## Course Detail

## Course Description

Course | Code | Semester | T+P (Hour) | Credit | ECTS |
---|---|---|---|---|---|

MATHEMATICS II | - | Spring Semester | 3+0 | 3 | 4 |

Course Program |

Prerequisites Courses | |

Recommended Elective Courses |

Language of Course | English |

Course Level | First Cycle (Bachelor's Degree) |

Course Type | Required |

Course Coordinator | Assist.Prof. Tuğba ASLAN KHALİFA |

Name of Lecturer(s) | Assist.Prof. Tuğba ASLAN KHALİFA |

Assistant(s) | |

Aim | The aim of this mathematics course is to equip students with the essential mathematical knowledge and skills necessary to excel in the world of business and economics. This course seeks to provide a solid foundation in mathematical concepts and techniques that are directly applicable to real-world business scenarios, enabling students to make informed decisions, solve practical problems, and enhance their quantitative reasoning abilities in a business context. |

Course Content | This course contains; The definition of limit, right and left limit,Infinite limit and limit at infinity,Continuity,Definition of limit, physical and geometric interpretation, tangent lines, rules of differentiation,Marginal analysis in business and economy, continuous compound interest,Derivative of logarithmic and exponential functions, product and quotient rules, chain rule,Implicit differentiation, related rates, elasticity of demand,Aplications of differentiation: graphs and derivatives, optimization,Anti derivatives and rules of indefinite integral calculation,Definite integral and Riemann Sums,Fundamental theorem of analysis and calculation of definite integrals,Sequences and series: definitions and terminology,Arithmetic and geometric sequences and series,Difference equations and its applications. |

Dersin Öğrenme Kazanımları | Teaching Methods | Assessment Methods |

1. Will be able to evaluate limits of one variable functions numerically, graphically, and algebraically. | 12, 14, 16, 9 | A, E, G |

1.1 Understand the concept of limit and its existence, analyse the concept of limit both graphicaly and algebraicly. | ||

1.2 Evaluate one-sided limits, limit at infinity, and infinite limits of various basic functions. | ||

2. Will be able to analyze the continuity of a function. | 12, 14, 16, 9 | A, E, G |

2.1 Determine continuity and points of discontinuity of functions with single variable both graphically and algebraically. | ||

2.2 Use the concept of continuity in applications. | ||

3. Will be able to comprehend basic theoretical and applicational aspects of differentiation. | 12, 14, 16, 9 | A, E, G |

3.1 Understand the concept of a derivative as the rate of change of a function at a given point, and be able to calculate it using the limit definition. | ||

3.2 Use differentiation rules to calculate derivatives of polynomial, rational, exponential and logarithmic functions. | ||

3.3 Sketch the graph of functions using differentiation. | ||

4. Will be able to use limit and derivative concepts in applications of the field of interest. | 12, 14, 16, 9 | A, E, G |

4.1 Comprehend the concept of continuous compound interest using limit. | ||

4.2 Solve optimization problems in the field of interest by using first and second derivative concepts. | ||

4.3 Explains the concept of demand elasticity. | ||

5. Will be able to comprehend basic theoretical and applicational aspects of integration. | 12, 14, 16, 9 | A, E, G |

5.1 Calculate indefinite integrals with algebraic techniques using the concept of anti-derivatives. | ||

5.2 Explain the concept of definite integral and its relation with areas under the curves using Riemann sums. | ||

5.3 Calculate definite integrals with algebraic techniques using the fundamental theorem of calculus. | 12, 14, 16, 9 | A, E, G |

6. Will be able to use the concepts of series and sequences in applications of the field of interest. | ||

6.1 Define the concepts of sequences and series. | ||

6.2 Comprehend the concepts of arithmetic and geometric series and sequences. | ||

6.3 Use the sequences and series in the applications of field of interest. | ||

7. Will be able to describe the phenomena related with the fields of study using difference equations. | 12, 14, 16, 9 | A, E, G |

