Ch3 Part 4 Fundemental Solutions and Abel's Theorem

Dr. Abdelrahim S. Mousa
Assistant Professor of Applied Mathematics
Department of Mathematics
Faculty of Science
Birzeit University
Palestine
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د. عبد الرحيم موسى
دائرة الرياضيات
جامعة بيرزيت
فلسطين
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Ordinary Differential Equations

1.1 Some Basic Mathematical Models and Direction Fields
1.2 Solutions of Some Differential Equations
1.3 Classification of Differential Equations

2.1 Linear Differential Equations and Method of Integrating Factors
2.2 Separable Differential Equations
2.3 Modeling with First Order Equations
2.4 Differences Between Linear and Nonlinear Differential Equations
2.5 Autonomous Differential Equations and Population Dynamics
2.6 Exact Differential Equations and Integrating Factors
2.7 Numerical Approximations and Euler Method
2.8 The Existence and Uniqueness Theorem
2.9 Solving some 2nd order Differential Equations

3.1 Homogeneous Equations with Constant Coefficients
3.2 Solutions of Linear Homogeneous Differential Equations; the Wronskian
3.3 Complex Roots of the Characteristic Equation
3.4 Repeated Roots; Reduction of Order Method
3.5 Nonhomogeneous Differential Equations; Method of Undetermined Coefficients
3.6 Variation of Parameters Method

4.1 General Theory of nth Order Linear Differential Equations
4.2 Homogeneous Differential Equations with Constant Coefficients
4.3 The Method of Undetermined Coefficients
4.4 The Method of Variation of Parameters for Higher Order Linear Differential Equations

5.1 Review of Power Series
5.2 Series Solutions Near an Ordinary Point I
5.3 Series Solutions Near an Ordinary Point II
5.4 Euler Differential Equations and Regular Singular Points
5.5 Series Solutions Near a Regular Singular Point I

6.1 Definition of the Laplace Transform
6.2 Solution of Initial Value Problems
6.3 Step Functions
6.4 Differential Equations with Discontinuous Forcing Functions
6.5 Impulse Functions
6.6 The Convolution Integral

7.5 Homogeneous Linear Systems with Constant Coefficients
7.6 Complex Eigenvalues
7.8 Repeated Eigenvalues