| Course Name | Code | Semester | T+U Hours | Credit | ECTS |
|---|---|---|---|---|---|
| Mathematics I | MAT 111 | 1 | 4 + 0 | 4 | 6 |
| Precondition Courses | |
| Recommended Optional Courses | |
| Course Language | English |
| Course Level | Bachelor's Degree |
| Course Type | Compulsory |
| Course Coordinator | Doç.Dr. SELMA ALTUNDAĞ |
| Course Lecturers | Doç.Dr. SELMA ALTUNDAĞ, Doç.Dr. MURAT SARDUVAN, Doç.Dr. MAHPEYKER ÖZTÜRK, Doç.Dr. MAHMUT AKYİĞİT, Doç.Dr. YALÇIN YILMAZ, Prof.Dr. MEHMET ÖZEN, Prof.Dr. REFİK KESKİN, Dr.Öğr.Üyesi MEHMET GÜNER, Prof.Dr. MEHMET ALİ GÜNGÖR, Öğr.Gör.Dr. EMİNE ÇELİK, |
| Course Assistants | Research Assistants in mathematics department |
| Course Category | Available Basic Education in the Field |
| Course Objective | To give fundamental conceptions of mathematical analysis and limit,continuity, derivative and applications of derivative in single-valued functions |
| Course Content | Foreknowledge, functions, Limit and continuity, Derivate, Application of derivative |
| # | Course Learning Outcomes | Teaching Methods | Assessment Methods |
|---|---|---|---|
| 1 | He/she defines sets and number set concepts. Explains equality, inequality and equation concepts. | Lecture, Question-Answer, Discussion, Drilland Practice, Problem Solving, | Testing, Oral Exam, Homework, |
| 2 | He/she recognizes functions and its properties. | Lecture, Drilland Practice, Problem Solving, | Testing, Homework, |
| 3 | He/she expresses trigonometric, reverse trigonometric and hyperbolic functions, partial function and special functions ( Absolute value, exact value and sign functions) | Lecture, Drilland Practice, Problem Solving, | Testing, Homework, |
| 4 | He/she expresses concept of limit and calculates. Can prove the rules which are used for limit. | Lecture, Drilland Practice, Problem Solving, | Testing, Homework, |
| 5 | He/she defines right and left approached limit. Knows the undetermined conditions. | Lecture, Drilland Practice, Problem Solving, | Testing, Homework, |
| 6 | He/she defines the concept of continuity and discontinuity. | Lecture, Drilland Practice, Problem Solving, | Testing, Oral Exam, Homework, |
| 7 | He/she can explain concept of derivative and calculates derivatives with this definition. Proves the derivative rules with the definition of derivative. | Lecture, Drilland Practice, Problem Solving, | Testing, Homework, |
| 8 | Can define the derivative of trigonometric, reverse trigonometric functions, Exponential and logarithmic function, hyperbolic and revere hyperbolic functions. | Lecture, Drilland Practice, Problem Solving, | Testing, Homework, |
| 9 | He/she calculates high order derivatives. Can define the derivatives of given functions and parametric equations. Express the derivative of implicit functions. | Lecture, Drilland Practice, Problem Solving, | Testing, Oral Exam, Homework, |
| 10 | Defines the increasing and decreasing functions with the help of tangent and normal equations. | Lecture, Question-Answer, Drilland Practice, Demonstration, Motivations to Show, | Testing, Oral Exam, |
| 11 | Can calculate the limit of undetermined conditions with the help of derivatives. | Lecture, Question-Answer, Problem Solving, | Testing, Oral Exam, |
| 12 | Can define the maximum, minimum and asymptote of functions. | Lecture, Question-Answer, Drilland Practice, Problem Solving, | Testing, Oral Exam, Homework, |
| 13 | Expresses the curve plot. | Lecture, Question-Answer, Problem Solving, | Testing, Oral Exam, |
| 14 | Solves the engineering problems with the help of derivative and approximates with differential approach. | Lecture, Question-Answer, Problem Solving, | Testing, Oral Exam, Homework, |
| Week | Course Topics | Preliminary Preparation |
|---|---|---|
| 1 | Sets. Number sets. Equations. Equality and inequality. | |
| 2 | Concept of function. Types of functions (Polynomial sets, rational function, exponential and logarithmic functions and the definition set of these functions) | |
| 3 | Function types (Trigonometric, reverse trigonometric and hyperbolic functions, Partial functions , special defined functions (Absolute value, exact value, sign functions) . | |
| 4 | Concept of limit and limit calculation with the definition of limit. Proof of the rules used for limit rule. Sandwich theorem. Limit of trigonometric functions. | |