7.1 Find the complementary function of a difference equation. | ||

7.2 Find the particular solution of a difference equation. | ||

7.3 Analyze the stability of economic systems. |

Teaching Methods: | 12: Problem Solving Method, 14: Self Study Method, 16: Question - Answer Technique, 9: Lecture Method |

Assessment Methods: | A: Traditional Written Exam, E: Homework, G: Quiz |

## Course Outline

Order | Subjects | Preliminary Work |
---|---|---|

1 | The definition of limit, right and left limit | |

2 | Infinite limit and limit at infinity | |

3 | Continuity | |

4 | Definition of limit, physical and geometric interpretation, tangent lines, rules of differentiation | |

5 | Marginal analysis in business and economy, continuous compound interest | |

6 | Derivative of logarithmic and exponential functions, product and quotient rules, chain rule | |

7 | Implicit differentiation, related rates, elasticity of demand | |

8 | Aplications of differentiation: graphs and derivatives, optimization | |

9 | Anti derivatives and rules of indefinite integral calculation | |

10 | Definite integral and Riemann Sums | |

11 | Fundamental theorem of analysis and calculation of definite integrals | |

12 | Sequences and series: definitions and terminology | |

13 | Arithmetic and geometric sequences and series | |

14 | Difference equations and its applications |

Resources |

Main sources: 1. Lecture Notes shared by instructor 2. Main text: Calculus for Business, Economics, Life Sciences, and Social Sciences, 14th edition Published by Pearson (2021), R. A. Barnett, M: R: Ziegler, K. E. Byleen. |

Other Recommended Sources: Introductory Mathematical Analysis for Business, Economics, and the Life and Social Sciences, 14th Edition by Ernest F. Haeussler, Jr., Richard S. Paul, and Richard J. Wood, published by Pearson Education 2019. Fundamental methods of mathematical economics, , Kevin Wainwright, 2005, McGraw Hill Education, 4th Edition İşletme Matematiği, Bülent Kobu, 2009, Beta Basım Yayım Dağıtım, 8. Edition |

## Course Contribution to Program Qualifications

Course Contribution to Program Qualifications | |||||||

No | Program Qualification | Contribution Level | |||||

1 | 2 | 3 | 4 | 5 | |||

1 | Defines the theoretical issues in the field of business administration | X | |||||

2 | Describes the necessary qualitative and quantitative methods in the field of business and management. | X | |||||

3 | Uses at least one computer program in the field of business and management | ||||||

4 | Sustains proficiency in a foreign language required for business and management. | ||||||

5 | Prepares managerial investment projects and work in a team. | ||||||

6 | Constantly renews himself / herself by following developments in business and management with an understanding of the importance of lifelong learning through critically evaluating the knowledge and skills that s/he has got. | ||||||

7 | Uses theoretical and practical expertise in the field of business administration | X | |||||

8 | Follows up-to-date technology using a foreign language at least A1 level, holds verbal / written communication. | ||||||

9 | Adopts organizational / institutional and social ethical values. | ||||||

10 | Within the framework of service responsiveness, adopts social responsibility principles and takes initiative when necessary. | ||||||

11 | Uses and analyses basic facts and data in different disciplines (economics, finance, sociology, law, business) in order to conduct interdisciplinary studies. | X | |||||

12 | Uses and Analyses the fundamental and advanced techniques in the field to enhance business performance, productivity, sustainability,innovation and research, efficiency and effectiveness. | X |

