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Differential Equations by Paul DawkinsFirst Order Differential Equations: Linear Equations, Separable Equations, Exact Equations, Equilibrium Solutions, Modeling Problems.
Second Order Differential Equations: Homogeneous and Nonhomogeneous Second Order Differential Equations, Fundamental Set of Solutions, Undetermined Coefficients, Variation of Parameters, Mechanical Vibrations
Laplace Transforms: Definition, Inverse Transforms, Step Functions, Heaviside Functions, Dirac-Delta Function, Solving IVPs, Nonhomogeneous IVP, Nonconstant Coefficient IVP, Convolution Integral.
Systems of Differential Equations: Matrix Form, Eigenvalues/Eigenvectors, Phase Plane, Nonhomogeneous Systems, Laplace Transforms.
Series Solutions: Series Solutions, Euler Differential Equations.
Higher Order Differential Equations: nth order differential equations, Undetermined Coefficients, Variation of Parameters, 3 x 3 Systems of Differential Equations.
Boundary Value Problems & Fourier Series: Boundary Value Problems, Eigenvalues and Eigenfunctions, Orthogonal Functions, Fourier Sine Series, Fourier Cosine Series, Fourier Series.
Parital Differential Equations: Heat Equation, Wave Equation, Laplaces Equation, Separation of Variables.
These notes assume no prior knowledge of differential equations. A good grasp of Calculus is required however. This includes a working knowledge of differentiation and integration.
Mathematics 3350 – Distance Education
The first special case of first order differential equations that we will look at is the linear first order differential equation. In this case, unlike most of the first order cases that we will look at, we can actually derive a formula for the general solution. The general solution is derived below. However, we would suggest that you do not memorize the formula itself. Instead of memorizing the formula you should memorize and understand the process that I'm going to use to derive the formula.
The first definition that we should cover should be that of differential equation. A differential equation is any equation which contains derivatives, either ordinary derivatives or partial derivatives. To see that this is in fact a differential equation we need to rewrite it a little. The order of a differential equation is the largest derivative present in the differential equation. We will be looking almost exclusively at first and second order differential equations in these notes. A differential equation is called an ordinary differential equation , abbreviated by ode, if it has ordinary derivatives in it. Likewise, a differential equation is called a partial differential equation , abbreviated by pde, if it has partial derivatives in it.
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Prerequisites: C in or equivalent transfer credit, according to existing university regulations. About the Course: This course covers topics in ordinary differential equations. Topics to be covered include: first-order differential equations; modeling with first-order differential equations; higher-order differential equations; modeling with higher-order differential equations; the Laplace transform and application to solving differential equations; power series solutions of differential equations. Zill and Michael R. In such cases students are encouraged to take advantage of a number of helpful sources. We mention several such sources here. There are some web sites that contain useful information to supplement the discussion in the book.