MATH 511 | Course Introduction and Application Information - Applied Mathematics and Statistics – With Thesis

Course Name

Multivariable and Dynamical Analysis

Code	Semester	Theory (hour/week)	Application/Lab (hour/week)	Local Credits	ECTS
MATH 511	Fall	3	0	3	7.5

Prerequisites	None
Course Language	English
Course Type	Required
Course Level	Second Cycle
Mode of Delivery	-
Teaching Methods and Techniques of the Course	Problem Solving Lecture / Presentation
National Occupation Classification	-
Course Coordinator	Doç. Dr. Sevin GÜMGÜM
Course Lecturer(s)	Doç. Dr. Sevin GÜMGÜM
Assistant(s)	Arş.Gör. Merve KAHRAMAN ARİMAN

Course Objectives	The course aims to present the theoretical framework of single and multivariable functions with an emphasis on the fundamental theorems of analysis, and to introduce solution methods for linear and differential equation systems.
Learning Outcomes	The students who succeeded in this course; Define limits and continuity. Obtain the derivatives of single-variable and multivariable functions. Explain the fundamental theorems. Evaluate definite and indefinite integrals of functions. Compute double and triple integrals. Find the eigenvalues and eigenvectors of systems of linear equations. Solve the first and the second order differential equations. Solve the systems of linear differential equations using the eigenvalue–eigenvector method.
Course Description	This course covers key concepts and theorems in analysis, focusing on the theoretical structure of single- and multivariable functions, and includes solution methods for systems of linear and differential equations.
Related Sustainable Development Goals

Course Category	Core Courses
	Major Area Courses
	Supportive Courses
	Media and Management Skills Courses
	Transferable Skill Courses

Week	Subjects	Related Preparation
1	Formal ε-δ Definition of Limits and Continuity of functions in one and multiple variables	Stewart, J., Clegg, D. K., and Watson, S. (2020). Multivariable Calculus (9th ed.). Cengage Learning. (Chapter 14)
2	Derivatives and Fundamental Theorems in one dimension: Proofs and Applications of Mean Value Theorem and Intermediate Value Theorem	Stewart, J., Clegg, D. K., and Watson, S. (2020). Multivariable Calculus (9th ed.). Cengage Learning. (Chapter 14)
3	Functions of Several Variables, Partial Derivatives	Stewart, J., Clegg, D. K., and Watson, S. (2020). Multivariable Calculus (9th ed.). Cengage Learning. (Chapter 14)
4	Comprehensive treatment of Riemann Sum, Definite Integrals, Indefinite Integrals, MVT for Integral, Theoretical Foundation of Fundamental Theorem Calculus	Stewart, J., Clegg, D. K., and Watson, S. (2020). Multivariable Calculus (9th ed.). Cengage Learning. (Chapter 15)
5	Double and Triple Integrals in Cartesian Coordinates	Stewart, J., Clegg, D. K., and Watson, S. (2020). Multivariable Calculus (9th ed.). Cengage Learning. (Chapter 15)
6	Change of Variables in Double and Triple Integrals, Jacobian Matrix	Stewart, J., Clegg, D. K., and Watson, S. (2020). Multivariable Calculus (9th ed.). Cengage Learning. (Chapter 15)
7	Systems of Linear Equations, Eigenvalues and Eigenvectors	Edwards, C. H., Penney, D. E., & Calvis, S. D. (2018). Differential equations and linear algebra (4th ed.). Pearson (Chapter 2 and 6)
8	Midterm
9	First Order Differential Equations: Separable, Linear, Homogeneous Differential Equations	Edwards, C. H., Penney, D. E., & Calvis, S. D. (2018). Differential equations and linear algebra (4th ed.). Pearson (Chapter 1)
10	Bernoulli and Exact Differential Equations	Edwards, C. H., Penney, D. E., & Calvis, S. D. (2018). Differential equations and linear algebra (4th ed.). Pearson (Chapter 1)
11	Second Order Differential Equations	Edwards, C. H., Penney, D. E., & Calvis, S. D. (2018). Differential equations and linear algebra (4th ed.). Pearson (Chapter 5)
12	Undetermined Coefficients	Edwards, C. H., Penney, D. E., & Calvis, S. D. (2018). Differential equations and linear algebra (4th ed.). Pearson (Chapter 5)
13	Variation of Parameters	Edwards, C. H., Penney, D. E., & Calvis, S. D. (2018). Differential equations and linear algebra (4th ed.). Pearson (Chapter 5)
14	Systems of Differential Equations, Solving by Eigenvalues and Eigenvectors	Edwards, C. H., Penney, D. E., & Calvis, S. D. (2018). Differential equations and linear algebra (4th ed.). Pearson (Chapter 7)
15	Semester Review
16	Final Exam

