| MATHEMATICS | |||||
| Bachelor | TR-NQF-HE: Level 6 | QF-EHEA: First Cycle | EQF-LLL: Level 6 | ||
| Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
| MAT1002 | Analysis II | Spring | 4 | 2 | 5 | 12 |
| Language of instruction: | English |
| Type of course: | Must Course |
| Course Level: | Bachelor’s Degree (First Cycle) |
| Mode of Delivery: | Face to face |
| Course Coordinator : | Instructor MOHAMED KHALIFA |
| Recommended Optional Program Components: | None |
| Course Objectives: | Upon completion of the course, students will have , a working knowledge of the fundamental definitions and theorems of mathematical analysis, to obtain skills and logical perspectives that prepare them for subsequent courses inside the department, be able to complete routine derivations associated with mathematical analysis, recognize elementary applications of differential and integral calculus, and be literate in the language and notation of mathematical analysis. |
|
The students who have succeeded in this course; 1) be able to calculate upper and lower sums, riemann sums, 2) be able to know the fundamental theorem, 3) be able to derive properties of definite integrals and adapt and apply them when necessary 4) be able to calculate the area, length of curves, 5) be able to derive fundamental inequalities and apply them effectively, 6) be able to calculate the improper integrals, 7) be able to evaluate area and length of curves in polar coordinates 8) be able to compute volume of solids,volumes and areas of surfaces of revolution, in various methods 9) be able to solve the problems involving work, moments and the center of mass, 10) be able to use taylor’s formula, effectively, and estimate for the remainder of elementary functions. 11) be able to calculate limits by using Taylor’s Formula, 12) be able to know convergency tests for series, and apply them effectively, 13) be able to calculate the radius of convergence and find the interval of convergence of a power series, 14) be able to give representations of functions as power series, 15) be able to know fundamental conditions for differentiation and ıntegration of power series, |
| Definite integrals ; upper and lower sums, Riemann sums, the fundamental theorem, Properties of definite integrals, the area, inequalities, Length of curves, the improper integrals, Polar coordinates , Parametric curves, area in polar coordinates, Volume of solids,volumes and areas of surfaces of revolution, Parametric equations, work, Moments and the center of mass, Taylor’s Formula, estimate for the remainder: Trigonometric functions, exponential function, logarithm, Estimate for the remainder: the arctangent, the binomial expension, Limits as an application of Taylor’s Formula, Series, Convergent series,series with positive terms, convergency tests for series , p-series, power series, the radius of covergence and the interval of convergence of a power series, Representation of functions as power series, Differentiation and Integration of power series, Taylor and Maclaurin series, Binomial series,Euler’s identity. |
| Week | Subject | Related Preparation |
| 1) | Indefinite Integrals. | |
| 2) | Trigonometric Integrals, Trigonometric Substitutions, Integration of Rational Functions by Partial Fractions. | |
| 3) | Additional methods of integration. | |
| 4) | Definite integrals ; Riemann sums, upper and lower sums. | |
| 5) | The fundamental theorem, Properties of definite integrals. | |
| 6) | Area, inequalities, Length of curves. Improper integrals. | |
| 7) | Polar coordinates, Parametric curves, area in polar coordinates. | |
| 8) | Volume of solids,volumes and areas of surfaces of revolution, Parametric equations.Work, Moments and the center of mass. | |
| 9) | Taylor’s Formula, estimate for the remainder.Estimating the remainder for Trigonometric functions, exponential function and the logarithm. | |
| 10) | Estimate for the remainder: the arctangent, the binomial expension, Limits as an application of Taylor’s Formula. | |
| 11) | Series, Convergent series,series with positive terms, convergency tests for series. | |
| 12) | p-series, power series, the radius of covergence and the interval of convergence of a power series, | |
| 13) | Representation of functions as power series, Differentiation and Integration of power series, | |
| 14) | Taylor and Maclaurin series, Binomial series,Euler’s identity. |
| Course Notes / Textbooks: | Serge Lang , Undergraduate Analysis, 2nd Ed./Springer Science+Business Media Inc. James Stewart ,Calculus, 5th Ed. Brooks/Cole Publishing Company Serge Lang , A First Course in Calculus, 4th Ed./Springer Science+Business Media Inc. |
| References: | C.H. Edwards,Jr. David E. Penney, Calculus with Analytic Geometry, Prentice- Hall Englewood Cliffs, New Jersey Richard A.Silverman, Calculus with Analytic Geometry, Prentice- Hall Englewood Cliffs, New Jersey |
| Semester Requirements | Number of Activities | Level of Contribution |
| Quizzes | 8 | % 8 |
| Homework Assignments | 1 | % 7 |
| Midterms | 2 | % 30 |
| Final | 1 | % 55 |
| Total | % 100 | |
| PERCENTAGE OF SEMESTER WORK | % 45 | |
| PERCENTAGE OF FINAL WORK | % 55 | |
| Total | % 100 | |
| Activities | Number of Activities | Duration (Hours) | Workload |
| Course Hours | 14 | 4 | 56 |
| Application | 14 | 2 | 28 |
| Study Hours Out of Class | 10 | 8 | 80 |
| Homework Assignments | 1 | 20 | 20 |
| Quizzes | 8 | 2 | 16 |
| Midterms | 2 | 30 | 60 |
| Final | 1 | 30 | 30 |
| Total Workload | 290 | ||
| No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
| Program Outcomes | Level of Contribution | |
| 1) | To have a grasp of basic mathematics, applied mathematics and theories and applications in Mathematics | 5 |
| 2) | To be able to understand and assess mathematical proofs and construct appropriate proofs of their own and also define and analyze problems and to find solutions based on scientific methods, | 5 |
| 3) | To be able to apply mathematics in real life with interdisciplinary approach and to discover their potentials, | 4 |
| 4) | To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself, | 4 |
| 5) | To be able to tell theoretical and technical information easily to both experts in detail and non-experts in basic and comprehensible way, | 4 |
| 6) | To be familiar with computer programs used in the fields of mathematics and to be able to use at least one of them effectively at the European Computer Driving Licence Advanced Level, | 2 |
| 7) | To be able to behave in accordance with social, scientific and ethical values in each step of the projects involved and to be able to introduce and apply projects in terms of civic engagement, | 3 |
| 8) | To be able to evaluate all processes effectively and to have enough awareness about quality management by being conscious and having intellectual background in the universal sense, | 3 |
| 9) | By having a way of abstract thinking, to be able to connect concrete events and to transfer solutions, to be able to design experiments, collect data, and analyze results by scientific methods and to interfere, | 4 |
| 10) | To be able to continue lifelong learning by renewing the knowledge, the abilities and the competencies which have been developed during the program, and being conscious about lifelong learning, | 3 |
| 11) | To be able to adapt and transfer the knowledge gained in the areas of mathematics ; such as algebra, analysis, number theory, mathematical logic, geometry and topology to the level of secondary school, | 4 |
| 12) | To be able to conduct a research either as an individual or as a team member, and to be effective in each related step of the project, to take role in the decision process, to plan and manage the project by using time effectively. | 1 |