Course Description
| Course | Code | Semester | T+P (Hour) | Credit | ECTS |
|---|---|---|---|---|---|
| MATHEMATICS I | - | Fall Semester | 3+0 | 3 | 5 |
| Course Program |
| Prerequisites Courses | |
| Recommended Elective Courses |
| Language of Course | Turkish |
| Course Level | Short Cycle (Associate's Degree) |
| Course Type | Elective |
| Course Coordinator | Lect. Hatice ÇAY |
| Name of Lecturer(s) | Lect. Hatice ÇAY |
| Assistant(s) | |
| Aim | The aim of this course is to explain fundamental math, calculus and linear algebra contents, methods, techniques and show how to use these methods in solving certain types of problems which might possibly be encountered in many branches of science. |
| Course Content | This course contains; Real integers; Basic Algebraic Calculus, Intervals, Absolute Value.,Functions: Functions and Their Graphs, Definition of Trigonometric Functions,Limits and Contiunity: Rates of Change and Tangents to Curves, Limit of a Function and Limit Laws, The Sandwich (The Squeeze theorem), The Precise Definition of a Limit, One-sided Limits,Contiunity: Types of Discontiunity, Continuous Functions, The İntermediate Value Theorem, Limits İnvolving İnfinity, Asymptotes of Graphs,Differentiation: Tangents ,Normal Lines , The Derivative at a Point, The Derivate as a Function, Differentiable on an İnterval, Onesided Derivatives, Differentiation Rules, High order Derivatives, The Derivative as a Rate of Change Derivatives of Trigonometric Fnctions, The chain rule ,Applications of derivatives: Extreme Values of Functions, Critical Points, Rolle’s Theorem, The Mean Value Theorem,Monotonic Functions and The First Derivative Test: Increasing Functions and Decrasing Functions, the First Derivative Test for Local Extrema Concavity and Curve Sketching ,Optimization ,Indefinite Integrals, Integration: Area and Estimating with Finite Sums ,Average Value of Nonnegative Continuous Functions, Sigma Notation and Limits of Finite Sums, Riemann Sums ,Definite İntegral, Properties of Definite İntegral ,Area Under the Graph of a Nonnegative Function, Average Value of Continuous Functions,practice. |
| Dersin Öğrenme Kazanımları | Teaching Methods | Assessment Methods |
| 1. Explain and recognize set of real numbers, absolute value and interval. | 12, 16, 6, 9 | A, D, E, G |
| 2. Explain functions and their graphics. | 12, 16, 6, 9 | A, D, E, G |
| 3. Calculate and explain derivatives. | 12, 16, 6, 9 | A, D, E, G |
| 4. Calculate integrals. | 12, 16, 6, 9 | A, D, E, G |
| 5. Prove the basic theorems about limits. | 12, 16, 6, 9 | A, D, E, G |
| Teaching Methods: | 12: Problem Solving Method, 16: Question - Answer Technique, 6: Experiential Learning, 9: Lecture Method |
| Assessment Methods: | A: Traditional Written Exam, D: Oral Exam, E: Homework, G: Quiz |
Course Outline
| Order | Subjects | Preliminary Work |
|---|---|---|
| 1 | Real integers; Basic Algebraic Calculus, Intervals, Absolute Value. | |
| 2 | Functions: Functions and Their Graphs, Definition of Trigonometric Functions | |
| 3 | Limits and Contiunity: Rates of Change and Tangents to Curves, Limit of a Function and Limit Laws, The Sandwich (The Squeeze theorem), The Precise Definition of a Limit, One-sided Limits | |
| 4 | Contiunity: Types of Discontiunity, Continuous Functions, The İntermediate Value Theorem, Limits İnvolving İnfinity, Asymptotes of Graphs | |
| 5 | Differentiation: Tangents ,Normal Lines , The Derivative at a Point, The Derivate as a Function, Differentiable on an İnterval, Onesided Derivatives, Differentiation Rules, High order Derivatives | |
| 6 | The Derivative as a Rate of Change Derivatives of Trigonometric Fnctions, The chain rule | |
| 7 | Applications of derivatives: Extreme Values of Functions, Critical Points, Rolle’s Theorem, The Mean Value Theorem | |
| 8 | Monotonic Functions and The First Derivative Test: Increasing Functions and Decrasing Functions, the First Derivative Test for Local Extrema Concavity and Curve Sketching | |
| 9 | Optimization | |
| 10 | Indefinite Integrals, Integration: Area and Estimating with Finite Sums | |
| 11 | Average Value of Nonnegative Continuous Functions, Sigma Notation and Limits of Finite Sums, Riemann Sums | |
| 12 | Definite İntegral, Properties of Definite İntegral | |
