NAMEPRACTICAL/TUTORIAL GROUP
Unit Course book
Ordinary Differential Equation
Course code:Mth 204 ODE
Unit Coordinator
Nowzad A Ahmed
2012/2013
Soran University
Faculty of Science
Department of Mathematics
Stage 2
Education Aims:
To provide an introduction to ordinary differential equation encompassing applications of ODE, history of ODE, and different techniques to solve ODE. . An understanding of calculus of differential and integrals is essential to many aspects of ODE. The module provides valuable information for the subsequent course partial differential equation.
Learning Outcomes:
* An appreciation of the way in which ordinary differential equation relates to other aspects of mathematics and the natural sciences
* An appreciation of classical techniques for solving different kinds of ODE and their applications in physics, chemistry, and other natural sciences.
* Understand theoretical concepts in ODE and relate these to specific problems in mathematics.
* Being able to work out problems on their own at home
* Undertake practical experiments with Matlab or Maple
* Apply basic knowledge of practical approaches and techniques
Communications with Academic Staff
This handbook gives information on how to contact and communicate with staff.
We provide room numbers and email addresses of staff to you. The staffs in this department want to help you as much as possible so that you will be successful in your programme. We also want to encourage you to take responsibility for yourselves and for your learning so it will help you in your future careers.
The email rules
* Write your email in acceptable English.
* In your emails you must include: full name, stage, department and the unit title.
* We only respond to queries from students using genuine/Soran University email accounts.
* Appointments can be arranged through the email system, if you wish.
* We respond to genuine problems and queries as soon as possible, normally within 7 days.
* We will not respond to emails which do not have a subject line.
Staff associated with the unit:
Staff
Room Number
Email
Farhad Djannaty
Head of Mathematics Dep. Room
fdjanaty@soranu.com
Soran University
Department of Mathematics
Unit: Ordinary Differential Equation
Credit 3
Method of Assessment:
1 x 3 h lectures and 1 h problem solving session.
Examination and grading
Theory (100% of total course marks)
* The average of 4 written examinations/assessments will stand for 35% of the total course marks.
* Written homeworks stands for 5% of the total marks
* A Final examination will stand for the remaining 60% of total course marks.
Marking System
The grades for each piece of assessed work are as follows:
* 90-100 % is excellent
* 80-89% is very good
* 70-79% is good
* 60-69% is a moderate pass
* 50-59% is a pass
* <49% is a fail
Unit Timetable/Content
Academic
Week
Lecture title and content1st weekDefinition of ODE, classification of ODE, solution of ODE in implicit and
Explicit functions, proving related theorems, and solving problems2nd weekDefining homogeneous functions, homogeneous ODE, separable equations,
Non homogeneous equations transferred into homogeneous ODE 3rd weekDefinition of exact equation, necessary and sufficient condition theorem,
Integrating factors in different cases.4th weekProblem solving sessions5th weekIntegrating factors that are a function of x, or y, or xy, or x+y. Integrating
Factors by derivative formulas6th week Answering questions about the first exam.
First examination7th weekFirst order linear equation, solving linear ODE, Bernoulli equation
Problem solving8th weekProblem solving sessions9th weekRiccati equation, application of ODE in Brachistochrone curve and hanging
Chain, and pursuit curve. 10th weekSolving second order equations by reduction of orders in a case where independent variable is not appeared and in a case where dependent variable
Is not appeared11th weekAnswering questions about the second exam
Second examination12th weekSecond order linear ODE and proving seven theorems, introducing Wronskian determinant , the use of a known solution to find another one 13th weekDifferential equations with constant coefficients and their solution. Method of
Undetermined coefficients to solve non homogeneous equations14th weekMethod of variation of parameters to solve non homogeneous differential
Equations of order two and higher. Problem solving15th weekEuler differential equation. Introducing equations in the form of operators
And solving them based on the derivative operator.16th weekProblem solving sessions17th weekAnswering questions about the third exam.
Third examination18th weekIntroducing series and their convergence, radius of convergence, power series, analytical functions and theorems related to analyticity19th weekProblem solving sessions20th weekDefining ordinary points, singular points, and regular singular points, solving
First order equations by power series and solving second order equations by
Power series about ordinary points21st weekSolving second order equations about non ordinary points. Solving Legender
Equation about a regular singular point, cases where both roots are equal22nd weekAnswering questions about the forth exam
Forth examination 23rd week Introducing Bessel differential equation and solving Bessel ODE introducing
Gamma function to solve Bessel ODE in the general case.24th weekBeltrami–klein model, incidence axioms in Klein model, Proving Hilbert axioms in Poincare model, orthogonal lines in this model, inversion in circles.25th weekIntroducing systems of differential equations. Solving systems of linear ODE
Systems by independent methods. Solving systems of general ODE systems by transforming them into one variable ordinary differential equation26th weekIntroducing Laplace transform and Laplace formulas. Solving ordinary
Differential equations by Laplace transforms, Solving systems of ODE by
Laplace transforms.27th weekProblem solving
Fifth examination
References:
1. Simmons, G ,F.; " Differential equations with application and historical
notes" Mc Graw Hill. 1993
2. Coddington, E.A. "An introduction to differential equations", Prentice
Hall, 1961
3. Diacu F. "An introduction to differential equations-order and Choas,
W.H. Freeman and Company, New York 2000
4. Edwards, C.H.. Penny, D.E. "Differential equations and Boundary value problems", 3rd edition, Pearson education, Inc. 2004