Course Detail
Course Description
| Course | Code | Semester | T+P (Hour) | Credit | ECTS |
|---|---|---|---|---|---|
| MATHEMATICS | - | Fall Semester | 2+0 | 2 | 2 |
| Course Program |
| Prerequisites Courses | |
| Recommended Elective Courses |
| Language of Course | Turkish |
| Course Level | First Cycle (Bachelor's Degree) |
| Course Type | Required |
| Course Coordinator | Lect. Naile Hande YAZICI |
| Name of Lecturer(s) | Assist.Prof. Hüseyin KOCAMAN |
| Assistant(s) | |
| Aim | The aim of the course is to teach the basic mathematical techniques for Business Administration and Medical Sciences , introducing a number of mathematical skills that can be used for the analysis of problems. |
| Course Content | This course contains; Functions: Functions and Their Graphs, Definition of Trigonometric Functions,Limit and Limit Rules of a Function, Limit and Continuity, Sandwich (Compression) Theorem, Continuity-Continuous Functions, Discontinuity-Discontinuous Functions, Variations of Change Rates and Tangents of Curves,Derivatives: Tangents, Derivatives at one point, Derivative as a Function, Derivatives, High Rank Derivatives, Derivatives as a Change Rate,Derivatives of Trigonometric Functions, Chain Rule,Applications of derivatives: Extreme values of functions, Critical Points, Monotonous Functions and First Derivative Test: Increasing- Decreasing Functions, First Derivative Test for Local Extremities,Concavity and Curve drawing, Second Derivative Test for Concavity, Bend points, Second Derivative Test for Local Extremity, Graph of y=f(x) Function, Reverse Derivatives, Optimization,Indefinite Integrals, Integration: Integral with Area and Finite Sums, Sigma Notation, Limits of Finite Sums, Riemann Sums, Definite Integral, Properties of Definite Integral, Area Under the Graph of a Nonnegative Function,Mean Value Theorem of Definite İntegrals,Indefinite İntegrals and the Substitution Method, Substitution and Area Between Curves, Integration with Respect to y,Applications of Definite Integrals: Volumes Using Cross-sections, The Disk Method, The Washer Method, The Cylindrical Shell Method, Arch Length, Areas of Surfuces of Revolution,Transcendental Functions: Inverse Functions and Their Derivatives, Natural Logarithms, Logarithms Functions and Their Derivatives, Logarithmic Differentiation, Integrals of Trigonometric Functions, Exponential Functions and Their Derivatives, Indeterminate Forms and L’Hospitals Rule, Cauchy’s Mean Value Theorem,Techniques of Integration: Integration by Parts, Integration by Parts Formula for Definite Integrals, Trigonometric Integrals, Reduction Formulas,Differential Equations: First Order Differential Equations, Applications in Biology,Mathematical Modelling: Physical and Biological Modelling with Differentials. |
| Dersin Öğrenme Kazanımları | Teaching Methods | Assessment Methods |
| Analyzes single variable functions. | 12, 13, 19, 9 | A, E |
| Plot graphs by using elementary graphing rules such as shifting, reflection, compressing/stretching | 12, 14, 9 | A, E |
| Define the concepts of limit and continuity in one-variable functions. | 12, 6, 9 | A, E |
| Explains the concept of derivative in functions. | 12, 9 | A, E |
| Explain the relation between derivative and continuity. | 12, 9 | A, E |
| Evaluating integrals by using the fundamental theorem of calculus. | 12, 6, 9 | A, E |
| Explain the concepts of monotonicity, convexity and concavity in functions. | 12, 9 | A, E |
| Solve basic optimization problems (local minima and maxima) in one-variable functions by applying the rules of derivatives. | 12, 6, 9 | A, E |
| Use differentials in physical and biyological modelling. | 12, 14, 9 | A, E |
| Teaching Methods: | 12: Problem Solving Method, 13: Case Study Method, 14: Self Study Method, 19: Brainstorming Technique, 6: Experiential Learning, 9: Lecture Method |
| Assessment Methods: | A: Traditional Written Exam, E: Homework |
Course Outline
| Order | Subjects | Preliminary Work |
