1.1 Some Basic Mathematical Models; Direction Fields
1.2 Solutions of Some Differential Equations
1.3 Classification of Differential Equations
2.1 Linear Equations; Method of Integrating Factor
2.2 Separable equations. Homogeneous equations
2.3 Modeling with First Order Equations
2.4 Differences betweenn linear and nonlinear equations
2.5 Autonomous Equations and Population Dynamics.
2.6 Exact Equations and Integrating Factors.
2.7 Numerical Approximations: Euler's Method
2.9 Some Special Second Order Equations
3.1 Introduction to Second Order Equations.
3.2 Fundamental Solutions. Wronskian
3.3 Complex Roots of the Characteristic Equation
3.4 Repeated Roots. Reduction of Order
3.5 Nonhomogeneous Equations. Method of Undetermined Coefficients
3.6 Nonhomogeneous Equations. Variations of Parameters
3.7 Mechanical and Electrical Vibrations.
4.2 Higher Order Homogeneous Linear Equations with Constant Coefficients
4.4 Variation of Parameters for Higher Order Equations
5.3 Series Solutions near Ordinary Points
6.1 Definition of Laplace Transform
6.2 Solutions of Initial Value Problems
6.3 Step Functions and Important theorems of Laplace Transform
6.4 Differential Equations with Discontinuous Forcing Functions.
6.5 Impulse Functions. The Dirac delta function.
10.5 Separation of Variables. Heat Conduction.
10.6 Other Heat Conduction Problems.
10.7 The Wave Equation . Vibrations of an Elastic String.
7.1,4 First Order Linear System of ODEs
7.5 Homogeneous Linear Systems with Constant Coefficients