COURSE INTRODUCTION AND APPLICATION INFORMATION


Course Name
Advanced Calculus I
Code
Semester
Theory
(hour/week)
Application/Lab
(hour/week)
Local Credits
ECTS
MATH 201
Fall
2
2
3
5
Prerequisites
None
Course Language
English
Course Type
Required
Course Level
First Cycle
Mode of Delivery -
Teaching Methods and Techniques of the Course
Course Coordinator -
Course Lecturer(s)
Assistant(s)
Course Objectives This advanced calculus course will rigorously develop multivariable calculus and vector analysis. The topics covered in this course include; Infinite Series, Power series, Curves and Parametrizations, Limits and partial derivatives of functions of Several Variables. Multiple integrals, and application of multiple integrals This course is a good preparation for students thinking of studying on the problems of engineering, administration and economics.
Learning Outcomes The students who succeeded in this course;
  • will be able to test series for convergence and, if convergence is established, find approximations to their magnitudes.
  • will be able to apply Taylor's and Maclaurin's series of a fucntion about given point.
  • will be able to use algebraic operations on power series.
  • will be able to calculate limits and partial derivatives of functions of several variables.
  • will be able to sketch the graphs of the functions by hand or computer
  • will be able to find critical point(s) of functions of several variables and find max/min values.
  • will be able to find the tanget plane to the function at given point
  • will be able to figure out the vetors, vector valued functions, and paremetric curves
  • will be able to evalute the double integrals,
  • will be able to evalute the volume, surface area, moments, and center of the mass
  • will be able to evaluate the triple integrals
Course Description In this course series; power series, limits and partial derivatives of functions of several variables chain rules, Taylor series, applications of partial derivatives, multiple integrals and their applications will be covered

 



Course Category

Core Courses
X
Major Area Courses
Supportive Courses
Media and Managment Skills Courses
Transferable Skill Courses

 

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week Subjects Required Materials
1 Series and Convergence “Calculus. A Complete Course (fifth edition)”, by Robert A. Adams. Addison Wesley Longman. ISBN 0201791315.: Chapter 9
2 Power series “Calculus. A Complete Course (fifth edition)”, by Robert A. Adams. Addison Wesley Longman. ISBN 0201791315.: Chapter 9. Section 9.19.2.
3 Taylor and Maclaurin series “Calculus. A Complete Course (fifth edition)”, by Robert A. Adams. Addison Wesley Longman. ISBN 0201791315. : Chapter 9
4 Limits, partial derivatives of function of several variables “Calculus. A Complete Course (fifth edition)”, by Robert A. Adams. Addison Wesley Longman. ISBN 0201791315. Chapter 12
5 The Chain Rule, Linear Approximation, and directional derivatives “Calculus. A Complete Course (fifth edition)”, by Robert A. Adams. Addison Wesley Longman. ISBN 0201791315. Chapter 12. Section 12.5
6 Taylor’s formula for two variables, Implicit functions “Calculus. A Complete Course (fifth edition)”, by Robert A. Adams. Addison Wesley Longman. ISBN 0201791315. Chapter 12. Section 12.9
7 Applications of Partial Derivatives “Calculus. A Complete Course (fifth edition)”, by Robert A. Adams. Addison Wesley Longman. ISBN 0201791315. Chapter 13
8 Lagrange Multipliers/ EXAM “Calculus. A Complete Course (fifth edition)”, by Robert A. Adams. Addison Wesley Longman. ISBN 0201791315. Chapter 13. Section 13.3
9 Double integrals “Calculus. A Complete Course (fifth edition)”, by Robert A. Adams. Addison Wesley Longman. ISBN 0201791315. Chapter 14. Section 14.1
10 Improper integrals and Mean Value Theorem “Calculus. A Complete Course (fifth edition)”, by Robert A. Adams. Addison Wesley Longman. ISBN 0201791315. Chapter 14. Section 14.3.
11 Applications of double integrals “Calculus. A Complete Course (fifth edition)”, by Robert A. Adams. Addison Wesley Longman. ISBN 0201791315. Chapter 14. Section 14.1
12 Triple Integrals “Calculus. A Complete Course (fifth edition)”, by Robert A. Adams. Addison Wesley Longman. ISBN 0201791315. Chapter 14. Section 14.5
13 Application of Triple Integrals “Calculus. A Complete Course (fifth edition)”, by Robert A. Adams. Addison Wesley Longman. ISBN 0201791315. Chapter 14 14.5
14 Moments and Center of Mass “Calculus. A Complete Course (fifth edition)”, by Robert A. Adams. Addison Wesley Longman. ISBN 0201791315. Chapter 14. Section 14.7
15 Review for the final exam “Calculus. A Complete Course (fifth edition)”, by Robert A. Adams. Addison Wesley Longman. ISBN 0201791315. Chapter 9-14
16 Review of the Semester  
Course Notes/Textbooks “Calculus. A Complete Course (fifth edition)”, by Robert A. Adams. Addison Wesley Longman. ISBN 0201791315.
Suggested Readings/Materials None

