ECTS - Calculus II
Calculus II (MATH152) Course Detail
| Course Name | Course Code | Season | Lecture Hours | Application Hours | Lab Hours | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| Calculus II | MATH152 | 2. Semester | 4 | 2 | 0 | 5 | 7 |
| Pre-requisite Course(s) |
|---|
| MATH151 |
| 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, Question and Answer, Problem Solving. |
| Course Lecturer(s) |
|
| Course Objectives | The course is designed as a continuation of MATH151 Calculus I and aims to give the students the computational skills in series, analytic geometry and multi-variable differential and integral calculus to handle engineering problems. |
| Course Learning Outcomes |
The students who succeeded in this course;
|
| Course Content | Infinite series, vectors in the plane and polar coordinates, vectors and motions in space, multivariable functions and their derivatives, multiple integrals: double integrals, areas, double integrals in polar coordinates, triple integrals in rectangular, cylindrical and spherical coordinates, line integrals, Independence of path,Green's theorem. |
Weekly Subjects and Releated Preparation Studies
| Week | Subjects | Preparation |
|---|---|---|
| 1 | 9.1. Sequences and Convergence, 9.2. Infinite Series, | pp:495-409 |
| 2 | 9.3. Convergence Tests for Positive Series (The Integral Test, Comparison Tests, The Ratio and Root Tests), 9.4. Absolute and Conditional Convergence, | pp:510-526 |
| 3 | 9.5. Power Series, 9.6. Taylor and Maclaurin Series (Convergence of Taylor Series; Error Estimates), | pp:526-545 |
| 4 | 9.7. Applications of Taylor and Maclaurin Series, 10.1. Analytic Geometry in Three Dimensions, | pp:546-549 pp:562-568 |
| 5 | 10.2. Vectors, 10.3. The Cross Product in 3-Space, | pp:568-585 |
| 6 | 10.4. Planes and Lines, 10.5. Quadric Surfaces, | pp:585-596 |
| 7 | Midterm, | |
| 8 | 12.1. Functions of Several Variables, 12.2. Limits and Continuity, | pp:669-681 |
| 9 | 12.3. Partial Derivatives, 12.4. Higher Order Derivatives, 12.5. The Chain Rule, | pp:681-703 |
| 10 | 12.6. Linear Approximations, Differentiability, and Differentials, 12.7. Gradient and Directional Derivatives, 12.8. Implicit Functions, | pp:703-705 pp:706-707 pp:714-726 |
| 11 | 13.1. Extreme Values, 13.2. Extreme Values of Functions Defined on Restricted Domains, | pp:743-754 |
| 12 | 13.3. Lagrange Multipliers, 14.1. Double Integrals, | pp:756-760 pp:790-796 |
| 13 | 14.2. Iteration of Double Integrals in Cartesian Coordinates, 14.4. Double Integrals in Polar Coordinates, | pp:796-802 pp:808-812 |
| 14 | 14.5. Triple Integrals, 14.6. Change of Variables in Triple Integrals (Cylindrical and Spherical Coordinates), | pp:818-830 |
| 15 | 14.6. Change of Variables in Triple Integrals (Cylindrical and Spherical Coordinates), | pp:824-830 |
| 16 | Final Exam |
Sources
| Course Book | 1. Calculus: A complete Course, R. A. Adams, C. Essex, 7th Edition; Pearson Addison Wesley |
|---|---|
| Other Sources | 2. Thomas’ Calculus Early Transcendentals, 11th Edition.( Revised by M. D. Weir, J.Hass and F. R. Giardano; Pearson , Addison Wesley) |
| 3. Calculus: A new horizon, Anton Howard, 6th Edition; John Wiley & Sons | |
| 4. Calculus with Analytic Geometry, C. H. Edwards; Prentice Hall | |
| 5. 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 | - | - |
| Presentation | - | - |
| Project | - | - |
| Report | - | - |
| Seminar | - | - |
| Midterms Exams/Midterms Jury | 2 | 60 |
| Final Exam/Final Jury | 1 | 40 |
| Toplam | 3 | 100 |
| Percentage of Semester Work | 60 |
|---|---|
| Percentage of Final Work | 40 |
| Total | 100 |
Course Category
| Core Courses | X |
|---|---|
| Major Area Courses | |
| 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 | Adequate knowledge in mathematics, science and engineering subjects pertaining to the relevant discipline; ability to use theoretical and applied knowledge in these areas in the solution of complex engineering problems. | X | ||||
| 2 | Ability to formulate, and solve complex mechatronics engineering problems; ability to select and apply proper analysis and modeling methods for this purpose. | X | ||||
| 3 | Ability to design a complex mechatronics engineering system, process, device or product under realistic constraints and conditions, in such a way as to meet the desired result; ability to apply modern design methods for this purpose. | X | ||||
| 4 | Ability to select and use modern techniques and tools needed for analyzing and solving complex problems encountered in mechatronics engineering and robot technology practices; ability to employ information technologies effectively. | |||||
| 5 | Ability to design and conduct experiments, gather data, analyze and interpret results for investigating complex mechatronics engineering and robot technology problems or research questions. | X | ||||
| 6 | Ability to work efficiently in intra-disciplinary and multi-disciplinary teams; ability to work individually. | |||||
| 7 | Ability to communicate effectively, both orally and in writing; knowledge of a minimum of one foreign language; ability to write effective reports and comprehend written reports, prepare design and production reports, make effective presentations, and give and receive clear and intelligible instructions. | |||||
| 8 | Awareness of the need for lifelong learning; ability to access information, to follow developments in science and technology, and to continue to educate him/herself | |||||
| 9 | a-) Knowledge on behavior according to ethical principles, professional and ethical responsibility b-) Knowledge on standards used in engineering practices. | |||||
| 10 | a-) Knowledge about business life practices such as project management, risk management, and change management b-) Awareness in entrepreneurship, innovation; knowledge about sustainable development. | |||||
| 11 | Knowledge about the global and social effects of engineering practices on health, environment, and safety, and contemporary issues of the century reflected into the field of engineering; awareness of the legal consequences of engineering solutions. | |||||
| 12 | Competency on defining, analyzing and surveying databases and other sources, proposing solutions based on research work and scientific results and communicate and publish numerical and conceptual solutions in the field of mechatronics engineering. | |||||
| 13 | Consciousness on the environment and social responsibility, competencies on observation, improvement and modify and implementation of projects for the society and social relations and be an individual within the society in such a way that planning, improving or changing the norms with a criticism. | |||||
ECTS/Workload Table
| Activities | Number | Duration (Hours) | Total Workload |
|---|---|---|---|
| Course Hours (Including Exam Week: 16 x Total Hours) | 16 | 4 | 64 |
| Laboratory | |||
| Application | 16 | 2 | 32 |
| Special Course Internship | |||
| Field Work | |||
| Study Hours Out of Class | 14 | 3 | 42 |
| Presentation/Seminar Prepration | |||
| Project | |||
| Report | |||
| Homework Assignments | |||
| Quizzes/Studio Critics | |||
| Prepration of Midterm Exams/Midterm Jury | 2 | 10 | 20 |
| Prepration of Final Exams/Final Jury | 1 | 18 | 18 |
| Total Workload | 176 | ||