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 |
|---|---|
| 1 | Reminders: Derivation, usual functions and limited developments |
| 2 | Primitives: Definition, Interpretation and Properties |
| 3 | Primitives: Calculation methods (integration by part) |
| 4 | Primitives: Calculation methods (integration by part) |
| 5 | Primitives: Calculation methods (cases requiring several successive methods) |
| 6 | Comparison of functions: Definition and interpretation |
| 7 | Comparing functions: Practical search for the equivalent of a function |
| 8 | Comparing functions: Practical search for the equivalent of a function (continued) |
| 9 | Midterm exam |
| 10 | Generalized integrals: Definition, Interpretation and Properties |
| 11 | Generalized integrals: Case of positive functions |
| 12 | Generalized integrals: Case of functions of any sign |
| 13 | Generalized integrals: Semi-convergent integrals |
| 14 | Preparing for the final exam |
Practice Topics
| Week | Weekly Contents |
|---|
Contribution to Overall Grade
| Number | Contribution | |
|---|---|---|
| Contribution of in-term studies to overall grade | 0 | 0 |
| Contribution of final exam to overall grade | 0 | 0 |
| Toplam | 0 | 0 |
In-Term Studies
| Number | Contribution | |
|---|---|---|
| Assignments | 0 | 0 |
| Presentation | 0 | 0 |
| Midterm Examinations (including preparation) | 0 | 0 |
| Project | 0 | 0 |
| Laboratory | 0 | 0 |
| Other Applications | 0 | 0 |
| Quiz | 0 | 0 |
| 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 | 0 | 0 |
| No | Program Learning Outcomes | Contribution | ||||
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | ||
| 1 | Knowledge and understanding of a wide range of basic sciences (math, physics, ...) and the main concepts of engineering | X | ||||
| 2 | Ability to combine the knowledge and skills to solve engineering problems and provide reliable solutions | X | ||||
| 3 | Ability to select and apply methods of analysis and modeling to ask, reformulate and solve the complex problems of industrial engineering | X | ||||
| 4 | Ability to conceptualize complex systems, processes or products under practical constraints to improve their performance, ability to use innovative methods of design | X | ||||
| 5 | Ability to design, select and apply methods and tools needed to solve problems related to the practice of industrial engineering, ability to use computer technology | X | ||||
| 6 | Ability to design experiments, collect and interpret data and analyze results | X | ||||
| 7 | Ability to work independently, ability to participate in working groups and have a multidisciplinary team spirit | X | ||||
| 8 | Ability to communicate effectively, ability to speak at least two foreign languages | X | ||||
| 9 | Awareness of the need for continuous improvement of lifelong learning, ability to keep abreast of scientific and technological developments to use the tools of information management | |||||
| 10 | Awareness of professional and ethical responsibility | |||||
| 11 | Knowledge of the concepts of professional life as "project management", "risk management" and "management of change" | |||||
| 12 | Knowledge on entrepreneurship, innovation and sustainability | |||||
| 13 | Understanding of the effects of Industrial Engineering applications on global and social health, environment and safety. | |||||
| Activities | Number | Period | Total Workload |
|---|---|---|---|
| Class Hours | 14 | 5 | 70 |
| Working Hours out of Class | 14 | 2 | 28 |
| Midterm Examinations (including preparation) | 2 | 10 | 20 |
| Final Examinations (including preparation) | 1 | 12 | 12 |
| Total Workload | 130 | ||
| Total Workload / 25 | 5.20 | ||
| Credits ECTS | 5 | ||