University :Mansoura University |
Faculty :Faculty of Science |
Department :Mathematics Department |
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| 1- Course data :- |
| | Code: | 11216 | | Course title: | تفاضل عالى ومعادلات تفاضلية | | Year/Level: | ثانية رياضه | | Program Title: | | | Specialization: | | | Teaching Hours: | Theoretical: | 4 | Tutorial: | 3 | Practical: | |
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| 2- Course aims :- |
| - The course provides an overview of standard methods for the solution of single ordinary differential equations and systems of equations, with an introduction to some of the underlying theory and calculus of functions of more than one variable.
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| 3- Course Learning Outcomes :- |
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| 4- Course contents :- |
| | No | Topics | Week |
|---|
| 1 | First Order Differential Equations :Linear equations with constant coefficients, Homogeneous equations, Exact equations and integrating factors, Riccati equations | | | 2 | Second Order Differential Equations: Homogeneous equations with constant coefficients, Fundamental solutions of linear homogeneous equations, Linear independence and the Wronskian (including Abel | | | 3 | Reduction of order and reduction to the normal form, Nonhomogeneous equations,Method of undetermined coefficients,Variation of parameters | | | 4 | Laplace transformation: Definition of the Laplace transform, Solutions of initial value problems by , Laplace transformation and ,inverse of laplace transformation ,the unit Step functions, First and second shift theorems, Convolution theorem | | | 5 | Series solutions of 2nd-order linear differential eq | | | 6 | Function of several variables, Partial differentiation .Continuity, differentiability, and the chain rule. | | | 7 | Taylor Theorem | | | 8 | Multiple integrals, Line integral, Elliptic integral | | | 9 | Line integral, Green’s Theorem, Elliptic integrals | |
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| 5- Teaching and learning methods :- |
| | S | Method |
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| 4 4houre lecture and 3 hours tutorials |
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| 6- Teaching and learning methods of disables :- |
| - all students are normal due to the nature of study
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| 7- Student assessment :- |
| A. Timing |
| | No | Method | Week |
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| 1 | Oral Examination | 14 | | 2 | Final_Term Examination | 15 |
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| B. Degree |
| | No | Method | Degree |
|---|
| 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 | http://www.sosmath.com/diffeq/diffeq.html | | | 2 | Avaliable in the Dept | | | 3 | C. H Edwards, Elementary differential equations with boundary value problems, Pearson Prentice Hall, 2004 | | | 4 | W.E. Boyce & R.C. Di Prima, "Elementary Differential Equations and Boundary Value Problems", Wiley | | | 5 | M. Braun, "Differential Equations and their Applications", Springer-Verlag. | | | 6 | C.H. Edwards & D.E. Penney, "Elementary Differential Equations with Boundary Value Problems", Prentice Hall. | | | 7 | R.K. Nagle & E.B. Saff, & A.D. Snider, "Fundamentals of Differential Equations and Boundary Value Problems", Addison-Wesley. | |
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| 9- Matrix of knowledge and skills of the course |
| | S | Content | Study week |
|---|
| First Order Differential Equations :Linear equations with constant coefficients, Homogeneous equations, Exact equations and integrating factors, Riccati equations | | | Second Order Differential Equations: Homogeneous equations with constant coefficients, Fundamental solutions of linear homogeneous equations, Linear independence and the Wronskian (including Abel | | | Reduction of order and reduction to the normal form, Nonhomogeneous equations,Method of undetermined coefficients,Variation of parameters | | | Laplace transformation: Definition of the Laplace transform, Solutions of initial value problems by , Laplace transformation and ,inverse of laplace transformation ,the unit Step functions, First and second shift theorems, Convolution theorem | | | Series solutions of 2nd-order linear differential eq | | | Function of several variables, Partial differentiation .Continuity, differentiability, and the chain rule. | | | Taylor Theorem | | | Multiple integrals, Line integral, Elliptic integral | | | Line integral, Green’s Theorem, Elliptic integrals | |
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| Course Coordinator(s): - |
| - Mohamed Kamal Abd Elsalam Auf Elkasar
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| Head of department: - |
| Ahmed Habeb Mohamed Nageb Elbassiony |
