MM214 : Vector analysis

Department

Department of Mathematics

Academic Program

Bachelor in mathematics

Type

Compulsory

Credits

Prerequisite

MM105 MM114

Overview

This course introduces the student to the basic concepts of vector functions, the scalar domain and the vector field. It also deals with finding linear, superficial and volumetric integrals. This course aims at developing the student's ability to define the integral theorems in vector analysis, orthogonal coordinate systems.

Intended learning outcomes

By the end of the course, the student should be able to:

1. Enumerate the Cartesian, polar, spherical, and cylindrical planes in two and three dimensions

2. Explain vector functions in three dimensions and find their vector derivatives

3. Explain methods of integration of vector functions in three dimensions (linear, surface, and volumetric).

4. Recognize the theories of Green and Stokes.

5. Show how to draw and represent vector functions in three dimensions.

6. Explain vector functions with two or more variables graphically.

7. Demonstrate some partial and total derivatives of vector functions.

8. Connect the methods of linear, surface and volumetric integration of vector functions and the relationship between them.

9. Analyze the applications of Green and Stokes theories.

10. Interpret and analyze the graph and representation of vector functions in three dimensions.

11. Solve a number of exercises and problems with more than one idea about vectors and operations on them (addition, scalar and vector multiplication of vectors).

12. The student should apply exercises and problems on the partial and total derivatives of vector functions.

13. It gives solutions to new, different and multiple problems to find the linear, surface and volumetric integration of vector functions

14. Use Cartesian, spherical, and cylindrical transformations to find the volumetric, surface, and linear integration of scalar and vector functions.

15. Draw and represent vector functions in three dimensions.

Teaching and learning methods

1- Practical and theoretical lectures .

2- Discussion and dialogue .

3- Brain storming .

4- Working papers, case study .

5- Presentations .

6- Videos and e-learning

7. Use of software and computer applications such as (MATLAB, Geogebra, Geometer)

8- Intensifying applications, solving problems, and linking ideas with reality and life situations.

Methods of assessments

1- A written exam (essay + objective) = 25 marks, or its assessment is left to the course instructor

2- Short tests (written or oral), demonstration tasks, tests, exercises, and presentation = 15 marks, or the assessment is left to the course instructor .

3- Written final exam (essay + objective) = 60 marks

Course Content:

Exercises	Lecture	Number of hours	Scientific topic	Week
Ö	Ö	3	Vectors: definition of vector and scalar-vector algebra	1
Ö	Ö	3	Unit vector and rectangular unit vector -vector compounds	2
Ö	Ö	3	scalar product - vector product - triple product	3
Ö	Ö	3	Vector function-end of function	4
	First midterm exam (2 hours)			5
Ö	Ö	4	Continuous Function and Derivation of Vector Function	6
Ö	Ö	3	Gradient-Spacing-Laplace-and their congruents	7
Ö	Ö	3	Differential geometry: the concept of curves and their classification - representation of the normal and natural medium - arc length	8
Ö	Ö	3	Basic triple lines and planes	9
	Second midterm exam (2 hours)			10
Ö	Ö	11	Tangent, binary perpendicular, and initial perpendicular	11
Ö	Ö	12	Ascending, vertical and forward levels - curvature and torsion	12
Ö	Ö	13	Integration Theorems in Vector Analysis: Green's Theorem - Applications of Green's Theorem	13
Ö	Ö	14	Divergence Theorem - Applications of the Divergence Theorem	14
Ö	Ö	3	Stokes Theorem – Applications of Stokes Theorem	14
	Final Exam
	Total	42	Total

References

Title of references	publisher	version	author	location
Vector analysis in space	The Arab Community Library for Publishing and Distribution	the first	Dr. Mahmoud Muhammad Selim	library of the department

Arabic language 1 (AR103)
Linear Algebra 1 (MM105)
Planar and Analytical Geometry (MM103)
Quranic Studies 1 (AR101)
computer 1 (CS100)
General Mathematics 1 (MM101)
General English1 (EN100)
Fundamentals of Education (EPSY101)
General Psychology (EPSY 100)
Introduction to Statistics (ST101)
Quranic studies2 (AR102)
Aerospace Engineering (MM114)
General Mathematics 2 (MM102)
Linear Algebra (2) (MM215)
Developmental Psychology (EPSY 203)
General Teaching Methods (EPSY 201)
General English2 (EN101)
Computer 2 (CS101)
Introduction to the science of Probabilities (ST102)
Arabic language 2 (AR104)
Basics Of Curriculums (EPSY 202)
Mathematical Logic (MM317)
Educational Psychology (EPSY 200)
Arabic language 3 (AR105)
Ordinary Differential Equations 1 (MM202)
Static (MM206)
General Mathematics3 (MM211)
Ordinary Differential Equations 2 (MM311)
Vector analysis (MM214)
Mathematical statistics (ST202)
Set Theory (MM213)
Arabic language 4 (AR106)
Research Methods (EPSY301)
Measurements and Evaluation (EPSY 302)
Methods of teaching mathematics (MM208)
Teaching learning Aids (EPSY 303)
Word processing (CS 202)
Psychological Health (EPSY 401)
School mathematics 1 (MM309)
Complex Analysis 1 (MM305)
Real Analysis 1 (MM303)
Dynamics (MM207)
Abstract Algebra 1 (MM302)
Complex Analysis 2 (MM306)
School mathematics2 (MM310)
Real Analysis 2 (MM304)
Abstract Algebra 2 (MM403)
Numerical Analysis (MM308)
measurement theory (MM410E)
Integral equations (MM409E)
Operations Research (MM408E)
History of Mathematics (MM407E)
Functional Analysis (MM406E)
linear programming (MM405E)
Partial Differential Equations (MM401)
Teaching applications (MM400)
Graduation project (MM404)
Teaching Practice (EPSY 402)