ADVANCED MATHEMATICS PROGRAMME COURSE DESCRIPTION

Code	Name of the Course Unit	Semester	In-Class Hours (T+P)	Credit	ECTS Credit
MAT451	ADVANCED MATHEMATICS	5	5	5	6

GENERAL INFORMATION
Language of Instruction :	Turkish
Level of the Course Unit :	BACHELOR'S DEGREE, TYY: + 6.Level, EQF-LLL: 6.Level, QF-EHEA: First Cycle
Type of the Course :	Elective
Mode of Delivery of the Course Unit	-
Coordinator of the Course Unit	Assist.Prof. OĞUZHAN ÖZTAŞ
Instructor(s) of the Course Unit
Course Prerequisite	No

OBJECTIVES AND CONTENTS
Objectives of the Course Unit:	The aim of this course is:To provide the ability to use concepts such as limits, continuity, partial derivatives, and multiple integrals in multivariable functions.To develop the skill to apply mathematical knowledge in solving engineering problems.
Contents of the Course Unit:	Multivariable functions; limits, continuity, partial derivatives, directional derivatives, gradient vector, tangent plane, normal line equation, linearization and differentiability, maxima and minima of multivariable functions, Lagrange multiplier method, Taylor's formula, double and triple integrals, change of variables and applications of multivariable integrals, generalized multivariable integrals, line integrals, vector fields, path independence, potential functions, fundamental theorems of line integrals, Green's theorem in the plane, surface area and surface integrals, Stokes' theorem, and the Divergence (Gauss) theorem.

KEY LEARNING OUTCOMES OF THE COURSE UNIT (On successful completion of this course unit, students/learners will or will be able to)
Being able to use the concepts of limits and continuity in multivariable functions. Calculating partial derivatives and finding the tangent plane, directional derivatives, and gradient. Solving extremum problems using the second derivative test and Lagrange multiplier method.
Solving multiple integrals and using them in area and volume calculations.
Computing line and surface integrals. Finding potential functions. Using Green's, Stokes', and Divergence theorems.

WEEKLY COURSE CONTENTS AND STUDY MATERIALS FOR PRELIMINARY & FURTHER STUDY
Week	Preparatory	Topics(Subjects)	Method
1	-	Multivariable Functions: Limit, Continuity, Partial Derivatives	-
2	-	Chain Rule, Directional Derivative, Gradient Vector	-
3	-	Tangent Plane and Normal Line Equations, Linearization, and Differentiability	-
4	-	Maximum and Minimum in Multivariable Functions	-
5	-	Lagrange Multiplier Method, Taylor’s Formula for Multivariable Functions	-
6	-	Double Integrals, Area, and Moment	-
7	-	Double Integrals in Polar Coordinates / Midterm I Triple Integrals, Cylindrical and Spherical Coordinates	-
8	-	MID-TERM EXAM	-
9	-	Change of Variables and Applications of Triple Integrals, Generalized Multivariable Integrals	-
10	-	Line Integrals, Vector Fields, Path Independence	-
11	-	Potential Function, Fundamental Theorems of Line Integrals	-
12	-	Green’s Theorem in the Plane	-
13	-	Surface Area and Surface Integrals	-
14	-	Stokes' and Divergence (Gauss) Theorems	-
15	-	Stokes' and Divergence (Gauss) Theorems	-
16	-	FINAL EXAM	-
17	-	FINAL EXAM	-

SOURCE MATERIALS & RECOMMENDED READING
Weir, M.D., J. Hass and F.R. Giardona, Thomas’ Calculus, 11th Edition, Pearson, Addison- Wesley, Boston, 2005 (Chapters: 8,10,11,12,13).
Thomas, Jr. G.B. and RiL. Finney, Calculus and Analytic Geometry 9th edition, Addision-Wesley, 1998 (Chapters: 0, 1, 2, 3, 4, 5, 6)
W.R. Parzynski and P.W. Zipse, Introduction to Mathematical Analysis, McGrawHill International Edition, 1987, (Chapter: 9.4)

ASSESSMENT
Assessment & Grading of In-Term Activities	Number of Activities	Degree of Contribution (%)	Description	Examination Method

Level of Contribution
0	1	2	3	4	5

KNOWLEDGE
Theoretical
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Explains the fundamental engineering concepts of computer science and relates them to the groundwork of computer science.				3

KNOWLEDGE
Factual
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Uses theoretical and practical knowledge coming from mathematics, probability, statistics and various other branches of life sciences, to find solutions to engineering problems.				3

SKILLS
Cognitive
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Determines the components and the underlying process of a system and designs an appropriate computational model under reasonable constraints.					4
2	Designs a computer-aided conceptual model with modern techniques.					4

SKILLS
Practical
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Determines, detects and analyzes the areas of computer science applications and develops appropriate solutions.				3
2	Identifies, models and solves computer engineering problems by applying appropriate analytical methods.				3
3	Determines and uses the necessary information technologies in an efficient way for engineering applications.					4

OCCUPATIONAL
Autonomy & Responsibility
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Possess the responsibility and ability to design and conduct experiments for engineering problems by collecting, analyzing and interpreting data.				3
2	Possess the ability to conduct effective individual study.					4
3	Takes responsibility as a team work and contributes in an effective way.					4

OCCUPATIONAL
Learning to Learn
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Monitors the developments in the field of information technologies by means of internet and related journals and possess the required knowledge for the management, control, development and security of information technologies.				3
2	Develops positive attitude towards lifelong learning.					4

OCCUPATIONAL
Communication & Social
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Communicates effectively by oral and/or written form and uses at least one foreign language.				3
2	Possess sufficient consciousness about the issues of project management, practical applications and also environmental protection, worker's health and security.					4

OCCUPATIONAL
Occupational and/or Vocational
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Possess professional and ethical responsibility and willingness to share it.					4
2	Possess sufficient consciousness about the universality of engineering solutions and applications and be well aware of the importance of innovation.					4

WORKLOAD & ECTS CREDITS OF THE COURSE UNIT
Workload for Learning & Teaching Activities
Type of the Learning Activites	Learning Activities (# of week)	Duration (hours, h)	Workload (h)
Lecture & In-Class Activities	14	5	70
Preliminary & Further Study	14	3	42
Land Surveying	0	0	0
Group Work	0	0	0
Laboratory	0	0	0
Reading	0	0	0
Assignment (Homework)	0	0	0
Project Work	0	0	0
Seminar	0	0	0
Internship	0	0	0
Technical Visit	0	0	0
Web Based Learning	0	0	0
Implementation/Application/Practice	0	0	0
Practice at a workplace	0	0	0
Occupational Activity	0	0	0
Social Activity	0	0	0
Thesis Work	0	0	0
Field Study	0	0	0
Report Writing	0	0	0
Final Exam	1	1	1
Preparation for the Final Exam	5	5	25
Mid-Term Exam	1	1	1
Preparation for the Mid-Term Exam	3	4	12
Short Exam	0	0	0
Preparation for the Short Exam	0	0	0
TOTAL	38	0	151