Elementary Mathematics Education  
Bachelor  Length of the Programme: 4  Number of Credits: 240  TRNQFHE: Level 6  QFEHEA: First Cycle  EQF: Level 6 
School/Faculty/Institute  Faculty of Education  
Course Code  MATH 134  
Course Title in English  Advanced Calculus  
Course Title in Turkish  Advanced Calculus  
Language of Instruction  EN  
Type of Course  Tersyüz öğrenme  
Level of Course  Seçiniz  
Semester  Spring  
Contact Hours per Week 


Estimated Student Workload  172 hours per semester  
Number of Credits  7 ECTS  
Grading Mode  Standard Letter Grade  
Prerequisites 
MATH 133  Calculus 

Corequisites  None  
Expected Prior Knowledge  Differentiation and integration of real valued function of a single variable.  
Registration Restrictions  Only Undergraduate Students  
Overall Educational Objective  To learn the differentiation of multivariable functions and multiple integration.  
Course Description  Polar coordinates, analytical geometry, infinite sequences and series, Taylor’s series, vectors, multivariable functions, partial derivatives and their applications, the gradient and directional derivative, extrema of functions of two variables, multiple integrals and their applications. 
Course Learning Outcomes and CompetencesUpon successful completion of the course, the learner is expected to be able to:1) expand a function in a Taylor series about a point; 2) use polar coordinates and classify conic sections; 3) identify and use vector operations; 4) calculate and differentiate multivariable functions; 5) identify local minima, local maxima and saddle points of a function of two variables 6) evaluate double and triple integrals. 
Program Learning Outcomes/Course Learning Outcomes  1  2  3  4  5  6 

