ECTS - Mathematical Analysis II
Mathematical Analysis II (MATH136) Course Detail
| Course Name | Course Code | Season | Lecture Hours | Application Hours | Lab Hours | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| Mathematical Analysis II | MATH136 | 2. Semester | 4 | 2 | 0 | 5 | 8.5 |
| Pre-requisite Course(s) |
|---|
| MATH135 |
| 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 | The course is designed as a continuation of Math 135 Mathematical Analysis I and aims to give the students the computational skills in techniques of integration, convergence for Improper Integrals, sequences, infinite series and power series. It also gives the students the computational skills using integrals to solve applied problems such as finding area of a region, volume of a solid and length of a curve. |
| Course Learning Outcomes |
The students who succeeded in this course;
|
| Course Content | Riemann integral, the fundamental theorem of calculus, integration techniques, applications of integrals: area, volume, arc length, improper integrals, sequences, infinite series, tests for convergence, functional sequences and series, interval of convergence, power series, Taylor series and its applications. |
Weekly Subjects and Releated Preparation Studies
| Week | Subjects | Preparation |
|---|---|---|
| 1 | Upper-Lower Sums, Riemann Integral, | pp. 299-317 |
| 2 | Properties of Definite Integral, Indefinite Integral , Fundamental Theorem, Substitution For Indefinite Integral and Definite Integral | pp. 317-338 |
| 3 | Area Under A Curve, Area Between The Curves, | pp. 338-344 |
| 4 | Techniques of Integration (Substitution, Integration By Parts, Trigonometric Integrals). | pp. 345-352 |
| 5 | Techniques of Integration (Trigonometric Substitutions, The Method of Partial Fractions, Tan(X/2) Sunstitution). Right Hand Point, Left Hand Point, Mid Point, Trapezoid Approximation For Definite Integral | pp. 352-368, pp. 382-394 |
| 6 | Volumes, Disk Method, Cylindrical Shells Method, Arclength and Surface Area of Revolution | pp. 406-428 |
| 7 | Midterm | |
| 8 | Parametric Curves, Arclength of A Parametric Curve, Sequences, Bounded Sequences | pp. 488-504 |
| 9 | İncreasing and Decreasing Sequences. Limit of A Sequence. Monotone Sequence. | pp. 518-526 |
| 10 | Improper Integrals. Comparison Test. Limit Comparison Test, | pp. 373-378 |
| 11 | Absolute Convergence, Conditional Convergence. | pp. 378-381 |
| 12 | Series, Integral Test, Comparison Test, Limit Comparison Test. | pp. 526-541 |
| 13 | Ratio and Root Tests, Absolute Convergence, Alternating Series Test | pp. 542-548 |
| 14 | Approximation and Error In Approximation. The Alternating Series, Power Series, Differentiation and Integration of Power Series | pp. 549-564 |
| 15 | Taylor’s and Maclaurin Series with applications | pp. 564-578 |
| 16 | Final Examination |
Sources
| Course Book | 1. A complete Course, R. A. Adams, 4th Edition; Addison Wesley |
|---|---|
| Other Sources | 2. Thomas' Calculus, Early Transcendentals, 11th Edition; 2003 Revised by R. L. Finney, M. D. Weir, and F. R. Giardano; Addison Wesley |
| 3. Calculus with Analytic Geometry, C. H. Edwards; Prentice Hall Calculus with Analytic Geometry, R. A. Silverman; Prentice Hall |
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 | |
|---|---|
| Percentage of Final Work | 100 |
| 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) | |||
| Laboratory | |||
| Application | 16 | 2 | 32 |
| Special Course Internship | |||
| Field Work | |||
| Study Hours Out of Class | 14 | 4 | 56 |
| Presentation/Seminar Prepration | |||
| Project | |||
| Report | |||
| Homework Assignments | 5 | 5 | 25 |
| Quizzes/Studio Critics | |||
| Prepration of Midterm Exams/Midterm Jury | 2 | 10 | 20 |
| Prepration of Final Exams/Final Jury | 1 | 15 | 15 |
| Total Workload | 148 | ||