 

EVALUATION SYSTEM

Semester Activities Number Weigthing
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques
5
25
Portfolio
Homework / Assignments
Presentation / Jury
Project
Seminar / Workshop
Oral Exam
Midterm
1
35
Final Exam
1
40
Total

Weighting of Semester Activities on the Final Grade
6
60
Weighting of End-of-Semester Activities on the Final Grade
1
40
Total

ECTS / WORKLOAD TABLE

Semester Activities Number Duration (Hours) Workload
Course Hours
(Including exam week: 16 x total hours)
16
4
64
Laboratory / Application Hours
(Including exam week: 16 x total hours)
16
Study Hours Out of Class
15
2
Field Work
Quizzes / Studio Critiques
5
2
Portfolio
Homework / Assignments
Presentation / Jury
Project
Seminar / Workshop
Oral Exam
Midterms
1
16
Final Exams
1
20
    Total
140

 

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

#
Program Competencies/Outcomes
* Contribution Level
1
2
3
4
5
1 To have a grasp of basic mathematics, applied mathematics and theories and applications of statistics. X
2 To be able to use theoretical and applied knowledge acquired in the advanced fields of mathematics and statistics, X
3 To be able to define and analyze problems and to find solutions based on scientific methods, X
4 To be able to apply mathematics and statistics in real life with interdisciplinary approach and to discover their potentials, X
5 To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself, X
6 To be able to criticize and renew her/his own models and solutions, X
7 To be able to tell theoretical and technical information easily to both experts in detail and nonexperts in basic and comprehensible way, X
8

To be able to use international resources in English and in a second foreign language from the European Language Portfolio (at the level of B1) effectively and to keep knowledge up-to-date, to communicate comfortably with colleagues from Turkey and other countries, to follow periodic literature,

X
9

To be familiar with computer programs used in the fields of mathematics and statistics and to be able to use at least one of them effectively at the European Computer Driving Licence Advanced Level,

10

To be able to behave in accordance with social, scientific and ethical values in each step of the projects involved and to be able to introduce and apply projects in terms of civic engagement,

X
11 To be able to evaluate all processes effectively and to have enough awareness about quality management by being conscious and having intellectual background in the universal sense, X
12

By having a way of abstract thinking, to be able to connect concrete events and to transfer solutions, to be able to design experiments, collect data, and analyze results by scientific methods and to interfere,

X
13

To be able to continue lifelong learning by renewing the knowledge, the abilities and the compentencies which have been developed during the program, and being conscious about lifelong learning,

14

To be able to adapt and transfer the knowledge gained in the areas of mathematics and statistics to the level of secondary school,

15

To be able to conduct a research either as an individual or as a team member, and to be effective in each related step of the project, to take role in the decision process, to plan and manage the project by using time effectively.

*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest

 

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