# 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)
None
Course Language English Compulsory Departmental Courses Bachelor’s Degree (First Cycle) Face To Face Lecture, Discussion, Problem Solving. 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. 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. 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 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 100 100

### Course Category

Core Courses X

### The Relation Between Course Learning Competencies and Program Qualifications

# Program Qualifications / Competencies Level of Contribution
1 2 3 4 5
1 Has the ability to apply scientific knowledge gained in the undergraduate education and to expand and extend knowledge in the same or in a different area X
2 Can apply gained knowledge and problem solving abilities in inter-disciplinary research X
3 Has the ability to work independently within research area, to state the problem, to develop solution techniques, to solve the problem, to evaluate the obtained results and to apply them when necessary X
4 Takes responsibility individually and as a team member to improve systematic approaches to produce solutions in unexpected complicated situations related to the area of study X
5 Can develop strategies, implement plans and principles on the area of study and can evaluate obtained results within the framework X
6 Can develop and extend the knowledge in the area and to use them with scientific, social and ethical responsibility X
7 Has the ability to follow recent developments within the area of research, to support research with scientific arguments and data, to communicate the information on the area of expertise in a systematically by means of written report and oral/visual presentation X
8 To have an oral and written communication ability in at least one of the common foreign languages ("European Language Portfolio Global Scale", Level B2) X
9 Has software and hardware knowledge in the area of expertise, and has proficient information and communication technology knowledge X
10 Follows scientific, cultural, and ethical criteria in collecting, interpreting and announcing data in the research area and has the ability to teach. X
11 Has professional 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

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