Mathematical Analysis I (MATH135) Course Detail

Course Name	Course Code	Season	Lecture Hours	Application Hours	Lab Hours	Credit	ECTS
Mathematical Analysis I	MATH135	1. Semester	4	2	0	5	8.5

Pre-requisite Course(s)
N/A

Course Language	English
Course Type	Compulsory Departmental Courses
Course Level	Bachelor’s Degree (First Cycle)
Mode of Delivery	Face To Face
Learning and Teaching Strategies	Lecture, Discussion, Problem Solving.
Course Coordinator
Course Lecturer(s)
Course Assistants
Course Objectives	The course is designed to fill the gaps in students knowledge that they have in their pre-college education and then to provide students with a theoretical foundation and computational skills for the concepts of one-variable differential calculus and to provide the background for more advanced courses in analysis.
Course Learning Outcomes	The students who succeeded in this course; comprehend, define and use functions, and represent them by means of graphs, comprehend fundamental concepts of limit and continuity and make computations, comprehend and analyze the derivative and calculate derivatives of one-variable functions, use derivatives to solve problems involving maxima, minima, and related rates, sketch the graphs of some functions.
Course Content	Preliminaries, functions and graphs, limits and continuity, derivatives, mean value theorem, applications of derivatives: monotonicity, local and absolute extrema, concavity, L?Hospital?s rule, graphs of functions.

Weekly Subjects and Releated Preparation Studies

Week	Subjects	Preparation
1	Sets and Numbers. Polynomials. Solving Equations and Inequalities.	pp. 3-48
2	Functions and Graphs. Exponential Functions. Logarithmic Functions.	pp. 19-38, 172-182
3	Trigonometric Functions. Inverse Trigonometric Functions.	pp. 41-50
4	Limit	pp. 60-68
5	Infinite Limits and Limits At Infinity	pp. 69-74
6	Continuity	pp. 76-81
7	Midterm
8	Differentiation	pp. 95-108
9	Definition and Properties of Derivative.	pp. 110-129
10	Implicit Differentiation, Logarithmic Differentiation.	pp. 183-191
11	The Mean Value Theorem and Some Applications	pp. 130-139, 273-278
12	L’hopital’s Rule	pp. 288-294
13	Absolute and Relative Extreme of Functions.	pp. 233-240
14	Concavity of Functions.	pp. 241-245
15	Sketching Graphs of Functions	pp. 246-255
16	Final Examination

Sources

Course Book	1. A complete Course, R. A. Adams, 4th Edition; Addison Wesley
Other Sources	2. Thomas' Calculus, Early Transcendentals, 11th Edition; 2003 Revised by R. L. Finney, M. D. Weir, and F. R. Giardano; Addison Wesley
	3. Calculus with Analytic Geometry, C. H. Edwards; Prentice Hall Calculus with Analytic Geometry, R. A. Silverman; Prentice Hall

Evaluation System

Requirements	Number	Percentage of Grade
Attendance/Participation	-	-
Laboratory	-	-
Application	-	-
Field Work	-	-
Special Course Internship	-	-
Quizzes/Studio Critics	-	-
Homework Assignments	5	10
Presentation	-	-
Project	-	-
Report	-	-
Seminar	-	-
Midterms Exams/Midterms Jury	2	50
Final Exam/Final Jury	1	40
Toplam	8	100

Percentage of Semester Work
Percentage of Final Work	100
Total	100

Course Category

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

The Relation Between Course Learning Competencies and Program Qualifications

#	Program Qualifications / Competencies	Level of Contribution
#	Program Qualifications / Competencies	1	2	3	4	5
1	Acquires skills to use the advanced theoretical and applied knowledge obtained at the mathematics bachelors program to do further academic and scientific research in both mathematics-based graduate programs and public or private sectors.					X
2	Transplants and applies the theoretical and applicable knowledge gained in their field to the secondary education by using suitable tools and devices.				X
3	Acquires the skill of choosing, using and improving problem solving techniques which are needed for modeling and solving current problems in mathematics or related fields by using the obtained knowledge and skills.				X
4	Acquires analytical thinking and uses time effectively in the process of deduction.					X
5	Acquires basic software knowledge necessary to work in the computer science related fields and together with the skills to use information technologies effectively.	X
6	Obtains the ability to collect data, to analyze, interpret and use statistical methods necessary in decision making processes.	X
7	Acquires the level of knowledge to be able to work in the mathematics and related fields and keeps professional knowledge and skills up-to-date with awareness in the importance of lifelong learning.					X
8	Takes responsibility in mathematics related areas and has the ability to work affectively either individually or as a member of a team.				X
9	Has proficiency in English language and has the ability to communicate with colleagues and to follow the innovations in mathematics and related fields.			X
10	Has the ability to communicate ideas with peers supported by qualitative and quantitative data.			X
11	Has professional and ethical consciousness and responsibility which takes into account the universal and social dimensions in the process of data collection, interpretation, implementation and declaration of results in mathematics and its applications.			X

ECTS/Workload Table

Activities	Number	Duration (Hours)	Total Workload
Course Hours (Including Exam Week: 16 x Total Hours)	16	4	64
Laboratory
Application	16	2	32
Special Course Internship
Field Work
Study Hours Out of Class	14	4	56
Presentation/Seminar Prepration
Project
Report
Homework Assignments	5	5	25
Quizzes/Studio Critics
Prepration of Midterm Exams/Midterm Jury	2	10	20
Prepration of Final Exams/Final Jury	1	15	15
Total Workload			212