University :Mansoura University |
Faculty :Faculty of Science |
Department :Physics Department |
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| 1- Course data :- |
| | Code: | 41119 | | Course title: | تفاضل وتكامل - جبر وهندسة | | Year/Level: | أولى بيولوجى | | Program Title: | | | Specialization: | | | Teaching Hours: | Theoretical: | 4 | Tutorial: | 4 | Practical: | |
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| 2- Course aims :- |
| - The programme unit aims to provide a firm foundation in the concepts and techniques of the calculus, including real numbers, standard functions, curve sketching, limits, continuity, differentiation, integration of functions of one variable. The core concepts of limits, differentiation and integration are revised. Techniques for applying the calculus are developed and strongly reinforced. Also, the aims of this course are to provide a basic introduction to various methods of proof used in mathematics and to the fundamental ideas in the study of sets, numbers, functions and conic sections. This course is basic course for biologically students and other students.
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| 3- Course Learning Outcomes :- |
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| 4- Course contents :- |
| | No | Topics | Week |
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| 1 | Differention: Functions. Limits and continuity. | | | 2 | Differentiation: (Basic ideas; tangent to a curve; the product and quotient rule; the chain rule for differentiating f(g(x)); higher derivatives, implicit differentiation) | | | 3 | Derivatives of trigonometric functions and their inverse. Derivatives of the log function ln; the exponential function exp and ax. | | | 4 | Derivatives of hyperbolic functions and their inverse. Applications of derivatives | | | 5 | Integration: Integration | | | 6 | Techniques of Integration: (Integration by substitution-Integration of trigonometric and hyperbolic functions - Integration of parts - Integration of rational functions by partial fractions- Integration of parameter dependent functions) | | | 7 | Applications of Integration | | | 8 | Algebra: sets. | | | 9 | Determinants – matrices | | | 10 | mathematical induction. Partial fractions . Geometry: Translation and Rotation of Axes, | | | 11 | complex numbers. Pairs of Straight Lines | | | 12 | Conic Sections | |
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| 5- Teaching and learning methods :- |
| | S | Method |
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| Lectures (4H/W). | | Tutorial (4H/w). |
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| 6- Teaching and learning methods of disables :- |
| - The same as normal students, only skeletal disabilities are allowed in the Faculty of Science.
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| 7- Student assessment :- |
| A. Timing |
| | No | Method | Week |
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| 1 | final exam | 14 | | 2 | oral exam | 14 |
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| B. Degree |
| | No | Method | Degree |
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| 1 | Mid_term examination | 0 | | 2 | Final_term examination | 90 | | 3 | Oral examination | 10 | | 4 | Practical examination | 0 | | 5 | Semester work | 0 | | 6 | Other types of asessment | 0 | | Total | 100% |
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| 8- List of books and references |
| | S | Item | Type |
|---|
| 1 | Course Notes: Available in the Dept. | | | 2 | H Edwards, Elementary differential equations with boundary value problems, Pearson Prentice Hall, 2004. | | | 3 | H. Anton, Elementary Linear Algebra, Wiley 1994. Linear Algebra, by Seymour Lip schuts. | | | 4 | 1- W.E. Boyce & R.C. Di Prima, "Elementary Differential Equations and Boundary Value Problems", Wiley. 2- M. Braun, "Differential Equations and their Applications", Springer-Verlag | | | 5 | C.H. Edwards & D.E. Penney, "Elementary Differential Equations with Boundary Value Problems", Prentice Hall. | | | 6 | 5- R.K. Nagle & E.B. Saff, & A.D. Snider, "Fundamentals of Differential Equations and Boundary Value Problems", Addison-Wesley. | | | 7 | 1- http://en.wikipedia.org/wiki/Calculus 2- http://www.math.niu.edu/~beachy/aaol / 3- http://www.sosmath.com/calculus/calculus.html | |
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| 9- Matrix of knowledge and skills of the course |
| | S | Content | Study week |
|---|
| Differention: Functions. Limits and continuity. | | | Differentiation: (Basic ideas; tangent to a curve; the product and quotient rule; the chain rule for differentiating f(g(x)); higher derivatives, implicit differentiation) | | | Derivatives of trigonometric functions and their inverse. Derivatives of the log function ln; the exponential function exp and ax. | | | Derivatives of hyperbolic functions and their inverse. Applications of derivatives | | | Integration: Integration | | | Techniques of Integration: (Integration by substitution-Integration of trigonometric and hyperbolic functions - Integration of parts - Integration of rational functions by partial fractions- Integration of parameter dependent functions) | | | Applications of Integration | | | Algebra: sets. | | | Determinants – matrices | | | mathematical induction. Partial fractions . Geometry: Translation and Rotation of Axes, | | | complex numbers. Pairs of Straight Lines | | | Conic Sections | |
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| Course Coordinator(s): - |
| - Ahmed Sadeq Omar Hegazy
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| Head of department: - |
| Ahmed Habeb Mohamed Nageb Elbassiony |
