Syllabus ( MATH 211 )

Basic information


Course title: 
Analysis III 
Course code: 
MATH 211 
Lecturer: 
Assist. Prof. Samire YAZAR

ECTS credits: 
7 
GTU credits: 
4 (3+2+0) 
Year, Semester: 
2, Fall 
Level of course: 
First Cycle (Undergraduate) 
Type of course: 
Compulsory

Language of instruction: 
English

Mode of delivery: 
Face to face

Pre and corequisites: 
None 
Professional practice: 
No 
Purpose of the course: 
To teach differential calculus and its applications for multivariate functions. 



Learning outcomes


Upon successful completion of this course, students will be able to:

Solve derivative problems related to multivariable functions
Contribution to Program Outcomes

Communicating between mathematics and other disciplines, and building mathematical models for interdisciplinary problems.

Describing, formulating, and analyzing reallife problems using mathematical and statistical techniques.

Having improved abilities in mathematics communications, problemsolving, and brainstorming skills.

Exhibiting professional and ethical responsibility.
Method of assessment

Homework assignment

Identify differential operators
Contribution to Program Outcomes

Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.

Describing, formulating, and analyzing reallife problems using mathematical and statistical techniques.

Having improved abilities in mathematics communications, problemsolving, and brainstorming skills.
Method of assessment

Written exam

Find out extremum points
Contribution to Program Outcomes

Describing, formulating, and analyzing reallife problems using mathematical and statistical techniques.

Having improved abilities in mathematics communications, problemsolving, and brainstorming skills.
Method of assessment

Written exam


Contents


Week 1: 
Euclidean Spaces. Topology of R^n 
Week 2: 
Convergence in R^n 
Week 3: 
Functions of Several Variables. Definition of the Limit 
Week 4: 
Continuity and Uniform Continuity

Week 5: 
Partial Derivatives and High Order Partial Derivatives 
Week 6: 
Definition of Differentiability 
Week 7: 
Tangent planes and Differentials 
Week 8: 
The Chain Rule 
Week 9: 
Directional Derivatives and Gradient Vectors 
Week 10: 
Midterm and solutions 
Week 11: 
Taylor Formula for Multivariable Functions 
Week 12: 
Implicit Function Theorem 
Week 13: 
Extrema of Functions of Several variables 
Week 14: 
Lagrange Multipliers with Applications 
Week 15*: 
 
Week 16*: 
Final examination 
Textbooks and materials: 
1. W. R. Wade; An Introduction to Analysis, Pearson Prentice Hall, 3rd Edition 2. Thomas’ Calculus, Pearson AddisonWesley, Eleventh Edition.

Recommended readings: 
1. W.Kaplan; Advanced Calculus, Pearson AddisonWesley, 1973 2nd Edition. 2. Apostol, Tom M. ; Calculus, Vol. 2: MultiVariable Calculus and Linear Algebra with Applications to Differential Equations and Probability. Wiley, 1969. ISBN: 9780471000075.


* Between 15th and 16th weeks is there a free week for students to prepare for final exam.




Assessment



Method of assessment 
Week number 
Weight (%) 

Midterms: 
10 
40 
Other interm studies: 
0 
0 
Project: 
0 
0 
Homework: 
0 
0 
Quiz: 
0 
0 
Final exam: 
16 
60 

Total weight: 
(%) 



Workload



Activity 
Duration (Hours per week) 
Total number of weeks 
Total hours in term 

Courses (Facetoface teaching): 
5 
14 

Own studies outside class: 
10 
5 

Practice, Recitation: 
2 
14 

Homework: 
0 
5 

Term project: 
0 
0 

Term project presentation: 
0 
0 

Quiz: 
0 
0 

Own study for midterm exam: 
10 
1 

Midterm: 
2 
1 

Personal studies for final exam: 
10 
1 

Final exam: 
2 
1 



Total workload: 



Total ECTS credits: 
* 

* ECTS credit is calculated by dividing total workload by 25. (1 ECTS = 25 work hours)



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