather data, analyze and interpret results for investigating complex Software Engineering problems.

6

To be able to work effectively in Software Engineering disciplinary and multi-disciplinary teams; to be able to work individually.

7

To be able to communicate effectively in Turkish, both orally and in writing; to be able to author and comprehend written reports, to be able to prepare design and implementation reports, to be able to present effectively, to be able to give and receive clear and comprehensible instructions.

8

To have knowledge about global and social impact of engineering practices and software applications on health, environment, and safety; to have knowledge about contemporary issues as they pertain to engineering; to be aware of the legal ramifications of Engineering and Software Engineering solutions.

9

To be aware of ethical behavior, professional and ethical responsibility; to have knowledge about standards utilized in engineering applications.

10

To have knowledge about industrial practices such as project management, risk management, and change management; to have awareness of entrepreneurship and innovation; to have knowledge about sustainable development.

11

To be able to collect data in the area of Software Engineering, and to be able to communicate with colleagues in a foreign language. ("European Language Portfolio Global Scale", Level B1)

12

To be able to speak a second foreign language at a medium level of fluency efficiently.

13

To recognize the need for lifelong learning; to be able to access information, to be able to stay current with developments in science and technology; to be able to relate the knowledge accumulated throughout the human history to Software Engineering.

X

*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest

 


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