|---|---|---|
| 1 | Functions: Functions and Their Graphs, Definition of Trigonometric Functions | Source 1 |
| 2 | Limit and Limit Rules of a Function, Limit and Continuity, Sandwich (Compression) Theorem, Continuity-Continuous Functions, Discontinuity-Discontinuous Functions, Variations of Change Rates and Tangents of Curves | Source 1 |
| 3 | Derivatives: Tangents, Derivatives at one point, Derivative as a Function, Derivatives, High Rank Derivatives, Derivatives as a Change Rate | Source 1 |
| 4 | Derivatives of Trigonometric Functions, Chain Rule | Source 2 |
| 5 | Applications of derivatives: Extreme values of functions, Critical Points, Monotonous Functions and First Derivative Test: Increasing- Decreasing Functions, First Derivative Test for Local Extremities | Source 2 |
| 6 | Concavity and Curve drawing, Second Derivative Test for Concavity, Bend points, Second Derivative Test for Local Extremity, Graph of y=f(x) Function, Reverse Derivatives, Optimization | Source 2 |
| 7 | Indefinite Integrals, Integration: Integral with Area and Finite Sums, Sigma Notation, Limits of Finite Sums, Riemann Sums, Definite Integral, Properties of Definite Integral, Area Under the Graph of a Nonnegative Function | Source 2 |
| 8 | Mean Value Theorem of Definite İntegrals | Source 2 |
| 9 | Indefinite İntegrals and the Substitution Method, Substitution and Area Between Curves, Integration with Respect to y | Source 2 |
| 10 | Applications of Definite Integrals: Volumes Using Cross-sections, The Disk Method, The Washer Method, The Cylindrical Shell Method, Arch Length, Areas of Surfuces of Revolution | Source 2 |
| 11 | Transcendental Functions: Inverse Functions and Their Derivatives, Natural Logarithms, Logarithms Functions and Their Derivatives, Logarithmic Differentiation, Integrals of Trigonometric Functions, Exponential Functions and Their Derivatives, Indeterminate Forms and L’Hospitals Rule, Cauchy’s Mean Value Theorem | Source 2 |
| 12 | Techniques of Integration: Integration by Parts, Integration by Parts Formula for Definite Integrals, Trigonometric Integrals, Reduction Formulas | Source 2 |
| 13 | Differential Equations: First Order Differential Equations, Applications in Biology | Source 3 |
| 14 | Mathematical Modelling: Physical and Biological Modelling with Differentials | Source 3 |
| Resources |
| 1. Thomas' Calculus, 14th Edition, George B. Thomas, Maurice D. Weir, Joel R. Hass, Pearson, 2020. 2. Kısa Teori ve Çözümlü Problemlerle Matematik Analiz 1, 2018. 3. Calculus for Business, Economics and Social Sciences, 9th Edition; R. A. Barnett/M: R: Ziegler/ K. E. Byleen, Prentice-Hall, 2019. |
| Calculus (9th Ed.), D. Varberg, E. Purcell, S. Rigdon, 2014, Pearson Education Int. Calculus: A Complete Course, 7th Edition; R. A. Adams, Addison-Wesley |
Course Contribution to Program Qualifications
| Course Contribution to Program Qualifications | |||||||
| No | Program Qualification | Contribution Level | |||||
| 1 | 2 | 3 | 4 | 5 | |||
| 1 | PQ-1. Has trustworthy, sufficient and up to date knowledge related with orthotics prosthetics. | ||||||
| 2 | PQ-2. Equipped with the knowledge about design, production and intervention of suitable devices by using assessment methods to people who need artificial limb and/or assistive devices. | X | |||||
| 3 | PQ-3. Analyses the issues, using the knowledge and skills based on evidence in orthotics prosthetics considering professional and ethical values; takes part in inter-disciplinary health research. | X | |||||
| 4 | PQ-4. Performs interventions on people who need artificial limb and/or assistive devices by using advanced technology and necessary materials to regain function and independence in their daily activities | X | |||||
| 5 | PQ-5. Using the knowledge in the field of orthotics prosthetics, by making analysis and synthesis, works independently and within the cooperation of the other healthcare staff, as a member of the team takes responsibility. | ||||||
