Nevşehir Hacı Bektaş Veli University Course Catalogue
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| Year/Semester of Study | 1 / Spring Semester | ||||
| Level of Course | 1st Cycle Degree Programme | ||||
| Type of Course | Compulsory | ||||
| Department | MATHEMATICS | ||||
| Pre-requisities and Co-requisites | None | ||||
| Mode of Delivery | Face to Face | ||||
| Teaching Period | 14 Weeks | ||||
| Name of Lecturer | ZARİFE ZARARSIZ (zarifezararsiz@nevsehir.edu.tr) | ||||
| Name of Lecturer(s) | ZARİFE ZARARSIZ, | ||||
| Language of Instruction | Turkish | ||||
| Work Placement(s) | None | ||||
| Objectives of the Course | |||||
| The aim of this course is to provide basic skills about indefinite shapes, curve drawings, polar coordinates, definite and indefinite integral concepts and integration methods, applications of integrals, and series topics. | |||||
| Learning Outcomes | PO | MME | |
| The students who succeeded in this course: | |||
| LO-1 | Calculates indefinite integrals using integration techniques. |
PO-2 Have the knowledge to critize, analyze, and evaluate the correctness, reliability, and validity of mathematical data. PO-11 With the knowledge he gain, they determine the learning needs of those working under him, execute the musts of graduate education. |
Examination |
| LO-2 | Understands the integrability of functions in the Riemann sense. |
PO-2 Have the knowledge to critize, analyze, and evaluate the correctness, reliability, and validity of mathematical data. PO-11 With the knowledge he gain, they determine the learning needs of those working under him, execute the musts of graduate education. |
Examination |
| LO-3 | Calculates space, cubage, curve length, surface space, and center of gravity using definite integrals. |
PO-2 Have the knowledge to critize, analyze, and evaluate the correctness, reliability, and validity of mathematical data. PO-11 With the knowledge he gain, they determine the learning needs of those working under him, execute the musts of graduate education. |
Examination |
| LO-4 | Able to use integrals to compute space, arc length, and cubage. |
PO-1 Have the ability to conceptualize the events and facts related to the field of mathematics such as Analysis, Geometry and Algebra with the help of the scientific methods and techniques and can define these concepts. PO-2 Have the knowledge to critize, analyze, and evaluate the correctness, reliability, and validity of mathematical data. PO-3 Define the some models of mathematical problems, evaluate with a critical approach, analyze with theoretical and applied knowledge. PO-11 With the knowledge he gain, they determine the learning needs of those working under him, execute the musts of graduate education. |
Examination |
| LO-5 | By determining the uncertainties in the limiting process, these uncertainties can be resolved. In this way, the limit value can be calculated. |
PO-1 Have the ability to conceptualize the events and facts related to the field of mathematics such as Analysis, Geometry and Algebra with the help of the scientific methods and techniques and can define these concepts. PO-2 Have the knowledge to critize, analyze, and evaluate the correctness, reliability, and validity of mathematical data. |
Examination |
| LO-6 | Express functions with polar coordinates and draw graphs of functions. |
PO-1 Have the ability to conceptualize the events and facts related to the field of mathematics such as Analysis, Geometry and Algebra with the help of the scientific methods and techniques and can define these concepts. PO-2 Have the knowledge to critize, analyze, and evaluate the correctness, reliability, and validity of mathematical data. PO-5 Develop suitable material for a subject on a mathematical area, to use the knowledge and experience gains with different methods PO-11 With the knowledge he gain, they determine the learning needs of those working under him, execute the musts of graduate education. |
Examination |
| LO-7 | By determining the uncertainties in the limiting process, these uncertainties can be resolved. In this way, the limit value can be calculated. |
PO- |
Examination |
| LO-8 | Determine the characters of the series using convergence tests. |
