ECTS - Calculus II
Calculus II (MATH152) Course Detail
| Course Name | Course Code | Season | Lecture Hours | Application Hours | Lab Hours | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| Calculus II | MATH152 | 4 | 2 | 0 | 5 | 7 |
| Pre-requisite Course(s) |
|---|
| MATH151 Calculus I |
| Course Language | English |
|---|---|
| Course Type | N/A |
| 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 engineering problems; ability to select and apply proper analysis and modeling methods for this purpose. | |||||
| 3 | Ability to design a complex 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. | |||||
| 4 | Ability to select and use modern techniques and tools needed for analyzing and solving complex problems encountered in engineering practice; ability to employ information technologies effectively. | |||||
| 5 | Ability to design and conduct experiments, gather data, analyze and interpret results for investigating complex engineering problems or discipline specific research questions. | |||||
| 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 | Knowledge on behavior according ethical principles, professional and ethical responsibility and standards used in engineering practices. | |||||
| 10 | Knowledge about business life practices such as project management, risk management, and change management; 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. | |||||
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 | ||