ECTS - Single Variable Calculus
Single Variable Calculus (MATH104) Course Detail
| Course Name | Course Code | Season | Lecture Hours | Application Hours | Lab Hours | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| Single Variable Calculus | MATH104 | Diğer Bölümlere Verilen Ders | 3 | 0 | 2 | 4 | 6 |
| Pre-requisite Course(s) |
|---|
| MATH103 General Mathematics |
| Course Language | English |
|---|---|
| Course Type | Service Courses Given to Other Departments |
| Course Level | Bachelor’s Degree (First Cycle) |
| Mode of Delivery | Face To Face |
| Learning and Teaching Strategies | Lecture, Discussion, Question and Answer, Problem Solving. |
| Course Lecturer(s) |
|
| Course Objectives | The objective of this course is to recall and use the functions and their properties, to teach the fundamental operations such as limit, derivative and integral and their applications, also it is aimed to develop the problem solving and analytic thinking skills of the student and to increase their ability to apply problems to real life. |
| Course Learning Outcomes |
The students who succeeded in this course;
|
| Course Content | Review of functions, trigonometric functions, exponential and logarithmic functions, limit and continuity, derivative, applications of the derivative, definite and indefinite integrals, techniques of integration, areas and volumes. |
Weekly Subjects and Releated Preparation Studies
| Week | Subjects | Preparation |
|---|---|---|
| 1 | Review of Functions: Domain, Range of a function; Equal functions; Examples of functions of a real variable, piecewise-defined functions, graphs of functions, sequences, combining functions | pp.34-52 |
| 2 | Inverse Functions: Onto, One-to-one Functions, The Graph of the Inverse Function, Vertical and Horizontal Translations, Even and Odd Functions, Parameterized Curves and Graphs of Functions, Trigonometric functions | pp. 52-75 |
| 3 | The concept of limit, Limit Theorems: One-sided limits, Basic limit theorems, A rule that tells when a limit does not exist, The Pinching Theorem, Some important trigonometric limits, The definition of a continuous function | pp. 85-108 |
| 4 | Continuous Extensions, One-Sided Continuity, Some Theorems about Continuity, Infinite Limits and Asymptotes, Exponential Functions and Logarithms | pp. 108-155 |
| 5 | Rates of Change and Tangent Lines, The Derivative, Rules for Differentiation | pp. 164-200 |
| 6 | Differentiation of Some Basic Functions, The Chain Rule, Derivatives of Exponential Functions, Derivatives of Inverse Functions | pp. 200-223 |
| 7 | Midterm | |
| 8 | Derivatives of Logarithms, Logarithmic Differentiation, Higher Derivatives, Implicit Differentiation, Differentials and Approximation of Functions: Linearization, Differentials | pp. 223-253 |
| 9 | Inverse Trigonometric Functions, Derivatives of Inverse Trigonometric Functions, Related Rates | pp. 253-268,282-289 |
| 10 | The Mean Value Theorem, Maxima and Minima of Functions, Applied Maximum-Minimum Problems | pp. 289-320 |
| 11 | Concavity, Graphing Functions, l’Hopital’s Rule | pp. 320-348 |
| 12 | Antidifferentiation and Applications: Indefinite Integral, Rules for Integration, The Fundamental Theorem of Calculus | pp. 357-366, 399-417 |
| 13 | Integration by Substitution, Calculating of Area, Techniques of Integration: Integration by Parts | pp. 428 - 446, 470-479 |
| 14 | Techniques of Integration: Powers and Products of Trigonometric Functions, Trigonometric Substitution, Partial Fractions—Linear Factors | pp. 479-506 |
| 15 | Techniques of Integration: Partial Fractions—Irreducible Quadratic Factors, Applications of the Integral: Volumes | pp. 506-551 |
Sources
| Course Book | 1. B.E. Blank and S.G. Krantz, Single Variable Calculus, 2.ed., John Wiley & Sons, Inc 2011. |
|---|---|
| Other Sources | 2. J. Stewart, Single Variable Calculus: Early Transcendentals, Brooks Cole, 6 ed., 2007 |
| 3. Matematik II, Atılım Üniversitesi Matematik Bölümü Uzaktan Eğitim Ders Notu |
Evaluation System
| Requirements | Number | Percentage of Grade |
|---|---|---|
| Attendance/Participation | - | - |
| Laboratory | - | - |
| Application | - | - |
| Field Work | - | - |
| Special Course Internship | - | - |
| Quizzes/Studio Critics | - | - |
| Homework Assignments | - | - |
| Presentation | - | - |
| Project | - | - |
| Report | - | - |
| Seminar | - | - |
| Midterms Exams/Midterms Jury | 2 | 60 |
| Final Exam/Final Jury | 1 | 40 |
| Toplam | 3 | 100 |
| Percentage of Semester Work | 60 |
|---|---|
| Percentage of Final Work | 40 |
| Total | 100 |
Course Category
| Core Courses | |
|---|---|
| Major Area Courses | |
| Supportive Courses | |
| Media and Managment Skills Courses | |
| Transferable Skill Courses |
The Relation Between Course Learning Competencies and Program Qualifications
| # | Program Qualifications / Competencies | Level of Contribution | ||||
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | ||
| 1 | Acquires skills to use the advanced theoretical and applied knowledge obtained at the mathematics bachelors program to do further academic and scientific research in both mathematics-based graduate programs and public or private sectors. | |||||
| 2 | Transplants and applies the theoretical and applicable knowledge gained in their field to the secondary education by using suitable tools and devices. | |||||
| 3 | Acquires the skill of choosing, using and improving problem solving techniques which are needed for modeling and solving current problems in mathematics or related fields by using the obtained knowledge and skills. | |||||
| 4 | Acquires analytical thinking and uses time effectively in the process of deduction | |||||
| 5 | Acquires basic software knowledge necessary to work in the computer science related fields and together with the skills to use information technologies effectively. | |||||
| 6 | Obtains the ability to collect data, to analyze, interpret and use statistical methods necessary in decision making processes. | |||||
| 7 | Acquires the level of knowledge to be able to work in the mathematics and related fields and keeps professional knowledge and skills up-to-date with awareness in the importance of lifelong learning. | |||||
| 8 | Takes responsibility in mathematics related areas and has the ability to work affectively either individually or as a member of a team. | |||||
| 9 | Has proficiency in English language and has the ability to communicate with colleagues and to follow the innovations in mathematics and related fields. | |||||
| 10 | Has the ability to communicate ideas with peers supported by qualitative and quantitative data. | |||||
| 11 | Has professional and ethical consciousness and responsibility which takes into account the universal and social dimensions in the process of data collection, interpretation, implementation and declaration of results in mathematics and its applications. | |||||
ECTS/Workload Table
| Activities | Number | Duration (Hours) | Total Workload |
|---|---|---|---|
| Course Hours (Including Exam Week: 16 x Total Hours) | |||
| Laboratory | |||
| Application | 14 | 2 | 28 |
| Special Course Internship | |||
| Field Work | |||
| Study Hours Out of Class | 14 | 3 | 42 |
| Presentation/Seminar Prepration | |||
| Project | |||
| Report | |||
| Homework Assignments | |||
| Quizzes/Studio Critics | |||
| Prepration of Midterm Exams/Midterm Jury | 2 | 10 | 20 |
| Prepration of Final Exams/Final Jury | 1 | 12 | 12 |
| Total Workload | 102 | ||