Course Detail
Course Description
Course | Code | Semester | T+P (Hour) | Credit | ECTS |
---|
CALCULUS III | BME3210783 | Spring Semester | 3+0 | 3 | 6 |
Prerequisites Courses | |
Recommended Elective Courses | |
Language of Course | English |
Course Level | First Cycle (Bachelor's Degree) |
Course Type | Elective |
Course Coordinator | Assoc.Prof. Hüseyin Şerif SAVCI |
Name of Lecturer(s) | Assoc.Prof. Hüseyin Şerif SAVCI |
Assistant(s) | |
Aim | 1. To provide the concepts of polar coordinates and limit, continuity, integral of vector valued functions
2. To provide the applications of multiple integrals
3. To compute the line integrals and surface integrals and apply Green’s theorem, Stokes Theorem and Divergence Theorem
|
Course Content | This course contains; Vector Valued Functions; Derivatives and Integrals of Vector Functions (T,N,B vectors),Directional Derivatives and the Gradient Vector,Maxima and Minima in Several Variables, Extrema of Functions,Lagrange Multipliers, Vector Fields,Line Integrals, Green's Theorem,Curl and Divergence,Parametric Surfaces and their Areas,Stoke's Theorem and Summary of Vector Calculus,Two Null Identities, Field Classification and Helmholtz's Theorem,Introduction to Electrostatic in Free Space and Coulomb's Law,Gauss Law and Applications, Electric Potential, Material Media in Static Electric Field,Flux Density, and Dielectric Constant,Electric Flux Density and Dielectric Constant ,Capacitance and Capacitors and Electrostatic Energy and Forces. |
Dersin Öğrenme Kazanımları | Teaching Methods | Assessment Methods |
Compute the standard representation of a vector in 3-space, compute the dot product and cross product of vectors; write equations of lines, planes and quadric surfaces in 3-space. | 12, 14, 9 | A, E |
Use the concepts of continuity, differentiation, and integration of vector-valued functions. | 12, 14, 9 | A, E |
Compute multiple integrals over rectangular coordinates, nonrectangular coordinates and in other coordinate systems; apply multiple integrals in problems involving area, volume and surface area | 12, 14, 9 | A, E |
Compute line integrals and surface integrals and apply Green’s Green’s theorem, Stokes Theorem and Divergence Theorem | 12, 14, 9 | A, E |
Understanding of electrostatic in free space | 12, 14, 9 | A, E |
Understanding of electric flux and its relation with dielectric constant | 12, 14, 9 | A, E |
Understanding of electrostatic energy and its storage via capacitors | 12, 14, 9 | A, E |
Teaching Methods: | 12: Problem Solving Method, 14: Self Study Method, 9: Lecture Method |
Assessment Methods: | A: Traditional Written Exam, E: Homework |
Course Outline
Order | Subjects | Preliminary Work |
---|
1 | Vector Valued Functions; Derivatives and Integrals of Vector Functions (T,N,B vectors) | |
2 | Directional Derivatives and the Gradient Vector | |
3 | Maxima and Minima in Several Variables, Extrema of Functions | |
4 | Lagrange Multipliers, Vector Fields | |
5 | Line Integrals, Green's Theorem | |
6 | Curl and Divergence | |
7 | Parametric Surfaces and their Areas | |
8 | Stoke's Theorem and Summary of Vector Calculus | |
9 | Two Null Identities, Field Classification and Helmholtz's Theorem | |
10 | Introduction to Electrostatic in Free Space and Coulomb's Law | |
11 | Gauss Law and Applications, Electric Potential, Material Media in Static Electric Field | |
12 | Flux Density, and Dielectric Constant | |
13 | Electric Flux Density and Dielectric Constant | |
14 | Capacitance and Capacitors and Electrostatic Energy and Forces | |
Resources |
Thomas’ Calculus, 12th Edition, G.B Thomas, R. L. Finney, M.D.Weir, F.R.Giordano, Addison |
1. Fundamentals of Engineering Electromagnetics by David Cheng, First edition (main text for Electromagnetism)
2. Vector Calculus, 4th edition, Susan Jane Colley, Pearson edn. |
Course Contribution to Program Qualifications
