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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 co-requisites: None
Professional practice: No
Purpose of the course: To teach differential calculus and its applications for multivariate functions.
   Learning outcomes Up

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

  1. Solve derivative problems related to multivariable functions

    Contribution to Program Outcomes

    1. Communicating between mathematics and other disciplines, and building mathematical models for interdisciplinary problems.
    2. Describing, formulating, and analyzing real-life problems using mathematical and statistical techniques.
    3. Having improved abilities in mathematics communications, problem-solving, and brainstorming skills.
    4. Exhibiting professional and ethical responsibility.

    Method of assessment

    1. Homework assignment
  2. Identify differential operators

    Contribution to Program Outcomes

    1. 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.
    2. Describing, formulating, and analyzing real-life problems using mathematical and statistical techniques.
    3. Having improved abilities in mathematics communications, problem-solving, and brainstorming skills.

    Method of assessment

    1. Written exam
  3. Find out extremum points

    Contribution to Program Outcomes

    1. Describing, formulating, and analyzing real-life problems using mathematical and statistical techniques.
    2. Having improved abilities in mathematics communications, problem-solving, and brainstorming skills.

    Method of assessment

    1. Written exam
   Contents Up
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 Addison-Wesley, Eleventh Edition.
Recommended readings: 1. W.Kaplan; Advanced Calculus, Pearson Addison-Wesley, 1973 2nd Edition.
2. Apostol, Tom M. ; Calculus, Vol. 2: Multi-Variable 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 Up
Method of assessment Week number Weight (%)
Mid-terms: 10 40
Other in-term studies: 0 0
Project: 0 0
Homework: 0 0
Quiz: 0 0
Final exam: 16 60
  Total weight:
(%)
   Workload Up
Activity Duration (Hours per week) Total number of weeks Total hours in term
Courses (Face-to-face 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 mid-term exam: 10 1
Mid-term: 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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