| 5 | Right and left limit. Undetermined conditions (0/0,infinity/infinity, 0.infinity, infinity-infinity,1^infinity) | |
| 6 | Continuity concept in functions. Types of discontinuity and characteristics of continuous functions (Mid value theorem, absolute maximum and minimum, concept of local maximum and minimum.. ) | |
| 7 | Concept of derivative, and calculation with derivative rule. Proof of derivate with derivative rule. Derivative of reverse function. | |
| 8 | Derivative of trigonometric and reverse trigonometric functions. Derivative of exponential and logarithmic functions. Derivative of hyperbolic and reverse hyperbolic functions | |
| 9 | High order derivatives. Derivatives of functions with parametric equations. Derivative of implicit functions. | |
| 10 | Equation of tangent and normal. Increasing and decreasing functions. | |
| 11 | Undetermined conditions ( Analyses of 8 condition with L’hopital Rule ) | |
| 12 | Maximum, minimum and asymptote of functions. | |
| 13 | Curve plotting. | |
| 14 | Engineering problems. Approximation with differential. |
| Resources | |
|---|---|
| Course Notes | <p>Lecture Notes</p> |
| Course Resources | [1] Thomas, G.B., Thomas Calculus, 11.baskı, çeviri:Recep Korkmaz, Beta Basım, 2010. |
| Order | Program Outcomes | Level of Contribution | |||||
|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | |||
| 1 | To have sufficient foundations on engineering subjects such as science and discrete mathematics, probability/statistics; an ability to use theoretical and applied knowledge of these subjects together for engineering solutions. | ||||||
| 2 | An ability to determine, describe, formulate and solve engineering problems; for this purpose, an ability to select and apply proper analytic and modeling methods,al background in describing, formulating, modeling and analyzing the engineering problem, with a consideration for appropriate analytical solutions in all necessary situations. | ||||||
| 3 | An ability to select and use modern techniques and tools for engineering applications; an ability to use information technologies efficiently. | ||||||
| 4 | An ability to analyze a system, a component or a process and design a system under real limits to meet desired needs; in this direction, an ability to apply modern design methods. | ||||||
| 5 | An ability to design, conduct experiment, collect data, analyze and comment on the results and consciousness of becoming a volunteer on research. | ||||||
| 6 | Understanding, awareness of administration, control, development and security/reliability issues about information technologies. | ||||||
| 7 | An ability to work efficiently in multidisciplinary teams, self confidence to take responsibility. | ||||||
| 8 | An ability to present himself/herself or a problem with oral/written techniques and have efficient communication skills; know at least one extra language. | ||||||
| 9 | An awareness about importance of lifelong learning; an ability to update his/her knowledge continuously by means of following advances in science and technology. | ||||||
| 10 | Understanding, practicing of professional and ethical responsibilities, an ability to disseminate this responsibility on society. | ||||||
| 11 | An understanding of project management, workplace applications, health issues of laborers, environment and job safety; an awareness about legal consequences of engineering applications. | ||||||
| 12 | An understanding universal and local effects of engineering solutions; awareness of entrepreneurial and innovation and to have knowledge about contemporary problems. | ||||||
| Evaluation System | |
|---|---|
| Semester Studies | Contribution Rate |
| 1. Ara Sınav | 70 |
| 1. Kısa Sınav | 10 |
| 2. Kısa Sınav | 10 |
| 3. Kısa Sınav | 10 |
| Total | 100 |
| 1. Yıl İçinin Başarıya | 50 |
| 1. Final | 50 |
| Total | 100 |
| ECTS - Workload Activity | Quantity | Time (Hours) | Total Workload (Hours) |
|---|---|---|---|
| Course Duration (Including the exam week: 16x Total course hours) | 16 | 4 | 64 |
| Hours for off-the-classroom study (Pre-study, practice) | 16 | 3 | 48 |
| Mid-terms | 1 | 10 | 10 |
| Assignment | 1 | 15 | 15 |
| Quiz | 2 | 12 | 24 |
| Total Workload | 161 | ||
| Total Workload / 25 (Hours) | 6.44 | ||
| dersAKTSKredisi | 6 | ||