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COURSE INFORMATION PACKAGE · MAT102

Single Variable Analysis II

Compulsory · French Open to Erasmus+ exchange students
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ECTS
7
Local Credit
5
Theory + Practice + Lab
5 + 0 + 0
Course Level
Bachelor Degree
Prerequisites
-
Semester
2
On this page
Content Weekly Contents Assessment System ECTS
Course Instructor(s)
Ayşegül ULUS
aulus@gsu.edu.tr

Content

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

Course Content

Course syllabus : Intermediate Value Theorem, Limit, Continuity, Trigonometric functions, Asymptotes, Differentiation, Mean Value Theorem, Rolle Theorem, L’Hospital Rule, Graphs of functions, Hyperbolic functions, Riemann integral- Darboux theorem, Area and volume calculation, Improper integral.

Course Learning Outcomes

The student is expected to learn the main notions and the teorems (Intermediate Value Theorem, Differentiation, Mean Value Theorem, Rolle Theorem, Riemann integral, Improper integral). The student will be able make the applications and he/she will be able to draw the usual functions graphics

Teaching and Learning Methods

Courses and the problem solving

References

A First Course in Real Analysis, Sterling K.Berberian, Springer

Calculus, TÜBA yayınları

Mathématiques de 1er cycle, 1er année, Dixmier

Weekly Contents

Theory Topics
Week Weekly Contents
1 Limit and continuity
2 Derivatives
3 Derivatability , l'Hopital Rule
4 Mean Value Theorem and Rolle Theorem
5 Derivative change, convex concave functions, asymptotes,
6 Graphs of Functions
7 Midterm Exam I
8 Taylor Theorem
9 Applications of Derivative
10 Integral and Primitive, Riemannian Integration
11 Theorem Combining Derivative and Integral for Continuous Functions: Fundamental Theorem of Calculus
12 Midterm exam II
13 Improper Integral
14 Applications of Integral

Assessment System

Contribution to Overall Grade
Activities Number Contribution
Contribution of in-term studies to overall grade 2 60
Contribution of final exam to overall grade 1 40
Total 3 100
In-Term Studies
Activities Number Contribution
Midterm Examinations (including preparation) 2 60
Total 2 60

ECTS

Activities Number Period Total Workload
Class Hours 14 5 70
Working Hours out of Class 14 5 70
Midterm Examinations (including preparation) 2 10 20
Final Examinations (including preparation) 1 10 10
Total Workload 170
Total Workload / 25 6.80
Credits ECTS 7