Differential Equations (math 1130)
Math 1130 - Differential Equations
Khalid Aref, Associate Professor of Chemical Engineering
College of Engineering/ Al-Muzahmiyah
Office Hours
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Text Book: Differential Equations with Boundary-Value Problems, seventh edition. Dennis G. Zill, Michael R Cullen. Copyright 2009, Brooks/Cole. ISBN-13: 978-0-495-10836-8
GRADING SYSTEM:
First Major Midterm 25%
Second Midterm 25%
Home works and Quizzes 10%
Final Exam: 40%
Total 100%
Exams’ dates and locations will be announced later
Objective: To identify and solve ordinary differential equation using different strategies
Chapter 1: Introduction to Differential Equations(6 lectures)
1.1 Definitions and Terminology
1.2 Initial-Value Problems
1.3 Differential Equations as Mathematical Models
Chapter 2:First order ordinary differential equations (ODE) (8 lectures)
2-1 : Basic concepts: differential equation, ordinary, order, linear, non-linear, solution, homogeneous , non-honogeneous initial value problem .
2-3 : First order Separable ODE, can be made separable.
2-4 : First order Exact ODE ,Test of Exactness, solution , can be made Exact ( Integrating factor ) ,
2-5 : First order Linear ODE, solution (Integrating factor ) can be made Linear ( Bernoulli equation ).
Chapter 3: Second order ODE (8 lectures)
3-1: Homogeneous, non-homogeneous, Linear independence, Basis, general solution, particular solution. Reduction of order: x-missing, y-missing, if one solution is known find another linearly independent solution,
3-2: Homogeneous Linear of constant coefficients, exponential solution, characteristic equation, three cases (two different real roots, one repeated real root, complex roots and Euler formula).
3-5 : Can be made equation with constant coefficients ( Euler- Cauchy equation ) auxiliary equation, solution, Three cases: Two distinct real roots, one repeated real root, complex roots.: Existence and uniqueness, Linear independence , Wronskian.
3-7: Non-homogeneous ODE, general solution of homogeneous + Particular solution of non-homogeneous = general solution of non-homogenous. Finding particular solution using Method of undetermined coefficients.
3-10: Finding Particular solution using Method of variation of parameters.
Chapter 4: Modeling with First-Order Differential Equations(5 lectures)
4.1 Linear Models
4.3 Modeling with Systems of First-Order DEs
Chapter 6 : Series solution of ODE . (5 lectures)
6-1, 6-2 : Review of basic properties of power series. Shifting of index, starting index of the sum, real analytic functions , existing of power series solution, regular points and singular points of a differential equation, Recurrence relation .
6-4 : Solution of ODE near regular singular points, (Frobenius Method), Indicial equation , roots , three cases .
Chapter 7 : Laplace Transform . (8 lectures)
7-1 : Definition of Laplace and inverse of Laplace Transform, Linearity, First shifting theorem, Existence and uniqueness of Laplace transform .
7-2 : Laplace Transform of derivative: Solving initial value problem using Laplace transform.
7-3 : Unit step function ,writing branch functions as a linear combination of functions using unit step function , Second shifting theorem , Solving initial value problems
Containing branch functions.
7-4 : Dirac -function
7-5 : Convolution (optional)