Advanced Mathematics I(ING251)
| Course Code | Course Name | Semester | Theory | Practice | Lab | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| ING251 | Advanced Mathematics I | 3 | 2 | 1 | 0 | 2.5 | 4 |
| Prerequisites | |
| Admission Requirements |
| Language of Instruction | French |
| 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 Math I 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 |
Theory Topics
| Week | Weekly Contents |
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Practice Topics
| Week | Weekly Contents |
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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 | ||