Series and Multivariable Functions(MAT201)
| Course Code | Course Name | Semester | Theory | Practice | Lab | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| MAT201 | Series and Multivariable Functions | 3 | 3 | 2 | 0 | 5 | 8 |
| Prerequisites | |
| Admission Requirements |
| Language of Instruction | |
| Course Type | Compulsory |
| Course Level | Bachelor Degree |
| Course Instructor(s) | Sylvain LAVAU sylvain.lavau@gmail.com (Email) |
| Assistant | |
| Objective |
To teach the notion of convergence of sequences and series To teach certain technics for testing their convergence To enable participants to work with multivariable functions, their limits and derivatives |
| Content |
Convergence of series and power series Convergence tests Taylor Series Multivariate functions and their graphs Their limits Notion of continuity for multivariate functions Partial and directional derivatives of multivariate functions Differentiability of multivariate functions |
| Course Learning Outcomes |
1.Treatment of convergence of series 2.Treatment of convergence of power series 3. Computation of Taylor Series 4. Graphing multivariate functions 5. Notions of limit and continuity of multivariate functions 6. Notions of partial and directional derivatives of multivariate functions 7. Differentiability of multivariate functions |
| Teaching and Learning Methods | Exercises, discussions and worksheets |
| References |
Analyse 2eme année, François Liret, Dominique Martinais Analiz 1,2, Ali Nesin Calculus, James Stewart |
Theory Topics
| Week | Weekly Contents |
|---|---|
| 1 | Series, Absolute convergence. |
| 2 | Series with positive terms. Comparison theorems. Riemann series. |
| 3 | Convergence tests: Cauchy, d'Alembert, Abel. |
| 4 | Alternating series |
| 5 | Power Series |
| 6 | Taylor Series |
| 7 | Midterm |
| 8 | Series of functions, pointwise and uniform convergence of series of functions. |
| 9 | Stone-Weierstrass theorem |
| 10 | Multivariate functions, their graphs |
| 11 | Limits of multivariate functions, continutiy |
| 12 | Partial derivatives, differentiability |
| 13 | Second derivatives, Schwarz theorem |
| 14 | Optimization of multivariate functions |
Practice Topics
| Week | Weekly Contents |
|---|---|
| 1 | Review on functions with one variable, their limits, continuity, differentiability, integrals |
| 2 | Series, Absolute convergence. |
| 3 | Series with positive terms. Comparison theorems. Riemann series. |
| 4 | Convergence tests: Cauchy, d'Alembert, Abel. |
| 5 | Alternating series |
| 6 | Power Series |
| 7 | Taylor Series |
| 8 | Solution of midterm |
| 9 | Series of functions, pointwise and uniform convergence of series of functions. |
| 10 | Stone-Weierstrass theorem |
| 11 | Multivariate functions, their graphs |
| 12 | Limits of multivariate functions, continutiy |
| 13 | Partial derivatives, differentiability |
| 14 | Second derivatives, Schwarz theorem |
Contribution to Overall Grade
| Number | Contribution | |
|---|---|---|
| Contribution of in-term studies to overall grade | 11 | 60 |
| Contribution of final exam to overall grade | 1 | 40 |
| Toplam | 12 | 100 |
In-Term Studies
| Number | Contribution | |
|---|---|---|
| Assignments | 10 | 30 |
| Presentation | 0 | 0 |
| Midterm Examinations (including preparation) | 1 | 30 |
| 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 | 11 | 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 | ||||
| Activities | Number | Period | Total Workload |
|---|---|---|---|
| Class Hours | 14 | 5 | 70 |
| Working Hours out of Class | 14 | 3 | 42 |
| Assignments | 10 | 5 | 50 |
| Presentation | 0 | 0 | 0 |
| Midterm Examinations (including preparation) | 1 | 10 | 10 |
| Project | 0 | 0 | 0 |
| Laboratory | 0 | 0 | 0 |
| Other Applications | 0 | 0 | 0 |
| Final Examinations (including preparation) | 1 | 10 | 10 |
| Quiz | 0 | 0 | 0 |
| Term Paper/ Project | 0 | 0 | 0 |
| 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 |
| Total Workload | 182 | ||
| Total Workload / 25 | 7.28 | ||
| Credits ECTS | 7 | ||