ECTS - Extended Calculus II
Extended Calculus II (MATH158) Course Detail
| Course Name | Course Code | Season | Lecture Hours | Application Hours | Lab Hours | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| Extended Calculus II | MATH158 | Diğer Bölümlere Verilen Ders | 4 | 2 | 0 | 5 | 7.5 |
| Pre-requisite Course(s) |
|---|
| Math 157 Extended Calculus I |
| Course Language | English |
|---|---|
| Course Type | Service Courses Given to Other Departments |
| 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 Math 157 Extended Calculus I and aims to give the students the computational skills in series, analytic geometry and multi-variable differential and integral calculus and line integrals 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 | 9.2 Infinite Series, 9.3 Convergence Tests for Positive Series (The Integral Test,Comparison Tests, The Ratio and Root Tests) | pp:503-519 |
| 2 | 9.4 Absolute and Conditional Convergence, 9.5 Power Series | pp:520-536 |
| 3 | 9.6 Taylor and Maclaurin Series (Convergence of Taylor Series; Error Estimates) 9.7 Applications of Taylor and Maclaurin Series, | pp:536-549 |
| 4 | 10.1 Analytic Geometry in Three Dimensions, 10.2 Vectors, 10.3 The Cross Product in 3-Space, | pp:562-585 |
| 5 | 10.4 Planes and Lines, 10.5 Quadric Surfaces, | pp:585-596 |
| 6 | 12.1 Functions of Several Variables, 12.2 Limits and Continuity | pp:669-681 |
| 7 | Midterm | |
| 8 | 12.3 Partial Derivatives, 12.4 Higher Order Derivatives, | pp:681-693 |
| 9 | 12.5 The Chain Rule, 12.6 Linear Approximations, Differentiability, and Differentials, | pp:693-705 pp:706-707 |
| 10 | 12.7 Gradient and Directional Derivatives, 12.8 Implicit Functions, | pp:714-726 |
| 11 | 13.1 Extreme Values, 13.2 Extreme Values of Functions Defined on Restricted Domains, 13.3 Lagrange Multipliers, | pp:743-754 pp:756-760 |
| 12 | 14.1 Double Integrals, 14.2 Iteration of Double Integrals in Cartesian Coordinates, | pp:790-802 |
| 13 | 14.4 Double Integrals in Polar Coordinates, 14.5 Triple Integrals | pp:808-812 pp:818-824 |
| 14 | 14.6 Change of Variables in Triple Integrals (Cylindrical and Spherical Coordinates) 15.1 Vector and Scalar Fields, 15.2 Conservative Fields | pp:824-830 pp:842-857 |
| 15 | 15.3 Line Integrals, 15.4 Line Integrals of Vector Fields, 16.3 Green’s Theorem in the Plane, | pp:858-869 pp:903-906 |
| 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 | |
|---|---|
| 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 | 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. | |||||
| 2 | Transplants and applies the theoretical and applicable knowledge gained in their field to the secondary education by using suitable tools and devices. | |||||
| 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. | |||||
| 4 | Acquires analytical thinking and uses time effectively in the process of deduction | |||||
| 5 | Acquires basic software knowledge necessary to work in the computer science related fields and together with the skills to use information technologies effectively. | |||||
| 6 | Obtains the ability to collect data, to analyze, interpret and use statistical methods necessary in decision making processes. | |||||
| 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. | |||||
| 8 | Takes responsibility in mathematics related areas and has the ability to work affectively either individually or as a member of a team. | |||||
| 9 | Has proficiency in English language and has the ability to communicate with colleagues and to follow the innovations in mathematics and related fields. | |||||
| 10 | Has the ability to communicate ideas with peers supported by qualitative and quantitative data. | |||||
| 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. | |||||
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 | 4 | 56 |
| Presentation/Seminar Prepration | |||
| Project | |||
| Report | |||
| Homework Assignments | |||
| Quizzes/Studio Critics | |||
| Prepration of Midterm Exams/Midterm Jury | |||
| Prepration of Final Exams/Final Jury | 1 | 16 | 16 |
| Total Workload | 168 | ||