# Single Variable Calculus (MATH104) Course Detail

Course Name Course Code Season Lecture Hours Application Hours Lab Hours Credit ECTS
Single Variable Calculus MATH104 3 0 2 4 6
Pre-requisite Course(s)
MATH103 General Mathematics
Course Language English N/A Bachelor’s Degree (First Cycle) Face To Face Lecture, Discussion, Question and Answer, Problem Solving. 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. The students who succeeded in this course; use the fundamentals notions of functions, understand limit of a function, understand the derivative and take the derivative of a function, understand the integral and take the integral of a function, understand the applications of the derivative and the integral. 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. 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

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 40 100

### Course Category

Core Courses X

### The Relation Between Course Learning Competencies and Program Qualifications

# Program Qualifications / Competencies Level of Contribution
1 2 3 4 5
1 An ability to apply airframe and powerplant maintenance skills for the candidates to prepare for the EASA JAR 66 certification.
2 To learn the technical terms and concepts in order to communicate verbally and in writing about the maintenance procedures, reports and results.
3 An ability to apply of knowledge and skills in solving aircraft maintenance problems.
4 An ability to understand and apply fundamental sciences and forethoughts the facts and precautions (such as physics).
5 The knowledge of operating principles of aircraft, and fundamental principles of aircraft flight and maintenance.
6 A standard and widespread understanding of professional and ethical responsibility.
7 Knowledge of the importance of the application of maintenance procedures correctly.
8 Knowledge of personal safety.
9 An ability to perform inspection techniques.

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