| MATHEMATICS | |||||
| Bachelor | TR-NQF-HE: Level 6 | QF-EHEA: First Cycle | EQF-LLL: Level 6 | ||
| Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
| MAT1001 | Analysis I | Fall | 4 | 2 | 5 | 11 |
| The course opens with the approval of the Department at the beginning of each semester |
| Language of instruction: | En |
| Type of course: | Must Course |
| Course Level: | Bachelor |
| Mode of Delivery: | Face to face |
| Course Coordinator : | Instructor MOHAMED KHALIFA |
| 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 explain reason for the ordering on real numbers, and also on the real axis 2) be able to evaluate limits by using the definition of limit of a function and test continuity of functions, know the properties of real number sequences, and calculate their limits 3) be able to calculate derivatives of functions 5) be able to solve the problems about the rate of changes, 6) be able to explain Mean Value Theorem and its results, 7) be able to evaluate limits of Indeterminate Forms by using L'Hopital's Rule, 8) be able to interpret successive derivations of a function, determines increasing and decreasing regions for a function and decide on convexity of its graph, 9) be able to sketch the graph of a function, 10) be able to solve applied maximum and minimum problems, 11) be able to test the existency of Inverse functions and calculate their derivatives, 12) be able to test the existency of Inverse trigonometric functions and calculate their derivatives, 13) be able to define exponential functions, Natural Logarithms, hyperbolic functions, obtain their fundamental properties, sketch the graphs of them be able to compute basic indefinite integrals by using their specific integration techniques |
| Sets and Mappings, Real Numbers, functions,Limits, sequences, Continuous Functions, Differentiation, Applications of Derivatives, rate of change, The Mean Value Theorem, Indeterminate Forms and L'Hopital's Rule,convexity, Curve Sketching, Applied Optimization, Inverse Functions and Their Derivatives, Inverse Trigonometric Functions,Exponential Functions, Natural Logarithms, Hyperbolic Functions, Indefinite Integrals,antiderivatives, Techniques of Integration. |
| Week | Subject | Related Preparation | |
| 1) | Sets and Mappings, Natural Numbers and Induction. | ||
| 2) | Real Numbers, Algebraic Axioms, Ordering Axioms, Integers and Rational Numbers, The Completeness Axiom, Relations and functions. | ||
| 3) | Limits , Limit of a function and limit theorems,One sided limits, Limits involving infinity. Sequnces and their limits. | ||
| 4) | Continuous Functions,properties of Continuous Functions, Continuous Functions on a closed interval,the intermediate value theorem, continiuty of Composite functions. | ||
| 5) | Differentiation, Tangents and the Derivative at a Point, The Derivative as a Function, Differentiation rules. | ||
| 6) | The Derivative as a Rate of Change and applications. | ||
| 7) | The Chain Rule, Implicit Differentiation, Related Rates. | ||
| 8) | The mean value theorem and its results; Extreme Values of Functions, critical points, the First Derivative Test, Cauchy mean value theorem, Indeterminate Forms and L'Hopital's Rule | ||
| 9) | Convexity, second derivative test and Curve Sketching, Applied Optimization. | ||
| 10) | Inverse Functions and Their Derivatives,arcsin, arccos, arctg functions and their graphs. | ||
| 11) | Exponential Functions; Definition and fundamental properties of exponential function. | ||
| 12) | Natural Logarithms, Hyperbolic Functions, Relative Rates of Growth. | ||
| 13) | Indefinite Integrals ,antiderivatives, Techniques of Integration, The Substitution Rule, Integration by Parts. | ||
| 14) | Summary of the course topics, directions and notices for the final exam. | ||
| Course Notes: | Serge Lang , Undergraduate Analysis, 2nd Ed./Springer Science+Business Media Inc. Walter Rudin, Principles Of Mathematical Analysis, 3rd Ed. 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 |
| Attendance | % 0 | |
| Laboratory | % 0 | |
| Application | % 0 | |
| Field Work | % 0 | |
| Special Course Internship (Work Placement) | % 0 | |
| Quizzes | % 0 | |
| Homework Assignments | % 0 | |
| Presentation | % 0 | |
| Project | % 0 | |
| Seminar | % 0 | |
| Midterms | 2 | % 45 |
| Preliminary Jury | % 0 | |
| Final | 1 | % 55 |
| Paper Submission | % 0 | |
| Jury | % 0 | |
| Bütünleme | % 0 | |
| 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 |
| Laboratory | 0 | 0 | 0 |
| Application | 14 | 2 | 28 |
| Special Course Internship (Work Placement) | 0 | 0 | 0 |
| Field Work | 0 | 0 | 0 |
| Study Hours Out of Class | 14 | 7 | 98 |
| Presentations / Seminar | 0 | 0 | 0 |
| Project | 0 | 0 | 0 |
| Homework Assignments | 0 | 0 | 0 |
| Quizzes | 0 | 0 | 0 |
| Preliminary Jury | 0 | 0 | 0 |
| Midterms | 2 | 30 | 60 |
| Paper Submission | 0 | 0 | 0 |
| Jury | 0 | 0 | 0 |
| Final | 1 | 30 | 30 |
| Total Workload | 272 | ||
| No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
| Program Outcomes | Level of Contribution |