| 13 | Area Under the Graph of a Nonnegative Function, Average Value of Continuous Functions | |
| 14 | practice |
| Resources |
| 1. Thomas' Calculus, 14th Edition, George B. Thomas, Maurice D. Weir, Joel R. Hass, Pearson. 2. Kısa Teori ve Çözümlü Problemlerle Matematik Analiz 1, Dr. Salih Çelik, Birsen Yayınevi 3. Lecture notes |
Course Contribution to Program Qualifications
| Course Contribution to Program Qualifications | |||||||
| No | Program Qualification | Contribution Level | |||||
| 1 | 2 | 3 | 4 | 5 | |||
| 1 | Has the background in algorithms, programming, and application development in software engineering projects; and has the ability to use them together in business. | X | |||||
| 2 | Chooses and uses the proper solution methods and special techniques for programming purpose. | X | |||||
| 3 | Uses modern techniques and tools for programming applications. | X | |||||
| 4 | Works effectively individually and in teams. | X | |||||
| 5 | Implements and follows test cases of developed software and applications. | ||||||
| 6 | Has the awareness in workplace practices, worker health, environmental and workplace safety, professional and ethical responsibility, and legal issues about programming practices. | X | |||||
| 7 | Reaches information, and surveys resources for this purpose. | X | |||||
| 8 | Aware of the necessity of life-long learning; follows technological advances and renews him/herself. | X | |||||
| 9 | Communicates, oral and written, effectively using modern tools. | X | |||||
| 10 | Aware of universal and social effects of software solutions and practices; develops new software tools for solving universal problems and social advance. | X | |||||
| 11 | Keeps attention in clean and readable code design. | ||||||
| 12 | Considers and follows user centered design principles. | ||||||
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 | 14 | 3 | 42 | |||
| Resolution of Homework Problems and Submission as a Report | 3 | 10 | 30 | |||
| Term Project | 0 | 0 | 0 | |||
| Presentation of Project / Seminar | 0 | 0 | 0 | |||
| Quiz | 1 | 2 | 2 | |||
| Midterm Exam | 1 | 17 | 17 | |||
| General Exam | 1 | 17 | 17 | |||
| Performance Task, Maintenance Plan | 0 | 0 | 0 | |||
| Total Workload(Hour) | 150 | |||||
| Dersin AKTS Kredisi = Toplam İş Yükü (Saat)/30*=(150/30) | 5 | |||||
| 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 I | - | Fall Semester | 3+0 | 3 | 5 |
| Course Program |
| Prerequisites Courses | |
| Recommended Elective Courses |
| Language of Course | Turkish |
| Course Level | Short Cycle (Associate's Degree) |
| Course Type | Elective |
| Course Coordinator | Lect. Hatice ÇAY |
| Name of Lecturer(s) | Lect. Hatice ÇAY |
| Assistant(s) | |
| Aim | The aim of this course is to explain fundamental math, calculus and linear algebra contents, methods, techniques and show how to use these methods in solving certain types of problems which might possibly be encountered in many branches of science. |
| Course Content | This course contains; Real integers; Basic Algebraic Calculus, Intervals, Absolute Value.,Functions: Functions and Their Graphs, Definition of Trigonometric Functions,Limits and Contiunity: Rates of Change and Tangents to Curves, Limit of a Function and Limit Laws, The Sandwich (The Squeeze theorem), The Precise Definition of a Limit, One-sided Limits,Contiunity: Types of Discontiunity, Continuous Functions, The İntermediate Value Theorem, Limits İnvolving İnfinity, Asymptotes of Graphs,Differentiation: Tangents ,Normal Lines , The Derivative at a Point, The Derivate as a Function, Differentiable on an İnterval, Onesided Derivatives, Differentiation Rules, High order Derivatives, The Derivative as a Rate of Change Derivatives of Trigonometric Fnctions, The chain rule ,Applications of derivatives: Extreme Values of Functions, Critical Points, Rolle’s Theorem, The Mean Value Theorem,Monotonic Functions and The First Derivative Test: Increasing Functions and Decrasing Functions, the First Derivative Test for Local Extrema Concavity and Curve Sketching ,Optimization ,Indefinite Integrals, Integration: Area and Estimating with Finite Sums ,Average Value of Nonnegative Continuous Functions, Sigma Notation and Limits of Finite Sums, Riemann Sums ,Definite İntegral, Properties of Definite İntegral ,Area Under the Graph of a Nonnegative Function, Average Value of Continuous Functions,practice. |