## Assessment Methods

Contribution Level | Absolute Evaluation | |

Rate of Midterm Exam to Success | 40 | |

Rate of Final Exam to Success | 60 | |

Total | 100 |

ECTS / Workload Table | ||||||

Activities | Number of | Duration(Hour) | Total Workload(Hour) | |||

Course Hours | 14 | 3 | 42 | |||

Guided Problem Solving | 0 | 0 | 0 | |||

Resolution of Homework Problems and Submission as a Report | 0 | 0 | 0 | |||

Term Project | 0 | 0 | 0 | |||

Presentation of Project / Seminar | 0 | 0 | 0 | |||

Quiz | 3 | 5 | 15 | |||

Midterm Exam | 1 | 26 | 26 | |||

General Exam | 1 | 37 | 37 | |||

Performance Task, Maintenance Plan | 0 | 0 | 0 | |||

Total Workload(Hour) | 120 | |||||

Dersin AKTS Kredisi = Toplam İş Yükü (Saat)/30*=(120/30) | 4 | |||||

ECTS of the course: 30 hours of work is counted as 1 ECTS credit. |

## Detail Informations of the Course

### Course Description

Course | Code | Semester | T+P (Hour) | Credit | ECTS |
---|---|---|---|---|---|

MATHEMATICS II | - | Spring Semester | 3+0 | 3 | 4 |

Course Program |

Prerequisites Courses | |

Recommended Elective Courses |

Language of Course | English |

Course Level | First Cycle (Bachelor's Degree) |

Course Type | Required |

Course Coordinator | Assist.Prof. Tuğba ASLAN KHALİFA |

Name of Lecturer(s) | Assist.Prof. Tuğba ASLAN KHALİFA |

Assistant(s) | |

Aim | The aim of this mathematics course is to equip students with the essential mathematical knowledge and skills necessary to excel in the world of business and economics. This course seeks to provide a solid foundation in mathematical concepts and techniques that are directly applicable to real-world business scenarios, enabling students to make informed decisions, solve practical problems, and enhance their quantitative reasoning abilities in a business context. |

Course Content | This course contains; The definition of limit, right and left limit,Infinite limit and limit at infinity,Continuity,Definition of limit, physical and geometric interpretation, tangent lines, rules of differentiation,Marginal analysis in business and economy, continuous compound interest,Derivative of logarithmic and exponential functions, product and quotient rules, chain rule,Implicit differentiation, related rates, elasticity of demand,Aplications of differentiation: graphs and derivatives, optimization,Anti derivatives and rules of indefinite integral calculation,Definite integral and Riemann Sums,Fundamental theorem of analysis and calculation of definite integrals,Sequences and series: definitions and terminology,Arithmetic and geometric sequences and series,Difference equations and its applications. |

Dersin Öğrenme Kazanımları | Teaching Methods | Assessment Methods |

1. Will be able to evaluate limits of one variable functions numerically, graphically, and algebraically. | 12, 14, 16, 9 | A, E, G |

1.1 Understand the concept of limit and its existence, analyse the concept of limit both graphicaly and algebraicly. | ||

1.2 Evaluate one-sided limits, limit at infinity, and infinite limits of various basic functions. | ||

2. Will be able to analyze the continuity of a function. | 12, 14, 16, 9 | A, E, G |

2.1 Determine continuity and points of discontinuity of functions with single variable both graphically and algebraically. | ||

2.2 Use the concept of continuity in applications. | ||

3. Will be able to comprehend basic theoretical and applicational aspects of differentiation. | 12, 14, 16, 9 | A, E, G |

3.1 Understand the concept of a derivative as the rate of change of a function at a given point, and be able to calculate it using the limit definition. | ||

3.2 Use differentiation rules to calculate derivatives of polynomial, rational, exponential and logarithmic functions. | ||

3.3 Sketch the graph of functions using differentiation. | ||

4. Will be able to use limit and derivative concepts in applications of the field of interest. | 12, 14, 16, 9 | A, E, G |

4.1 Comprehend the concept of continuous compound interest using limit. | ||

4.2 Solve optimization problems in the field of interest by using first and second derivative concepts. | ||

4.3 Explains the concept of demand elasticity. | ||

5. Will be able to comprehend basic theoretical and applicational aspects of integration. | 12, 14, 16, 9 | A, E, G |

5.1 Calculate indefinite integrals with algebraic techniques using the concept of anti-derivatives. | ||

5.2 Explain the concept of definite integral and its relation with areas under the curves using Riemann sums. | ||

5.3 Calculate definite integrals with algebraic techniques using the fundamental theorem of calculus. | 12, 14, 16, 9 | A, E, G |