| 6 | PQ-6. Execution, organizing, presenting the services of the orthotics prosthetics in daily practices and within the scope of planning project, solving problem, manages plans while watching the process and evaluating. | X | |||||
| 7 | PQ-7. By adopting such particulars as adaptation to new conditions lifelong learning, developing new ideas, considering importance to quality, evaluates the knowledge sources through a critical approach. | X | |||||
| 8 | PQ-8. Evaluates the vocational knowledge by researching on the field of orthotics prosthetics. Adopts positive manner and attitude model and describes learning targets. | ||||||
| 9 | PQ-9. With the conscious of understanding and estimating the multiculturalism with the individuals who have taken orthotics prosthetics service, by making effective contact with other relevant people and colleagues, informs the individual who gets service, records the knowledge systematically by conforming the privacy policy. | ||||||
| 10 | PQ-10. Possesses the competence of English in B1 general level so as to follow English sources in orthotics and prosthetics field. | ||||||
| 11 | PQ-11. Uses the information and communication technologies related with the orthotics prosthetics field by communicating verbal and written ways, expresses himself effectively. | ||||||
| 12 | PQ-12. In the orthotics prosthetics interventions, by looking after the duty, rights and responsibilities, within the cooperation of the related disciplines, acts appropriately to the professional ethical rules and legislation. | ||||||
| 13 | PQ-13. Performs the orthotics and prosthetics interventions under the professional honesty by bearing responsibility and by providing safety in every step. | 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 | 2 | 28 | |||
| Guided Problem Solving | 5 | 2 | 10 | |||
| 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 | 0 | 0 | 0 | |||
| Midterm Exam | 4 | 3 | 12 | |||
| General Exam | 0 | 0 | 0 | |||
| Performance Task, Maintenance Plan | 0 | 0 | 0 | |||
| Total Workload(Hour) | 50 | |||||
| Dersin AKTS Kredisi = Toplam İş Yükü (Saat)/30*=(50/30) | 2 | |||||
| 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 | - | Fall Semester | 2+0 | 2 | 2 |
| Course Program |
| Prerequisites Courses | |
| Recommended Elective Courses |
| Language of Course | Turkish |
| Course Level | First Cycle (Bachelor's Degree) |
| Course Type | Required |
| Course Coordinator | Lect. Naile Hande YAZICI |
| Name of Lecturer(s) | Assist.Prof. Hüseyin KOCAMAN |
| Assistant(s) | |
| Aim | The aim of the course is to teach the basic mathematical techniques for Business Administration and Medical Sciences , introducing a number of mathematical skills that can be used for the analysis of problems. |
| Course Content | This course contains; Functions: Functions and Their Graphs, Definition of Trigonometric Functions,Limit and Limit Rules of a Function, Limit and Continuity, Sandwich (Compression) Theorem, Continuity-Continuous Functions, Discontinuity-Discontinuous Functions, Variations of Change Rates and Tangents of Curves,Derivatives: Tangents, Derivatives at one point, Derivative as a Function, Derivatives, High Rank Derivatives, Derivatives as a Change Rate,Derivatives of Trigonometric Functions, Chain Rule,Applications of derivatives: Extreme values of functions, Critical Points, Monotonous Functions and First Derivative Test: Increasing- Decreasing Functions, First Derivative Test for Local Extremities,Concavity and Curve drawing, Second Derivative Test for Concavity, Bend points, Second Derivative Test for Local Extremity, Graph of y=f(x) Function, Reverse Derivatives, Optimization,Indefinite Integrals, Integration: Integral with Area and Finite Sums, Sigma Notation, Limits of Finite Sums, Riemann Sums, Definite Integral, Properties of Definite Integral, Area Under the Graph of a Nonnegative Function,Mean Value Theorem of Definite İntegrals,Indefinite İntegrals and the Substitution