| Dersin Öğrenme Kazanımları | Teaching Methods | Assessment Methods |
| 1. Explain and recognize set of real numbers, absolute value and interval. | 12, 16, 6, 9 | A, D, E, G |
| 2. Explain functions and their graphics. | 12, 16, 6, 9 | A, D, E, G |
| 3. Calculate and explain derivatives. | 12, 16, 6, 9 | A, D, E, G |
| 4. Calculate integrals. | 12, 16, 6, 9 | A, D, E, G |
| 5. Prove the basic theorems about limits. | 12, 16, 6, 9 | A, D, E, G |
| Teaching Methods: | 12: Problem Solving Method, 16: Question - Answer Technique, 6: Experiential Learning, 9: Lecture Method |
| Assessment Methods: | A: Traditional Written Exam, D: Oral Exam, E: Homework, G: Quiz |
Course Outline
| Order | Subjects | Preliminary Work |
|---|---|---|
| 1 | Real integers; Basic Algebraic Calculus, Intervals, Absolute Value. | |
| 2 | Functions: Functions and Their Graphs, Definition of Trigonometric Functions | |
| 3 | Limits and Contiunity: Rates of Change and Tangents to Curves, Limit of a Function and Limit Laws, The Sandwich (The Squeeze theorem), The Precise Definition of a Limit, One-sided Limits | |
| 4 | Contiunity: Types of Discontiunity, Continuous Functions, The İntermediate Value Theorem, Limits İnvolving İnfinity, Asymptotes of Graphs | |
| 5 | Differentiation: Tangents ,Normal Lines , The Derivative at a Point, The Derivate as a Function, Differentiable on an İnterval, Onesided Derivatives, Differentiation Rules, High order Derivatives | |
| 6 | The Derivative as a Rate of Change Derivatives of Trigonometric Fnctions, The chain rule | |
| 7 | Applications of derivatives: Extreme Values of Functions, Critical Points, Rolle’s Theorem, The Mean Value Theorem | |
| 8 | Monotonic Functions and The First Derivative Test: Increasing Functions and Decrasing Functions, the First Derivative Test for Local Extrema Concavity and Curve Sketching | |
| 9 | Optimization | |
| 10 | Indefinite Integrals, Integration: Area and Estimating with Finite Sums | |
| 11 | Average Value of Nonnegative Continuous Functions, Sigma Notation and Limits of Finite Sums, Riemann Sums | |
| 12 | Definite İntegral, Properties of Definite İntegral | |
| 13 | Area Under the Graph of a Nonnegative Function, Average Value of Continuous Functions | |
| 14 | practice |
| Resources |
| 1. Thomas' Calculus, 14th Edition, George B. Thomas, Maurice D. Weir, Joel R. Hass, Pearson. 2. Kısa Teori ve Çözümlü Problemlerle Matematik Analiz 1, Dr. Salih Çelik, Birsen Yayınevi 3. Lecture notes |
Course Contribution to Program Qualifications
| Course Contribution to Program Qualifications | |||||||
| No | Program Qualification | Contribution Level | |||||
| 1 | 2 | 3 | 4 | 5 | |||
| 1 | Has the background in algorithms, programming, and application development in software engineering projects; and has the ability to use them together in business. | X | |||||
| 2 | Chooses and uses the proper solution methods and special techniques for programming purpose. | X | |||||
| 3 | Uses modern techniques and tools for programming applications. | X | |||||
| 4 | Works effectively individually and in teams. | X | |||||
| 5 | Implements and follows test cases of developed software and applications. | ||||||
| 6 | Has the awareness in workplace practices, worker health, environmental and workplace safety, professional and ethical responsibility, and legal issues about programming practices. | X | |||||
| 7 | Reaches information, and surveys resources for this purpose. | X | |||||
| 8 | Aware of the necessity of life-long learning; follows technological advances and renews him/herself. | X | |||||
| 9 | Communicates, oral and written, effectively using modern tools. | X | |||||
| 10 | Aware of universal and social effects of software solutions and practices; develops new software tools for solving universal problems and social advance. | X | |||||
| 11 | Keeps attention in clean and readable code design. | ||||||
| 12 | Considers and follows user centered design principles. | ||||||
Assessment Methods
| Contribution Level | Absolute Evaluation | |
| Rate of Midterm Exam to Success | 40 | |
| Rate of Final Exam to Success | 60 | |
| Total | 100 | |