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. SERKAN GÖNEN
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	Ability to identify, analyze, design, model and solve complex engineering problems based on engineering, science and mathematics fundamentals				3

KNOWLEDGE
Factual
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Ability to apply engineering design to produce solutions that meet specific needs, taking into account global, cultural, social, environmental and economic factors as well as public health, safety and well-being				3

SKILLS
Cognitive
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Ability to communicate effectively with various stakeholders					4

SKILLS
Practical
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	The ability to recognize ethical and professional responsibilities in engineering and make informed decisions considering the impact of engineering solutions in their global, economic, environmental and social contexts				3

OCCUPATIONAL
Autonomy & Responsibility
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	The ability to recognize ethical and professional responsibilities in engineering and make informed decisions considering the impact of engineering solutions in their global, economic, environmental and social contexts					4

OCCUPATIONAL
Learning to Learn
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Ability to acquire new knowledge and find ways to apply it when necessary, using appropriate learning strategies				3

OCCUPATIONAL
Communication & Social
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Ability to work effectively in a team where its members lead together, create a collaborative and inclusive environment, set goals, plan tasks, and meet goals					4

OCCUPATIONAL
Occupational and/or Vocational
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Ability to design and conduct appropriate experiments, analyze and interpret data, and apply engineering principles to draw conclusions					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