Method, Substitution and Area Between Curves, Integration with Respect to y,Applications of Definite Integrals: Volumes Using Cross-sections, The Disk Method, The Washer Method, The Cylindrical Shell Method, Arch Length, Areas of Surfuces of Revolution,Transcendental Functions: Inverse Functions and Their Derivatives, Natural Logarithms, Logarithms Functions and Their Derivatives, Logarithmic Differentiation, Integrals of Trigonometric Functions, Exponential Functions and Their Derivatives, Indeterminate Forms and L’Hospitals Rule, Cauchy’s Mean Value Theorem,Techniques of Integration: Integration by Parts, Integration by Parts Formula for Definite Integrals, Trigonometric Integrals, Reduction Formulas,Differential Equations: First Order Differential Equations, Applications in Biology,Mathematical Modelling: Physical and Biological Modelling with Differentials. |
| Dersin Öğrenme Kazanımları | Teaching Methods | Assessment Methods |
| Analyzes single variable functions. | 12, 13, 19, 9 | A, E |
| Plot graphs by using elementary graphing rules such as shifting, reflection, compressing/stretching | 12, 14, 9 | A, E |
| Define the concepts of limit and continuity in one-variable functions. | 12, 6, 9 | A, E |
| Explains the concept of derivative in functions. | 12, 9 | A, E |
| Explain the relation between derivative and continuity. | 12, 9 | A, E |
| Evaluating integrals by using the fundamental theorem of calculus. | 12, 6, 9 | A, E |
| Explain the concepts of monotonicity, convexity and concavity in functions. | 12, 9 | A, E |
| Solve basic optimization problems (local minima and maxima) in one-variable functions by applying the rules of derivatives. | 12, 6, 9 | A, E |
| Use differentials in physical and biyological modelling. | 12, 14, 9 | A, E |
| Teaching Methods: | 12: Problem Solving Method, 13: Case Study Method, 14: Self Study Method, 19: Brainstorming Technique, 6: Experiential Learning, 9: Lecture Method |
| Assessment Methods: | A: Traditional Written Exam, E: Homework |
Course Outline
| Order | Subjects | Preliminary Work |
|---|---|---|
| 1 | Functions: Functions and Their Graphs, Definition of Trigonometric Functions | Source 1 |
| 2 | Limit and Limit Rules of a Function, Limit and Continuity, Sandwich (Compression) Theorem, Continuity-Continuous Functions, Discontinuity-Discontinuous Functions, Variations of Change Rates and Tangents of Curves | Source 1 |
| 3 | Derivatives: Tangents, Derivatives at one point, Derivative as a Function, Derivatives, High Rank Derivatives, Derivatives as a Change Rate | Source 1 |
| 4 | Derivatives of Trigonometric Functions, Chain Rule | Source 2 |
| 5 | Applications of derivatives: Extreme values of functions, Critical Points, Monotonous Functions and First Derivative Test: Increasing- Decreasing Functions, First Derivative Test for Local Extremities | Source 2 |
| 6 | Concavity and Curve drawing, Second Derivative Test for Concavity, Bend points, Second Derivative Test for Local Extremity, Graph of y=f(x) Function, Reverse Derivatives, Optimization | Source 2 |
| 7 | Indefinite Integrals, Integration: Integral with Area and Finite Sums, Sigma Notation, Limits of Finite Sums, Riemann Sums, Definite Integral, Properties of Definite Integral, Area Under the Graph of a Nonnegative Function | Source 2 |
| 8 | Mean Value Theorem of Definite İntegrals | Source 2 |
| 9 | Indefinite İntegrals and the Substitution Method, Substitution and Area Between Curves, Integration with Respect to y | Source 2 |
| 10 | Applications of Definite Integrals: Volumes Using Cross-sections, The Disk Method, The Washer Method, The Cylindrical Shell Method, Arch Length, Areas of Surfuces of Revolution | Source 2 |
| 11 | Transcendental Functions: Inverse Functions and Their Derivatives, Natural Logarithms, Logarithms Functions and Their Derivatives, Logarithmic Differentiation, Integrals of Trigonometric Functions, Exponential Functions and Their Derivatives, Indeterminate Forms and L’Hospitals Rule, Cauchy’s Mean Value Theorem | Source 2 |
