ECTS - Advanced Calculus I
Advanced Calculus I (MATH251) Course Detail
| Course Name | Course Code | Season | Lecture Hours | Application Hours | Lab Hours | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| Advanced Calculus I | MATH251 | 3. Semester | 3 | 2 | 0 | 4 | 8 |
| Pre-requisite Course(s) |
|---|
| MATH136 |
| Course Language | English |
|---|---|
| Course Type | Compulsory Departmental Courses |
| Course Level | Bachelor’s Degree (First Cycle) |
| Mode of Delivery | Face To Face |
| Learning and Teaching Strategies | Lecture, Discussion, Problem Solving. |
| Course Lecturer(s) |
|
| Course Objectives | This course is desined to introduce higher-level aspects of the calculus through a rigorous development of the fundamental ideas in the topic and to achieve a further development of the math student’s ability to deal with abstract mathematics and proofs. |
| Course Learning Outcomes |
The students who succeeded in this course;
|
| Course Content | Vector and matrix algebra, functions of several variables: limit, continuity, partial derivatives, chain rule; implicit functions. inverse functions, directional derivatives, maxima and minima of functions of several variables, extrema for functions with side conditions. |
Weekly Subjects and Releated Preparation Studies
| Week | Subjects | Preparation |
|---|---|---|
| 1 | Vectors and Matrix Algebra (a very brief review). | pp. 1-31, 50-56, 60-66 |
| 2 | Functions of several variables, | pp. 77-78 |
| 3 | Domain and Regions, Functional Notation, | pp. 78-81 |
| 4 | Limits and continuity, | pp. 82-87 |
| 5 | Partial Derivatives, Total differential (fundamental lemma), | pp. 88-93 |
| 6 | Differential of functions of n variables (The Jacobian matrix), | pp. 94-100 |
| 7 | Midterm | |
| 8 | Derivatives and differentials of composite functions, | pp. 101-105 |
| 9 | The general chain rule, Implicit functions, Proof of a case of the implicit function theorem, | pp. 106-121 |
| 10 | Inverse functions (curvilinear coordinates), Geometrical applications (tangent plane, tangent line, etc.) | pp. 122-134 |
| 11 | The directional derivatives, Partial derivatives of higher order, | pp. 135-142 |
| 12 | Higher derivatives of composite functions, The Laplacian in polar, cylindrical, and spherical coordinates, | pp. 143-145 |
| 13 | Higher derivatives of implicit functions, Maxima and minima of functions of several variables, | pp. 146-158 |
| 14 | Extrema for functions with side conditions (Lagrange Multipliers). | pp. 159-160 |
| 15 | Review | |
| 16 | Final |
Sources
| Course Book | 1. W. Kaplan, Advanced Calculus. Addison-Wesley, 1993 |
|---|---|
| Other Sources | 2. H. Helson. Honors Calculus |
| 3. B. Demidovich. Problem book in mathematical analysis |
Evaluation System
| Requirements | Number | Percentage of Grade |
|---|---|---|
| Attendance/Participation | - | - |
| Laboratory | - | - |
| Application | - | - |
| Field Work | - | - |
| Special Course Internship | - | - |
| Quizzes/Studio Critics | - | - |
| Homework Assignments | 5 | 10 |
| Presentation | - | - |
| Project | - | - |
| Report | - | - |
| Seminar | - | - |
| Midterms Exams/Midterms Jury | 2 | 50 |
| Final Exam/Final Jury | 1 | 40 |
| Toplam | 8 | 100 |
| Percentage of Semester Work | 60 |
|---|---|
| Percentage of Final Work | 40 |
| Total | 100 |
Course Category
| Core Courses | |
|---|---|
| Major Area Courses | X |
| Supportive Courses | |
| Media and Managment Skills Courses | |
| Transferable Skill Courses |
The Relation Between Course Learning Competencies and Program Qualifications
| # | Program Qualifications / Competencies | Level of Contribution | ||||
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | ||
| 1 | Acquires skills to use the advanced theoretical and applied knowledge obtained at the mathematics bachelors program to do further academic and scientific research in both mathematics-based graduate programs and public or private sectors. | X | ||||
| 2 | Transplants and applies the theoretical and applicable knowledge gained in their field to the secondary education by using suitable tools and devices. | X | ||||
| 3 | Acquires the skill of choosing, using and improving problem solving techniques which are needed for modeling and solving current problems in mathematics or related fields by using the obtained knowledge and skills. | X | ||||
| 4 | Acquires analytical thinking and uses time effectively in the process of deduction | X | ||||
| 5 | Acquires basic software knowledge necessary to work in the computer science related fields and together with the skills to use information technologies effectively. | X | ||||
| 6 | Obtains the ability to collect data, to analyze, interpret and use statistical methods necessary in decision making processes. | X | ||||
| 7 | Acquires the level of knowledge to be able to work in the mathematics and related fields and keeps professional knowledge and skills up-to-date with awareness in the importance of lifelong learning. | X | ||||
| 8 | Takes responsibility in mathematics related areas and has the ability to work affectively either individually or as a member of a team. | X | ||||
| 9 | Has proficiency in English language and has the ability to communicate with colleagues and to follow the innovations in mathematics and related fields. | X | ||||
| 10 | Has the ability to communicate ideas with peers supported by qualitative and quantitative data. | X | ||||
| 11 | Has professional and ethical consciousness and responsibility which takes into account the universal and social dimensions in the process of data collection, interpretation, implementation and declaration of results in mathematics and its applications. | X | ||||
ECTS/Workload Table
| Activities | Number | Duration (Hours) | Total Workload |
|---|---|---|---|
| Course Hours (Including Exam Week: 16 x Total Hours) | 16 | 3 | 48 |
| Laboratory | |||
| Application | 16 | 2 | 32 |
| Special Course Internship | |||
| Field Work | |||
| Study Hours Out of Class | 16 | 4 | 64 |
| Presentation/Seminar Prepration | |||
| Project | |||
| Report | |||
| Homework Assignments | 5 | 3 | 15 |
| Quizzes/Studio Critics | |||
| Prepration of Midterm Exams/Midterm Jury | 2 | 10 | 20 |
| Prepration of Final Exams/Final Jury | 1 | 21 | 21 |
| Total Workload | 200 | ||