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Ders Tanıtım Bilgileri (İngilizce) DERS TANITIM BİLGİLERİ (İNGİLİZCE) Course Information Course Name Single Variable Calculus Code Semester Math 104 Spring Theory Application Laboratuary National ECTS (Saat/Hafta) (Saat/hafta) (hours/week) Credit 3 2 0 4 6 Prequisites Course Language Couse Type Mode of Delivery (face to face, distance learning) Learning and Teaching Strategies Instructor(s) Course Objective Math 103 English Learning Outcomes 1) use the fundamentals notions of functions, 2) understand limit of a function, 3) understand the derivative and take the derivative of a function, 4) understand the integral and take the integral of a function, 5) understand the applications of the derivative and the integral. 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. Course Book B.E. Blank and S.G. Krantz, Single Variable Calculus, 2.ed., John Wiley & Sons, Inc 2011. Other Sources 1) J. Stewart, Single Variable Calculus: Early Transcendentals, Brooks Cole, 6 ed., 2007 2) Matematik II, Atılım Üniversitesi Matematik Bölümü Uzaktan Eğitim Ders Notu References Compulsory Face to face Lecture, Question and Answer, Discussion, 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. 1 Ders Tanıtım Bilgileri (İngilizce) Weekly Course outline Weeks Topics 1. Week 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 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 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 Continuous Extensions, One-Sided Continuity, Some Theorems about Continuity, Infinite Limits and Asymptotes, Exponential Functions and Logarithms Rates of Change and Tangent Lines, The Derivative, Rules for Differentiation Differentiation of Some Basic Functions, The Chain Rule, Derivatives of Exponential Functions, Derivatives of Inverse Functions 2. Week 3. Week 4. Week 5. Week 6. Week Pre-study pp.34-52 pp. 52-75 pp. 85-108 pp. 108-155 pp. 164-200 pp. 200-223 7. Week Midterm 8. Week Derivatives of Logarithms, Logarithmic Differentiation, Higher Derivatives, Implicit Differentiation, Differentials pp. 223-253 and Approximation of Functions: Linearization, Differentials Inverse Trigonometric Functions, Derivatives of Inverse pp. 253-268,282-289 Trigonometric Functions, Related Rates The Mean Value Theorem, Maxima and Minima of pp. 289-320 Functions, Applied Maximum-Minimum Problems 9. Week 10. Week 11. Week Concavity, Graphing Functions, l’Hopital’s Rule 12. Week Antidifferentiation and Applications: Indefinite Integral, Rules for Integration, The Fundamental Theorem of Calculus Integration by Substitution, Calculating of Area, Techniques of Integration: Integration by Parts Techniques of Integration: Powers and Products of Trigonometric Functions, Trigonometric Substitution, Partial Fractions—Linear Factors Techniques of Integration: Partial Fractions—Irreducible Quadratic Factors, Applications of the Integral: Volumes Final Exam 13. Week 14. Week 15. Week 16. Week pp. 320-348 pp. 357-366, 399-417 pp. 428 - 446, 470-479 pp. 479-506 pp. 506-551 2 Ders Tanıtım Bilgileri (İngilizce) Assesment methods Course Activities Number Attendance Laboratory Application Field Activities Specific Practical Training (if any) Assignments Presentation Projects Seminars Midterms Final Exam Percentage % 2 1 60 40 Total 3 100 60 Percentage of semester activities contributing grade success Percentage of final exam contributing grade success 40 100 Total Course Category Core Courses Major Area Courses Supportive Courses Media and Management Skills Courses Transferable Skill Courses Workload and ECTS Calculation Activities Course Duration ( Including Exam Week: 16 x Total Hours) Laboratory Application Specific practical training (if any) Field Activities Study Hours Out of Class (Preliminary work, reinforcement, ect) Presentation / Seminar Preparation Projects Homework assignment Number Duration (Hours) Total Work Load 16 3 48 14 2 28 14 4 56 3 Ders Tanıtım Bilgileri (İngilizce) Midterms ( Study duration ) 2 Final ( Study duration ) 1 Total Workload 13 22 4 26 22 180 Matrix of the Course Learning Outcomes Versus Program Outcomes Program Outcomes 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. Contribution Level* 1 2 3 4 5 Ders Tanıtım Bilgileri (İngilizce) 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. 1: Lowest, 2: Low, 3: Average, 4: High, 5: Highest 5