| 12 | Techniques of Integration: Integration by Parts, Integration by Parts Formula for Definite Integrals, Trigonometric Integrals, Reduction Formulas | Source 2 |
| 13 | Differential Equations: First Order Differential Equations, Applications in Biology | Source 3 |
| 14 | Mathematical Modelling: Physical and Biological Modelling with Differentials | Source 3 |
| Resources |
| 1. Thomas' Calculus, 14th Edition, George B. Thomas, Maurice D. Weir, Joel R. Hass, Pearson, 2020. 2. Kısa Teori ve Çözümlü Problemlerle Matematik Analiz 1, 2018. 3. Calculus for Business, Economics and Social Sciences, 9th Edition; R. A. Barnett/M: R: Ziegler/ K. E. Byleen, Prentice-Hall, 2019. |
| Calculus (9th Ed.), D. Varberg, E. Purcell, S. Rigdon, 2014, Pearson Education Int. Calculus: A Complete Course, 7th Edition; R. A. Adams, Addison-Wesley |
Course Contribution to Program Qualifications
| Course Contribution to Program Qualifications | |||||||
| No | Program Qualification | Contribution Level | |||||
| 1 | 2 | 3 | 4 | 5 | |||
| 1 | PQ-1. Has trustworthy, sufficient and up to date knowledge related with orthotics prosthetics. | ||||||
| 2 | PQ-2. Equipped with the knowledge about design, production and intervention of suitable devices by using assessment methods to people who need artificial limb and/or assistive devices. | X | |||||
| 3 | PQ-3. Analyses the issues, using the knowledge and skills based on evidence in orthotics prosthetics considering professional and ethical values; takes part in inter-disciplinary health research. | X | |||||
| 4 | PQ-4. Performs interventions on people who need artificial limb and/or assistive devices by using advanced technology and necessary materials to regain function and independence in their daily activities | X | |||||
| 5 | PQ-5. Using the knowledge in the field of orthotics prosthetics, by making analysis and synthesis, works independently and within the cooperation of the other healthcare staff, as a member of the team takes responsibility. | ||||||
| 6 | PQ-6. Execution, organizing, presenting the services of the orthotics prosthetics in daily practices and within the scope of planning project, solving problem, manages plans while watching the process and evaluating. | X | |||||
| 7 | PQ-7. By adopting such particulars as adaptation to new conditions lifelong learning, developing new ideas, considering importance to quality, evaluates the knowledge sources through a critical approach. | X | |||||
| 8 | PQ-8. Evaluates the vocational knowledge by researching on the field of orthotics prosthetics. Adopts positive manner and attitude model and describes learning targets. | ||||||
| 9 | PQ-9. With the conscious of understanding and estimating the multiculturalism with the individuals who have taken orthotics prosthetics service, by making effective contact with other relevant people and colleagues, informs the individual who gets service, records the knowledge systematically by conforming the privacy policy. | ||||||
| 10 | PQ-10. Possesses the competence of English in B1 general level so as to follow English sources in orthotics and prosthetics field. | ||||||
| 11 | PQ-11. Uses the information and communication technologies related with the orthotics prosthetics field by communicating verbal and written ways, expresses himself effectively. | ||||||
| 12 | PQ-12. In the orthotics prosthetics interventions, by looking after the duty, rights and responsibilities, within the cooperation of the related disciplines, acts appropriately to the professional ethical rules and legislation. | ||||||
| 13 | PQ-13. Performs the orthotics and prosthetics interventions under the professional honesty by bearing responsibility and by providing safety in every step. | X | |||||
Assessment Methods
| Contribution Level | Absolute Evaluation | |
| Rate of Midterm Exam to Success | 40 | |
| Rate of Final Exam to Success | 60 | |
| Total | 100 | |