Course Contribution to Program Qualifications |
No | Program Qualification | Contribution Level |
1 | 2 | 3 | 4 | 5 |
1 | An ability to apply knowledge of mathematics, science, and engineering | | | | | X |
2 | An ability to identify, formulate, and solve engineering problems | X | | | | |
3 | An ability to design a system, component, or process to meet desired needs within realistic constraints such as economic, environmental, social, political, ethical, health and safety, manufacturability, and sustainability | X | | | | |
4 | An ability to use the techniques, skills, and modern engineering tools necessary for engineering practice | | X | | | |
5 | An ability to use the techniques, skills, and modern engineering tools necessary for engineering practice | | X | | | |
6 | An ability to function on multidisciplinary teams | | | | | |
7 | An ability to communicate effectively | | | | | |
8 | A recognition of the need for, and an ability to engage in life-long learning | | | | | |
9 | An understanding of professional and ethical responsibility | | | | | |
10 | A knowledge of contemporary issues | | | | | |
11 | The broad education necessary to understand the impact of engineering solutions in a global, economic, environmental, and societal context | | | | | |
12 | Capability to apply and decide on engineering principals while understanding and rehabilitating the human body | | | | | |
Assessment Methods
Contribution Level | Absolute Evaluation |
Rate of Midterm Exam to Success | | 30 |
Rate of Final Exam to Success | | 70 |
Total | | 100 |
ECTS / Workload Table |
Activities | Number of | Duration(Hour) | Total Workload(Hour) |
Course Hours | 13 | 4 | 52 |
Guided Problem Solving | 14 | 2 | 28 |
Resolution of Homework Problems and Submission as a Report | 5 | 10 | 50 |
Term Project | 0 | 0 | 0 |
Presentation of Project / Seminar | 0 | 0 | 0 |
Quiz | 2 | 6 | 12 |
Midterm Exam | 1 | 14 | 14 |
General Exam | 1 | 24 | 24 |
Performance Task, Maintenance Plan | 0 | 0 | 0 |
Total Workload(Hour) | 180 |
Dersin AKTS Kredisi = Toplam İş Yükü (Saat)/30*=(180/30) | 6 |
ECTS of the course: 30 hours of work is counted as 1 ECTS credit. |
Detail Informations of the Course
Course Description
Course | Code | Semester | T+P (Hour) | Credit | ECTS |
---|
CALCULUS III | BME3210783 | Spring Semester | 3+0 | 3 | 6 |
Prerequisites Courses | |
Recommended Elective Courses | |
Language of Course | English |
Course Level | First Cycle (Bachelor's Degree) |
Course Type | Elective |
Course Coordinator | Assoc.Prof. Hüseyin Şerif SAVCI |
Name of Lecturer(s) | Assoc.Prof. Hüseyin Şerif SAVCI |
Assistant(s) | |
Aim | 1. To provide the concepts of polar coordinates and limit, continuity, integral of vector valued functions
2. To provide the applications of multiple integrals
3. To compute the line integrals and surface integrals and apply Green’s theorem, Stokes Theorem and Divergence Theorem
|
Course Content | This course contains; Vector Valued Functions; Derivatives and Integrals of Vector Functions (T,N,B vectors),Directional Derivatives and the Gradient Vector,Maxima and Minima in Several Variables, Extrema of Functions,Lagrange Multipliers, Vector Fields,Line Integrals, Green's Theorem,Curl and Divergence,Parametric Surfaces and their Areas,Stoke's Theorem and Summary of Vector Calculus,Two Null Identities, Field Classification and Helmholtz's Theorem,Introduction to Electrostatic in Free Space and Coulomb's Law,Gauss Law and Applications, Electric Potential, Material Media in Static Electric Field,Flux Density, and Dielectric Constant,Electric Flux Density and Dielectric Constant ,Capacitance and Capacitors and Electrostatic Energy and Forces. |
Dersin Öğrenme Kazanımları | Teaching Methods | Assessment Methods |
Compute the standard representation of a vector in 3-space, compute the dot product and cross product of vectors; write equations of lines, planes and quadric surfaces in 3-space. | 12, 14, 9 | A, E |
