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 design and conduct experiments, as well as to analyze and interpret data
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
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
-
Spring Semester
3+0
3
6
Course Program
Prerequisites Courses
Recommended Elective Courses
Language of Course
English
Course Level
First Cycle (Bachelor's Degree)
Course Type
Required
Course Coordinator
Assoc.Prof. Hüseyin Şerif SAVCI
Name of Lecturer(s)
Prof.Dr. Ercümend ARVAS
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 design and conduct experiments, as well as to analyze and interpret data
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
