Computer Engineering Department

Advanced Mathematics I(ING203)

Course Code Course Name Semester Theory Practice Lab Credit ECTS
ING203 Advanced Mathematics I 3 3 2 0 4 5
Prerequisites
Admission Requirements
Language of Instruction
Course Type Compulsory
Course Level Bachelor Degree
Course Instructor(s) Marie Christine PEROUEME mcperoueme@voila.fr (Email)
Assistant
Objective This course is the continuation of the ING 104 course.
In this context, the objectives of this course are:

- Demonstrate to the students the classical techniques [integration by parts and change of variables] to calculate a primitive,
- Teach students to handle the comparison relations "to be negligible in front of" and "to be equivalent to" on functions,
- Teach how to find a "" simple "" equivalent of a point function to find its limit,
- Demonstrate the different convergence criteria for the integrals of positive functions,
- Explain in which cases a limited expansion makes it possible to determine the nature of an integral,
- Demonstrate the different convergence criteria for series with positive terms,
- Explain in which cases a limited development makes it possible to determine the nature of a series
Content 1. Primitives: Definition, properties and first examples.
2. Primitives: Calculation rules [integration by parts and change of variable]
3. Comparison relations: function negligible in front of another, function equivalent to another
4. Comparison relations: calculation rules, comparative growth of logarithms, powers and exponential in 0 and infinity.
5. Comparison relations: Application to the search for limits.
6. Generalized integrals: definition, properties and first examples [Riemann integrals and Bertrand integrals].
7. Generalized integrals: comparison theorems for positive functions.
8. Generalized integrals: case of functions of any sign.
9. Partial Examination / Ara sinav
10. Generalized integrals: Integrals depending on a parameter
11. Numerical series: definition, properties and first examples [Riemann series and Bertrand series].
12. Numerical series: comparison theorems for series with positive terms.
13. Numerical series: Case of series of any sign. Convergence criterion of alternating series.
14. Digital Series: Series depending on a parameter
Course Learning Outcomes The student who will take this course will develop the following skill elements and will be able to:

1. Make an integration by parts and / or a change of variable to calculate the integral of a function,
2. Compare two functions at a given point,
3. Determine a "simple" equivalent of a function to calculate its limit at a point,
4. Apply comparison theorems to determine if a positive function admits a generalized integral,
5. Know how to use a Taylor expansion to determine the nature of an integral [absolutely convergent, semi-convergent or divergent],
6. Apply comparison theorems to determine if a series with positive terms is convergent,
7. Know how to use a lTaylor expansion to determine the nature of a series [absolutely convergent, semi-convergent or divergent]
Teaching and Learning Methods Lectures and supervised works/tutorials
References 1. Lectures notes ans worksheets
2. http://braise.univ-rennes1.fr/braise.cgi
3. http://www.unisciel.fr
Print the course contents
Theory Topics
Week Weekly Contents
Practice Topics
Week Weekly Contents
Contribution to Overall Grade
  Number Contribution
Toplam 0 0
In-Term Studies
  Number Contribution
Toplam 0 0
No Program Learning Outcomes Contribution
1 2 3 4 5
Activities Number Period Total Workload
Total Workload 0
Total Workload / 25 0,00
Credits ECTS 0
Scroll to Top