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 | Knowledge of mathematics, natural sciences, engineering fundamentals, computing, and topics specific to the relevant engineering discipline; the ability to use this knowledge in the solution of complex engineering problems. | X | ||||
| 2 | The ability to identify, formulate, and analyze complex engineering problems using knowledge of basic sciences, mathematics, and engineering, and considering the UN Sustainable Development Goals relevant to the problem. | X | ||||
| 3 | The ability to design creative solutions for complex engineering problems; the ability to design complex systems, processes, devices, or products to meet current and future requirements, considering realistic constraints and conditions. | X | ||||
| 4 | The ability to select and use appropriate techniques, resources, and modern engineering and IT tools, including prediction and modeling, for the analysis and solution of complex engineering problems, with an awareness of their limitations. | X | ||||
| 5 | The ability to use research methods for the investigation of complex engineering problems, including literature search, designing and conducting experiments, collecting data, and analyzing and interpreting results. | X | ||||
| 6 | Knowledge of the effects of engineering practices on society, health and safety, the economy, sustainability, and the environment within the scope of the UN Sustainable Development Goals; awareness of the legal consequences of engineering solutions. | |||||
| 7 | Acting in accordance with engineering professional principles, knowledge of ethical responsibility; awareness of acting impartially without discrimination on any grounds and being inclusive of diversity. | |||||
| 8 | The ability to work effectively individually and in intra-disciplinary and multi-disciplinary teams (face-to-face, remote, or hybrid) as a team member or leader. | |||||
| 9 | "The ability to communicate effectively orally and in writing on technical topics, considering the various differences of the target audience (such as education, language, profession). | |||||
| 10 | Knowledge of practices in business life such as project management and economic feasibility analysis; awareness of entrepreneurship and innovation. | |||||
| 11 | The ability to engage in life-long learning, including independent and continuous learning, adapting to new and emerging technologies, and thinking inquisitively regarding technological changes. | |||||
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 | ||