Course Notes/Textbooks

Stewart, J., Clegg, D. K., and Watson, S. (2020). Multivariable Calculus (9th ed.). Cengage Learning. ISBN 9780357042922

Suggested Readings/Materials

Edwards, C. H., Penney, D. E., & Calvis, S. D. (2018). Differential equations and linear algebra (4th ed.). Pearson. ISBN 978-0-13-449718-1

Semester Activities	Number	Weigthing
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments	1	20
Presentation / Jury
Project
Seminar / Workshop
Oral Exams
Midterm	1	30
Final Exam	1	50
Total

Weighting of Semester Activities on the Final Grade	2	50
Weighting of End-of-Semester Activities on the Final Grade	1	50
Total

Semester Activities	Number	Duration (Hours)	Workload
Theoretical Course Hours (Including exam week: 16 x total hours)	16	3	48
Laboratory / Application Hours (Including exam week: '.16.' x total hours)	16		0
Study Hours Out of Class	14	5	70
Field Work			0
Quizzes / Studio Critiques			0
Portfolio			0
Homework / Assignments	1	25	25
Presentation / Jury			0
Project			0
Seminar / Workshop			0
Oral Exam			0
Midterms	1	32	32
Final Exam	1	50	50
		Total	225

#

Program Competencies/Outcomes

* Contribution Level

1

2

3

4

5

1

To be able to demonstrate independent and critical thinking in Applied Mathematics and Statistics.

-

X

2

To be able to define problems in Applied Mathematics/Statistics and verify whether they are mathematically/statistically consistent.

-

X

3

To be able to analyse and solve real life problems using applied methods and interdisciplinary approach of Mathematics/Statistics.

-

X

4

To be able to independently conduct, conclude, and report on specialized research in Applied Mathematics and Statistics.

-

5

To be able to efficiently use national and international resources, for staying updated in the field, communicating with colleagues, and following the related literature.

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6

To be able to develop proficiency in using computer software widely utilized in the fields of Applied Mathematics and Statistics.

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7

To be able to evaluate solution processes efficiently using mathematical reasoning and modeling in order to contribute to the solutions of social and scientific problems.

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8

To be able to synthesize theoretical frameworks with practical applications through mathematical and statistical methods.

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9

To be able to develop strategies, policies and plans for problems and research areas in Applied Mathematics/Statistics in order to interpret the results and translate them into practice.

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10

To be able to translate key topics, events, and phenomena in Applied Mathematics and Statistics into the context of other scientific disciplines.

-

X

-

11

To be able to engage in lifelong learning by continuously updating and improving knowledge and skills in Applied Mathematics and Statistics.

-

MATH 511 | Course Introduction and Application Information

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

EVALUATION SYSTEM

ECTS / WORKLOAD TABLE

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

IZMIR UNIVERSITY OF ECONOMICS GÜZELBAHÇE CAMPUS

GLOBAL CAREER

CONTRIBUTION TO SCIENCE

VALUING PEOPLE

BENEFIT TO SOCIETY