1) Apply effective and studentcentered specific teaching methods and strategies in order to improve students’ mathematical thinking and problem solving skills.  
2) Design lesson plans based on how students learn mathematics and students’ difficulties in learning mathematics.  
3) Demonstrate knowledge in various areas of mathematics (such as analysis, algebra, linear algebra, geometry, topology, mathematical modeling, statistics and probability, differential equations) and nature of science and mathematics.  
4) Display knowledge and skills in developing programs, teaching technologies and materials in order to teach mathematics in effective and meaningful ways based on student needs.  
5) Evaluate and assess students’ individual developmental paths, difficulties in understanding mathematics in multiple ways and use assessment results in improving teaching and learning.  
6) Have an awareness of students’ social, cultural, economic and cognitive differences and plan the lessons and activities based on this awareness.  
7) Collaborate and respectively communicate with colleagues and student parents such that students learn mathematics in best ways and at the same time feel happy and safe. Work effectively within teams of their own discipline and multidisciplinary as well as take individual responsibility when they work alone.  
8) Have awareness of need for lifelong learning. Access information and following developments in education, science and technology. Display skills of solving problems related to their field, renew and improve themselves and critically analyze and question their own work. Use information technologies in effective ways.  
9) Use scientific investigation effectively to solve problems in mathematics teaching and learning based on scientific methods. Critically investigate, analyze and make a synthesis of data, and develop solutions to problems based on data and scientific sources.  
10) Exhibit skills of communicating effectively in oral and written Turkish and command of English at least at B2 general level of European Language Portfolio.  
11) Have awareness of and sensitivity to different cultures, values and students’ democratic rights.  
12) Display ethical and professional responsibilities. Have awareness of national and universal sensitivities that are expressed in National Education Fundamentals Laws.  
13) Demonstrate consciousness and sensitivity towards preserving nature and environment in the process of developing lesson activities.  
14) Display knowledge in national culture and history as well as international cultures and recognize their richness. Have awareness of and participate to developments in society, culture, arts and technology. 
N None  S Supportive  H Highly Related 
Program Outcomes and Competences  Level  Assessed by  
1)  Apply effective and studentcentered specific teaching methods and strategies in order to improve students’ mathematical thinking and problem solving skills.  S  Derse Katılım 
2)  Design lesson plans based on how students learn mathematics and students’ difficulties in learning mathematics.  N  
3)  Demonstrate knowledge in various areas of mathematics (such as analysis, algebra, linear algebra, geometry, topology, mathematical modeling, statistics and probability, differential equations) and nature of science and mathematics.  H  Exam,Derse Katılım 
4)  Display knowledge and skills in developing programs, teaching technologies and materials in order to teach mathematics in effective and meaningful ways based on student needs.  S  Derse Katılım 
5)  Evaluate and assess students’ individual developmental paths, difficulties in understanding mathematics in multiple ways and use assessment results in improving teaching and learning.  N  
6)  Have an awareness of students’ social, cultural, economic and cognitive differences and plan the lessons and activities based on this awareness.  S  Proje 
7)  Collaborate and respectively communicate with colleagues and student parents such that students learn mathematics in best ways and at the same time feel happy and safe. Work effectively within teams of their own discipline and multidisciplinary as well as take individual responsibility when they work alone.  H  Exam,Derse Katılım 
8)  Have awareness of need for lifelong learning. Access information and following developments in education, science and technology. Display skills of solving problems related to their field, renew and improve themselves and critically analyze and question their own work. Use information technologies in effective ways.  S  Exam 
9)  Use scientific investigation effectively to solve problems in mathematics teaching and learning based on scientific methods. Critically investigate, analyze and make a synthesis of data, and develop solutions to problems based on data and scientific sources.  N  
10)  Exhibit skills of communicating effectively in oral and written Turkish and command of English at least at B2 general level of European Language Portfolio.  S  Exam,Derse Katılım 
11)  Have awareness of and sensitivity to different cultures, values and students’ democratic rights.  N  
12)  Display ethical and professional responsibilities. Have awareness of national and universal sensitivities that are expressed in National Education Fundamentals Laws.  N  
13)  Demonstrate consciousness and sensitivity towards preserving nature and environment in the process of developing lesson activities.  N  
14)  Display knowledge in national culture and history as well as international cultures and recognize their richness. Have awareness of and participate to developments in society, culture, arts and technology.  N 
Prepared by and Date  CANFUAD DELALE , 
Course Coordinator  BENGİ BİRGİLİ 
Semester  Spring 
Name of Instructor  Asst. Prof. Dr. İLKER ARSLAN 
Week  Subject 
1)  Infinite sequences and series 
2)  Infinite sequences and series 
3)  Infinite sequences and series 
4)  Polar coordinates and analytical geometry 
5)  Polar coordinates and analytical geometry 
6)  Vectors, Vector algebra 
7)  Geometric applications: Equations of planes and lines in space 
8)  Multivariable functions, partial derivatives 
9)  Partial derivatives and their applications 
10)  Partial derivatives and their applications 
11)  The Gradient and Directional Derivative 
12)  Extrema of a function of two variables 
13)  Multiple integrals and their applications 
14)  Multiple integrals and their applications 
15)  Final Examination/Project/Presentation Period 
16)  Final Examination/Project/Presentation Period 
Required/Recommended Readings  Thomas' Calculus, 13th Ed., G. Thomas, M. Weir, J. Hass, F. Giordano, Pearson/ Addison Wesley, 2010.  
Teaching Methods  Lectures/contact hours using “flipped classroom” as an active learning technique  
Homework and Projects    
Laboratory Work    
Computer Use    
Other Activities    
Assessment Methods 


Course Administration 
cafuat.delale@mef.edu.tr 
Activity  No/Weeks  Hours  Calculation  
No/Weeks per Semester  Preparing for the Activity  Spent in the Activity Itself  Completing the Activity Requirements  
Course Hours  14  2  4  2  112  
Quiz(zes)  2  6  1  14  
Midterm(s)  1  12  2  14  
Final Examination  1  30  2  32  
Total Workload  172  
Total Workload/25  6.9  
ECTS  7 