Use the concepts of continuity, differentiation, and integration of vector-valued functions. | 12, 14, 9 | A, E |
Compute multiple integrals over rectangular coordinates, nonrectangular coordinates and in other coordinate systems; apply multiple integrals in problems involving area, volume and surface area | 12, 14, 9 | A, E |
Compute line integrals and surface integrals and apply Green’s Green’s theorem, Stokes Theorem and Divergence Theorem | 12, 14, 9 | A, E |
Understanding of electrostatic in free space | 12, 14, 9 | A, E |
Understanding of electric flux and its relation with dielectric constant | 12, 14, 9 | A, E |
Understanding of electrostatic energy and its storage via capacitors | 12, 14, 9 | A, E |
Teaching Methods: | 12: Problem Solving Method, 14: Self Study Method, 9: Lecture Method |
Assessment Methods: | A: Traditional Written Exam, E: Homework |
Course Outline
Order | Subjects | Preliminary Work |
---|
1 | Vector Valued Functions; Derivatives and Integrals of Vector Functions (T,N,B vectors) | |
2 | Directional Derivatives and the Gradient Vector | |
3 | Maxima and Minima in Several Variables, Extrema of Functions | |
4 | Lagrange Multipliers, Vector Fields | |
5 | Line Integrals, Green's Theorem | |
6 | Curl and Divergence | |
7 | Parametric Surfaces and their Areas | |
8 | Stoke's Theorem and Summary of Vector Calculus | |
9 | Two Null Identities, Field Classification and Helmholtz's Theorem | |
10 | Introduction to Electrostatic in Free Space and Coulomb's Law | |
11 | Gauss Law and Applications, Electric Potential, Material Media in Static Electric Field | |
12 | Flux Density, and Dielectric Constant | |
13 | Electric Flux Density and Dielectric Constant | |
14 | Capacitance and Capacitors and Electrostatic Energy and Forces | |
Resources |
Thomas’ Calculus, 12th Edition, G.B Thomas, R. L. Finney, M.D.Weir, F.R.Giordano, Addison |
1. Fundamentals of Engineering Electromagnetics by David Cheng, First edition (main text for Electromagnetism)
2. Vector Calculus, 4th edition, Susan Jane Colley, Pearson edn. |
Course Contribution to Program Qualifications
Course Contribution to Program Qualifications |
No | Program Qualification | Contribution Level |
1 | 2 | 3 | 4 | 5 |
1 | An ability to apply knowledge of mathematics, science, and engineering | | | | | X |
2 | An ability to identify, formulate, and solve engineering problems | X | | | | |
3 | An ability to design a system, component, or process to meet desired needs within realistic constraints such as economic, environmental, social, political, ethical, health and safety, manufacturability, and sustainability | X | | | | |
4 | An ability to use the techniques, skills, and modern engineering tools necessary for engineering practice | | X | | | |
5 | An ability to use the techniques, skills, and modern engineering tools necessary for engineering practice | | X | | | |
6 | An ability to function on multidisciplinary teams | | | | | |
7 | An ability to communicate effectively | | | | | |
8 | A recognition of the need for, and an ability to engage in life-long learning | | | | | |
9 | An understanding of professional and ethical responsibility | | | | | |
10 | A knowledge of contemporary issues | | | | | |
11 | The broad education necessary to understand the impact of engineering solutions in a global, economic, environmental, and societal context | | | | | |
12 | Capability to apply and decide on engineering principals while understanding and rehabilitating the human body | | | | | |
Assessment Methods
Contribution Level | Absolute Evaluation |
Rate of Midterm Exam to Success | | 30 |
Rate of Final Exam to Success | | 70 |
Total | | 100 |
Numerical Data
Ekleme Tarihi: 09/10/2023 - 10:40Son Güncelleme Tarihi: 09/10/2023 - 10:41
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