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| MAT 128 | Analysis - II | 4+2+0 | ECTS:10 | | Year / Semester | Spring Semester | | Level of Course | First Cycle | | Status | Compulsory | | Department | DEPARTMENT of MATHEMATICS | | Prerequisites and co-requisites | None | | Mode of Delivery | Face to face, Practical | | Contact Hours | 14 weeks - 4 hours of lectures and 2 hours of practicals per week | | Lecturer | Doç. Dr. Ali Hikmet DEĞER | | Co-Lecturer | | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | The course aims to teach the students indefinite integrals, definite integrals in sense of Darboux-Riemann-Stieltjes , and to give some applications of definite integrals such as calculations lengths of curves in the plane and three dimensional space, areas and volumes of some geometric figures in in the plane and the three dimensional space. |
| Learning Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | LO - 1 : | Use both the definition of derivative as a limit and the rules of differentiation to differentiate functions.
| 1,2,3,4,5,6,7,8 | 1,3,6 | | LO - 2 : | sketch the graph of a function using asymptotes, critical points, and the derivative test for increasing/decreasing and concavity properties. | 1,2,3,4,5,6,7,8 | 1,3,6 | | LO - 3 : | set up max/min problems and use differentiation to solve them. | 1,2,3,4,5,6,7,8 | 1,3,6 | | LO - 4 : | evaluate integrals by using the Fundamental Theorem of Calculus.
| 1,2,3,4,5,6,7,8 | 1,3,6 | | LO - 5 : | apply integration to compute areas and volumes by slicing, volumes of revolution, arclength, and surface areas of revolution. | 1,2,3,4,5,6,7,8 | 1,3,6 | | LO - 6 : | Evaluate integrals using some techniques of integration, such as substitution, inverse substitution, partial fractions and integration by parts, | 1,2,3,4,5,6,7,8 | 1,3,6 | | LO - 7 : | use L'Hospital's rule, | 1,2,3,4,5,6,7,8 | 1,3,6 | | LO - 8 : | find the Taylor series expansion of a function near a point, with emphasis on the first two or three terms,
| 1,2,3,4,5,6,7,8 | 1,3,6 | | LO - 9 : | determine convergence/divergence of improper integrals, and evaluate convergent improper integrals.
| 1,2,3,4,5,6,7,8 | 1,3,6 | | LO - 10 : | gather some knowlege about Fourier seies and caltulate the Fourier series some functions. | 1,2,3,4,5,6,7,8 | 1,3,6 | | CTPO : Contribution to programme outcomes, TOA :Type of assessment (1: written exam, 2: Oral exam, 3: Homework assignment, 4: Laboratory exercise/exam, 5: Seminar / presentation, 6: Term paper), LO : Learning Outcome | | |
| Derivation, Taylor Polynomials of differentiable functions, Maximum and Minimun problems of real valued differentiable functions of one real variable, Indefinite integrals and Calculation Methods , Darboux-Riemann-Stieltjes Integrals, Fundamental Theorems of Integral Calculus, Applications of Riemannian integrals, Function Sequences and Series, Fourier Series, Generalized Riemann Integrals. |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Differentiable functions of one real variable and real valued,
| | | Week 2 | Chain rule for differentiation ,
| | | Week 3 | Mean value theorems,
| | | Week 4 | Power series and elementary functions,
| | | Week 5 | L'Hospital's rule, Taylor's Formula, Taylor series, | | | Week 6 | Extremum and critical points of one real variable and real valued differential functions, | | | Week 7 | Darboux sums ,Darboux Integrals, the integrability criterion, | | | Week 8 | Riemann sums, Riemann Integrals, and the integrability criterion | | | Week 9 | Mid-term exam
| | | Week 10 | Riemann-Stieltjes integral, | | | Week 11 | Properties of the integral,
| | | Week 12 | The fundamental theorems of Calculus ,
| | | Week 13 | Applications of the Integral,
| | | Week 14 | Interchanging limit processes, Negative examples,Uniform convergence, | | | Week 15 | Uniform convergence and continuity, uniform convergence and integration, | | | Week 16 | End-of-term exam | | | |
| 1 | Kenneth A. Ross.1980; Elementary Analysis : The Theory of Calculus, Springer-Verlag | | | |
| 1 | Gaughan,Edward D. 1998; Introduction to Analysis , Springer Verlag -Undergraduate Series in Mathematics ,5th edition | | | 2 | Rudin,Walter.1976; Principles of Mathematical Analysis,3rdEdition,McGraw-Hill | | | 3 | Howie,John M. 2006; Real Analysis , Springer Verlag -Undergraduate Series in Mathematics ,3rd edition | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 08/04/2014 | 2 | 50 | | End-of-term exam | 16 | 04/06/2014 | 2 | 50 | | |
| Student Work Load and its Distribution | | Type of work | Duration (hours pw) | No of weeks / Number of activity | Hours in total per term | | Yüz yüze eğitim | 4 | 14 | 56 | | Sınıf dışı çalışma | 7 | 14 | 98 | | Arasınav için hazırlık | 10 | 1 | 10 | | Arasınav | 2 | 1 | 2 | | Uygulama | 2 | 14 | 28 | | Ödev | 10 | 1 | 10 | | Kısa sınav | 2 | 1 | 2 | | Dönem sonu sınavı için hazırlık | 12 | 1 | 12 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 220 |
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