## Single Variable Analysis I(MAT101)

Course Code Course Name Semester Theory Practice Lab Credit ECTS
MAT101 Single Variable Analysis I 1 5 0 0 5 7
 Language of Instruction French Course Type Compulsory Course Level Bachelor Degree Course Instructor(s) Ayşegül ULUS aulus@gsu.edu.tr (Email) Assistant Objective To build, with appropriate rigour, the foundations of calculus and along the way to develop the skills to enable us to continue studying mathematics Content Course syllabus : Real Numbers, Sequences, Topology of R, Continuity, Limits Course Learning Outcomes The student is expected to learn the main notions ( Real Numbers, Sequences, Topology of R, Continuity, Limits). Teaching and Learning Methods Course and the problem solving References Course book : First Course in Real Analysis, Sterling K.Berberian, Springer
###### Theory Topics
Week Weekly Contents
1 Properties of reel numbers
2 Properties of reel numbers
3 İnfimum- Supremum
4 İnfimum- Supremum
5 Midterm Exam
6 Sequences : Definitions and examples
7 Sequences : Limits
8 Sequences : Convergence theorem
9 Sequences : Convergence theorem
10 Midterm Exam- Notions of function
11 Limits and continuous functions : Limits
12 Limits and continuous functions : Continuity in one point
13 Limits and continuous functions : Continuity on an interval
14 Limits and continuous functions : Elemamtary functions
###### Practice Topics
Week Weekly Contents
Number Contribution
Contribution of in-term studies to overall grade 7 60
Contribution of final exam to overall grade 1 40
Toplam 8 100
###### In-Term Studies
Number Contribution
Assignments 2 5
Presentation 2 5
Midterm Examinations (including preparation) 2 40
Project 0 0
Laboratory 0 0
Other Applications 0 0
Quiz 1 10
Term Paper/ Project 0 0
Portfolio Study 0 0
Reports 0 0
Learning Diary 0 0
Thesis/ Project 0 0
Seminar 0 0
Other 0 0
Toplam 7 60
No Program Learning Outcomes Contribution
1 2 3 4 5
1 understands principles of deductive reasoning; has experience to verify well-foundedness and exactness of mathematical statements in systematic ways; X
2 can properly state and use concepts and results of major mathematical interest; X
3 masters current computational techniques and algorithms; has a good ability in their use; can identify relevant tools, among those one has learned, suitable to solve a problem and is able to judge whether or not one is in possession of these tools; X
4 is able to express one’s mathematical ideas in an organised way both in written and oral forms; X
5 understands relations connecting substantial concepts and results; can switch from one viewpoint to another on mathematical objects (pictures, formulae, precise statements, heuristic trials, list of examples,...); X
6 has followed individually a guided learning strategy; has pursued steps toward the resolution of unfamiliar problems; X
7 has a theoretical and practical knowledge in computer science well adapted for learning a programming language; X
8 has investigated the relevance of modeling and using mathematical tools in natural sciences and in the professional life; is conscious about historical development of mathematical notions; X
9 has followed introduction to some mathematical or non-mathematical disciplines after one’s proper choice; had experience to learn selected subjects according to one’s proper arrangement; X
10 masters French language as well as other foreign languages, to a level sufficient to study or work abroad. X
Class Hours 14 5 70
Working Hours out of Class 14 3 42
Assignments 2 3 6
Presentation 2 3 6
Midterm Examinations (including preparation) 2 12 24
Project 0 0 0
Laboratory 0 0 0
Other Applications 0 0 0
Final Examinations (including preparation) 1 15 15
Quiz 0 0 0
Term Paper/ Project 1 3 3
Portfolio Study 0 0 0
Reports 0 0 0
Learning Diary 0 0 0
Thesis/ Project 0 0 0
Seminar 0 0 0
Other 0 0 0