Course Information
SemesterCourse Unit CodeCourse Unit TitleL+PCreditNumber of ECTS Credits
3MATH251VECTOR ANALYSIS4+256

Course Details
Language of Instruction English
Level of Course Unit First Cycle
Department / Program MATHEMATICS
Mode of Delivery Face to Face
Type of Course Unit Compulsory
Objectives of the Course Vector analysis aims to teach limit, continuity, differentiability and integration concepts for several variable real-valued and vector valued functions.
Course Content Functions of several variables. Limits and continuity. Partial derivatives. Derivatives of composite fuctions. Jacobian matrix. Implicit functions and implicit function theorems. The directional derivatives. Higher order derivatives. Maxima and minima of functions of several variables. Lagrange multipliers method. Multiple integrals. Polar, Cylindirical and Spherical coordinates. Change of variables in Double and triple integrals. Parametrization of paths and surfaces. Vector Fields, divergence and curl. Line integrals. Surface integrals. Related theorems to line and surface integrals. Green's Theorem. Stokes Theorem. Divergence Theorem.
Course Methods and Techniques
Prerequisites and co-requisities None
Course Coordinator None
Name of Lecturers Dr.Öğr.Üyesi NESLIHAN GUGUMCU
Assistants None
Work Placement(s) No

Recommended or Required Reading
Resources VECTOR CALCULUS. J. Marsden and A. Tromba, 5th edition

Course Category

Planned Learning Activities and Teaching Methods
Activities are given in detail in the section of "Assessment Methods and Criteria" and "Workload Calculation"

Assessment Methods and Criteria
In-Term Studies Quantity Percentage
Midterm exams 2 % 60
Quizzes 0 % 0
Homeworks 0 % 0
Other activities 0 % 0
Laboratory works 0 % 0
Projects 0 % 0
Final examination 1 % 40
Total
3
% 100

ECTS Allocated Based on Student Workload
Activities Quantity Duration Total Work Load
Weekly Course Time 1 48 48
Outside Activities About Course (Attendance, Presentation, Midterm exam,Final exam, Quiz etc.) 1 47 47
Application (Homework, Reading, Self Study etc.) 1 0 0
Exams and Exam Preparations 2 48 96
Total Work Load   Number of ECTS Credits 6 191

Course Learning Outcomes: Upon the successful completion of this course, students will be able to:
NoLearning Outcomes
1 The ability of the analyzing of multivariable functions
2 To learn the fundemental structure and theorems about the derivation and integral of multivariable functions
3 The ability about the usage of Polar, Cylindirical and Spherical coordinates
4 To have knowledge on the main theorems of vector calculus such as Green's Theorem, Stokes Theorem and Divergence Theorem


Weekly Detailed Course Contents
WeekTopicsStudy MaterialsMaterials
1 Vector-valued functions and their graphs, a gentle introduction to paths, and surfaces J. Marsden, A. Tromba Vector Calculus, 5th Edition.
2 Basic topology of R^2 and R^3 Limits and continuity of several valued functions J. Marsden, A. Tromba Vector Calculus
3 Differentiation: Partial Derivatives Differentiabilty, Fundamental lemma Properties of derivative: Sums, Products, Quotients, Chain Rule J. Marsden, A. Tromba Vector Calculus
4 Directional Derivative, Parametrization of paths, Arclength, Gradient: Tangent Planes to level surfaces, normal vectors J. Marsden, A. Tromba Vector Calculus
5 Higher-order partial derivatives, Extrema of Real-valued functions J. Marsden, A. Tromba Vector Calculus
6 Vector Fields, Divergence and Curl, Curl of a vector field, Basic identities of vector analysis Geometrical interpretation of divergence J. Marsden, A. Tromba Vector Calculus
7 Multiple integrals: Double integral over a rectangle, Fubini's Theorem, Properties of Integration:Linearity, Homogeneity, Monotonicity, Additivity J. Marsden, A. Tromba Vector Calculus.
8 Double Integral over general regions, Changing the order of integration J. Marsden, A. Tromba Vector Calculus.
9 Triple Integral, The change of variables in integration, applications of integration J. Marsden, A. Tromba Vector Calculus.
10 Line Integrals J. Marsden, A. Tromba Vector Calculus.
11 Green's Theorem J. Marsden, A. Tromba Vector Calculus.
12 Parametrized surfaces, orientation, area of a surface, Surface Integrals of real-valued functions J. Marsden, A. Tromba Vector Calculus.
13 Surface integrals of vector valued functions, Divergence and Stokes Theorems J. Marsden, A. Tromba Vector Calculus.
14 Divergence Theorem, Stokes Theorem continue, Conservative vector fields J. Marsden, A. Tromba Vector Calculus.


Contribution of Learning Outcomes to Programme Outcomes
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14
C1 4 4 4
C2 4 4 4
C3 4 4 4
C4 4 4 4

Contribution: 0: Null 1:Slight 2:Moderate 3:Significant 4:Very Significant


https://obs.iyte.edu.tr/oibs/bologna/progCourseDetails.aspx?curCourse=254336&lang=en