6. Will be able to use the concepts of series and sequences in applications of the field of interest. | ||

6.1 Define the concepts of sequences and series. | ||

6.2 Comprehend the concepts of arithmetic and geometric series and sequences. | ||

6.3 Use the sequences and series in the applications of field of interest. | ||

7. Will be able to describe the phenomena related with the fields of study using difference equations. | 12, 14, 16, 9 | A, E, G |

7.1 Find the complementary function of a difference equation. | ||

7.2 Find the particular solution of a difference equation. | ||

7.3 Analyze the stability of economic systems. |

Teaching Methods: | 12: Problem Solving Method, 14: Self Study Method, 16: Question - Answer Technique, 9: Lecture Method |

Assessment Methods: | A: Traditional Written Exam, E: Homework, G: Quiz |

### Course Outline

Order | Subjects | Preliminary Work |
---|---|---|

1 | The definition of limit, right and left limit | |

2 | Infinite limit and limit at infinity | |

3 | Continuity | |

4 | Definition of limit, physical and geometric interpretation, tangent lines, rules of differentiation | |

5 | Marginal analysis in business and economy, continuous compound interest | |

6 | Derivative of logarithmic and exponential functions, product and quotient rules, chain rule | |

7 | Implicit differentiation, related rates, elasticity of demand | |

8 | Aplications of differentiation: graphs and derivatives, optimization | |

9 | Anti derivatives and rules of indefinite integral calculation | |

10 | Definite integral and Riemann Sums | |

11 | Fundamental theorem of analysis and calculation of definite integrals | |

12 | Sequences and series: definitions and terminology | |

13 | Arithmetic and geometric sequences and series | |

14 | Difference equations and its applications |

Resources |

Main sources: 1. Lecture Notes shared by instructor 2. Main text: Calculus for Business, Economics, Life Sciences, and Social Sciences, 14th edition Published by Pearson (2021), R. A. Barnett, M: R: Ziegler, K. E. Byleen. |

Other Recommended Sources: Introductory Mathematical Analysis for Business, Economics, and the Life and Social Sciences, 14th Edition by Ernest F. Haeussler, Jr., Richard S. Paul, and Richard J. Wood, published by Pearson Education 2019. Fundamental methods of mathematical economics, , Kevin Wainwright, 2005, McGraw Hill Education, 4th Edition İşletme Matematiği, Bülent Kobu, 2009, Beta Basım Yayım Dağıtım, 8. Edition |

### Course Contribution to Program Qualifications

Course Contribution to Program Qualifications | |||||||

No | Program Qualification | Contribution Level | |||||

1 | 2 | 3 | 4 | 5 | |||

1 | Defines the theoretical issues in the field of business administration | X | |||||

2 | Describes the necessary qualitative and quantitative methods in the field of business and management. | X | |||||

3 | Uses at least one computer program in the field of business and management | ||||||

4 | Sustains proficiency in a foreign language required for business and management. | ||||||

5 | Prepares managerial investment projects and work in a team. | ||||||

6 | Constantly renews himself / herself by following developments in business and management with an understanding of the importance of lifelong learning through critically evaluating the knowledge and skills that s/he has got. | ||||||

7 | Uses theoretical and practical expertise in the field of business administration | X | |||||

8 | Follows up-to-date technology using a foreign language at least A1 level, holds verbal / written communication. | ||||||

9 | Adopts organizational / institutional and social ethical values. | ||||||

10 | Within the framework of service responsiveness, adopts social responsibility principles and takes initiative when necessary. | ||||||

11 | Uses and analyses basic facts and data in different disciplines (economics, finance, sociology, law, business) in order to conduct interdisciplinary studies. | X | |||||

12 | Uses and Analyses the fundamental and advanced techniques in the field to enhance business performance, productivity, sustainability,innovation and research, efficiency and effectiveness. | X |

### Assessment Methods

Contribution Level | Absolute Evaluation | |

Rate of Midterm Exam to Success | 40 | |

Rate of Final Exam to Success | 60 | |

Total | 100 |