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 | Possesses sufficient knowledge in mathematics, natural sciences, and discipline-specific topics in Electrical and Electronics Engineering; uses this theoretical and practical knowledge to solve complex engineering problems. | X | ||||
| 2 | Identifies, defines, formulates, and solves complex engineering problems; selects and applies appropriate analytical and modeling methods for this purpose. | X | ||||
| 3 | Designs complex systems, processes, devices, or products under realistic constraints and conditions to meet specific requirements; applies modern design methods for this purpose. (Realistic constraints and conditions may include factors such as economy, environmental issues, sustainability, manufacturability, ethics, health, safety, social and political issues, depending on the nature of the design.) | X | ||||
| 4 | Selects and uses modern techniques and tools necessary for the analysis and solution of complex problems encountered in engineering applications; effectively uses information technologies. | |||||
| 5 | Designs experiments, conducts tests, collects data, analyzes, and interprets results to investigate complex engineering problems or discipline-specific research topics. | X | ||||
| 6 | Works effectively in disciplinary and interdisciplinary teams; develops the ability to work independently. | |||||
| 7 | Communicates effectively in both written and verbal forms; possesses proficiency in at least one foreign language; writes effective reports, understands written reports, prepares design and production reports, delivers effective presentations, and gives and receives clear instructions. | X | ||||
| 8 | Recognizes the need for lifelong learning; accesses information, follows developments in science and technology, and continuously renews oneself. | |||||
| 9 | Acts in accordance with ethical principles, assumes professional and ethical responsibility, and possesses knowledge about the standards used in engineering practices. | |||||
| 10 | Possesses knowledge about professional practices such as project management, risk management, and change management; gains awareness of entrepreneurship and innovation; understands the principles of sustainable development. | |||||
| 11 | Understands the universal and societal impacts of engineering practices on health, environment, and safety; recognizes the contemporary issues reflected in the field of engineering and understands the legal implications 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 | ||