PO-1 Have the ability to conceptualize the events and facts related to the field of mathematics such as Analysis, Geometry and Algebra with the help of the scientific methods and techniques and can define these concepts. PO-2 Have the knowledge to critize, analyze, and evaluate the correctness, reliability, and validity of mathematical data. PO-3 Define the some models of mathematical problems, evaluate with a critical approach, analyze with theoretical and applied knowledge. PO-4 Analytically use the interdisciplinary approach at learning process. PO-11 With the knowledge he gain, they determine the learning needs of those working under him, execute the musts of graduate education. |
Examination |
| PO: Programme Outcomes MME:Method of measurement & Evaluation |
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| Course Contents | ||
| Indefinite expressions, Polar coordinates, Asymptote concept and curve drawing, Graphs of functions of one variable, Differential of a function, Integral concept, Indefinite integral methods of functions of one variable, Partitioning of intervals, Staircase functions, Staircase function integral, Riemann integral, Integration in the sense of Riemann, Area calculation with the help of integral, Arc length, Volume calculation, Area calculation of surfaces of revolution, Series concept and its properties. | ||
| Weekly Course Content | ||
| Week | Subject | Learning Activities and Teaching Methods |
| 1 | Indeterminate Symbols | Oral represantation, questioning - answering, problem solving |
| 2 | Polar Coordinates-Curve drawing | Oral represantation, questioning - answering, problem solving |
| 3 | Indefinite Integrals and Their Properties | Oral represantation, questioning - answering, problem solving |
| 4 | Integration Methods-Change of Variable Method | Oral represantation, questioning - answering, problem solving |
| 5 | Integration Methods-Partial Integration Method-Recurrence Formulas | Oral represantation, questioning - answering, problem solving |
| 6 | Integration Methods-Partial Integration Method-Recurrence Formulas | Oral represantation, questioning - answering, problem solving |
| 7 | Integration Methods - Separating into Simple Fractions-Binomial integral | Oral represantation, questioning - answering, problem solving |
| 8 | mid-term exam | |
| 9 | Definite Integrals and Their Properties, Partitioning of Intervals, Staircase Functions and Integrals, Riemann Integrals | Oral represantation, questioning - answering, problem solving |
| 10 | Definite Integrals and Their Properties, Partitioning of Intervals, Staircase Functions and Integrals, Riemann Integrals | Oral represantation, questioning - answering, problem solving |
| 11 | Calculating space with the help of integral | Oral represantation, questioning - answering, problem solving |
| 12 | Arc length calculation with the help of integral | Oral represantation, questioning - answering, problem solving |
| 13 | Cubage with the help of integral and Calculation of space of surfaces of revolution | Oral represantation, questioning - answering, problem solving |
| 14 | Series Concept and Properties and Tests | Oral represantation, questioning - answering, problem solving |
| 15 | Series Concept and Properties and Tests | oral represantation, questioning - answering, problem solving |
| 16 | final exam | |
| Recommend Course Book / Supplementary Book/Reading | ||
| 1 | Analize Giriş, Giacomo SABAN | |
| 2 | Matematik Analiz I, Mustafa Balcı, Palme Yayınevi. | |
| 3 | Thomas Kalkülüs, G.B. Thomas, M.D. Weir , J.R. Hass, Pearson. | |
| 4 | A Course in Calculus and Real Analysis, S.R. Ghorpade, B.V. Limaye, Springer. | |
| Required Course instruments and materials | ||
| Books, Internet | ||
| Assessment Methods | |||
| Type of Assessment | Week | Hours | Weight(%) |
| mid-term exam | 8 | 2 | 40 |
| Other assessment methods | |||
| 1.Oral Examination | |||
| 2.Quiz | |||
| 3.Laboratory exam | |||
| 4.Presentation | |||
| 5.Report | |||
| 6.Workshop | |||
| 7.Performance Project | |||
| 8.Term Paper | |||
| 9.Project | |||
| final exam | 15 | 2 | 60 |
| Student Work Load | |||
| Type of Work | Weekly Hours | Number of Weeks | Work Load |
| Weekly Course Hours (Theoretical+Practice) | 5 | 14 | 70 |
| Outside Class | |||
| a) Reading | 4 | 5 | 20 |
| b) Search in internet/Library | 3 | 5 | 15 |
| c) Performance Project | 0 | ||
| d) Prepare a workshop/Presentation/Report | 0 | ||
| e) Term paper/Project | 0 | ||
| Oral Examination | 0 | ||
| Quiz | 0 | ||
| Laboratory exam | 0 | ||
| Own study for mid-term exam | 2 | 8 | 16 |
| mid-term exam | 2 | 1 | 2 |
| Own study for final exam | 5 | 5 | 25 |
| final exam | 2 | 1 | 2 |
| 0 | |||
| 0 | |||
| Total work load; | 150 | ||