Course Name  Advanced Calculus II 
Code  Semester  Theory (hour/week)  Application/Lab (hour/week)  Local Credits  ECTS 

MATH 202  Spring  2  2  3  5 
Prerequisites 
 
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  The main objective of this course is to introduce the fundamental concepts of multivariable calculus and vector analysis. Advanced Calculus is one of the most useful of all mathematical tools, and this quarter we develop one of the basic concepts, the double integrals, and discuss its applications and consequences. The course begins with an introduction of double integrals, vector fields, line integrals. At the last stage of the course, some applications of flux integral and the triple integrals will be addressed. This course will conclude with an introduction to vector fields in 3D and surface integrals. The concept of line integrals in space and Stokes' theorem is an essential part of advanced calculus and mathematics in general. 
Learning Outcomes  The students who succeeded in this course;

Course Description  In this course vector fields and vector calculus will be discussed. Line integrals, surface integrals, flux integrals will be calculated. Green's theorem, divergence theorem and Stokes' theorem will be discussed and some physical applications will be solved. 
 Core Courses  X 
Major Area Courses  
Supportive Courses  
Media and Managment Skills Courses  
Transferable Skill Courses 
Week  Subjects  Required Materials 
1  Triple Integrals. Application of Triple Integrals  "Calculus. A Complete Course (eight edition)", by Robert A. Adams. Addison Wesley Longman. Section 14.5 
2  Curves and Parametrizations  "Calculus. A Complete Course (eight edition)", by Robert A. Adams. Addison Wesley Longman. Section 11.3 
3  Vector and Scalar fields: Field Lines  "Calculus. A Complete Course (eight edition)", by Robert A. Adams. Addison Wesley Longman. Section 15.1 
4  Line Integrals  "Calculus. A Complete Course (eight edition)", by Robert A. Adams. Addison Wesley Longman. Section 15.3 
5  Line Integrals of Vector Fields  "Calculus. A Complete Course (eight edition)", by Robert A. Adams. Addison Wesley Longman. Section 15.4 
6  Surface and Surface Integrals  "Calculus. A Complete Course (eight edition)", by Robert A. Adams. Addison Wesley Longman. Section 15.5 
7  Oriented Surfaces and Flux Integrals  "Calculus. A Complete Course (eight edition)", by Robert A. Adams. Addison Wesley Longman. Section 15.6 
8  Gradient, Divergent, and Curl  "Calculus. A Complete Course (eight edition)", by Robert A. Adams. Addison Wesley Longman. Section 16.1 
9  Green’s Theorem in the Plane  "Calculus. A Complete Course (eight edition)", by Robert A. Adams. Addison Wesley Longman. Section 16.3 
10  Review and Midterm Exam   
11  The Divergence Theorem in 3Space  "Calculus. A Complete Course (eight edition)", by Robert A. Adams. Addison Wesley Longman. Section 16.4 
12  The Stoke’s Theorem  "Calculus. A Complete Course (eight edition)", by Robert A. Adams. Addison Wesley Longman. Section 16.5 
13  Some Physical Applications of Vector Calculus: Fluid Dynamics, Electromagnetism  "Calculus. A Complete Course (eight edition)", by Robert A. Adams. Addison Wesley Longman. Section 16.6 
14  Electrostatics, Magnetostatics, Maxwell’s Equations  "Calculus. A Complete Course (eight edition)", by Robert A. Adams. Addison Wesley Longman. Section 16.6 
15  Orthogonal Curvilinear Coordinates  "Calculus. A Complete Course (eight edition)", by Robert A. Adams. Addison Wesley Longman. Section 16.7 
16  Review of the semester 
Course Notes/Textbooks  Calculus. A Complete Course (eight edition)", by Robert A. Adams. Addison Wesley Longman. 
Suggested Readings/Materials  None 
Semester Activities  Number  Weigthing 
Participation  
Laboratory / Application  
Field Work  
Quizzes / Studio Critiques  4  20 
Portfolio  
Homework / Assignments  1  10 
Presentation / Jury  
Project  
Seminar / Workshop  
Oral Exam  
Midterm  1  30 
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  3  
Field Work  
Quizzes / Studio Critiques  2  4  
Portfolio  
Homework / Assignments  1  1  
Presentation / Jury  
Project  
Seminar / Workshop  
Oral Exam  
Midterms  1  15  
Final Exams  1  15  
Total  148 
#  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