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;

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 
 Core Courses  X 
Major Area Courses  
Supportive Courses  
Media and Managment Skills Courses  
Transferable Skill Courses 
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 914 
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 
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 EndofSemester Activities on the Final Grade  1  40 
Total 
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 
#  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 uptodate, 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