Single Variable Analysis II(MAT102)
| Course Code | Course Name | Semester | Theory | Practice | Lab | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| MAT102 | Single Variable Analysis II | 2 | 5 | 0 | 0 | 5 | 7 |
| Prerequisites | |
| Admission Requirements |
| Language of Instruction | French |
| Course Type | Compulsory |
| Course Level | Bachelor Degree |
| Course Instructor(s) | Begüm Gülşah ÇAKTI (Email) Gönenç ONAY gonay@gsu.edu.tr (Email) |
| Assistant | |
| Objective | Establish the fundamental concepts of real analysis with appropriate mathematical precision and learn the methods and knowledge necessary for continuing mathematics education |
| Content | Derivatives, Integrals, Known Functions, Parametric Curves (if time permits) |
| 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 |
Theory Topics
| Week | Weekly Contents |
|---|---|
| 1 | Derivatites |
| 2 | Derivatives |
| 3 | Derivatability , l'Hopital Rule |
| 4 | Mean Value Theorem and Rolle Theorem |
| 5 | Applications of Derivative |
| 6 | Usual Functions |
| 7 | Introduction to Integration |
| 8 | Midterm Exam I |
| 9 | Primitives |
| 10 | Integral and Primitive, Riemannian Integration |
| 11 | Theorem Combining Derivative and Integral for Continuous Functions: Fundamental Theorem of Calculus |
| 12 | Improper Integral |
| 13 | Parametric Curves |
| 14 | Summary |
Practice Topics
| Week | Weekly Contents |
|---|
Contribution to Overall Grade
| Number | Contribution | |
|---|---|---|
| Contribution of in-term studies to overall grade | 4 | 60 |
| Contribution of final exam to overall grade | 1 | 40 |
| Toplam | 5 | 100 |
In-Term Studies
| Number | Contribution | |
|---|---|---|
| Assignments | 0 | 0 |
| Presentation | 0 | 0 |
| Midterm Examinations (including preparation) | 1 | 30 |
| Project | 0 | 0 |
| Laboratory | 0 | 0 |
| Other Applications | 0 | 0 |
| Quiz | 3 | 30 |
| 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 | 4 | 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 | 70 | 1 | 70 |
| Working Hours out of Class | 70 | 1 | 70 |
| Assignments | 0 | 0 | 0 |
| 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 | 3 | 3 | 9 |
| 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 | 169 | ||
| Total Workload / 25 | 6,76 | ||
| Credits ECTS | 7 | ||