Appendix D. List of Symbols
The following table defines the notation used in this book. References point to the first appearance of each symbol.
| Symbol | Description | Location |
|---|---|---|
| \(C\) | arbitrary constant of integration | Paragraph |
| \(\mu(x)\) | integrating factor | Paragraph |
| \(h\) | step size in Euler’s method | Paragraph |
| \(y(t_N)\) | exact solution value at the final step | 📙 Definition 132 |
| \(y_N\) | Euler approximation at the final step | 📙 Definition 132 |
| \(\tilde{y}_{k+1}\) | Improved Euler predictor value | 📙 Definition 135 |
| \(r\) | root of the characteristic equation | Paragraph |
| \(y_p\) | particular solution | Paragraph |
| \(y_h\) | homogeneous solution | Paragraph |
| \(\lap{f(t)}\) | the Laplace transform operator applied to a function | 📙 Definition 195 |
| \(F(s)\) | the Laplace transform of a function, in the s-domain | 📙 Definition 195 |
| \(\laplacesym^{-1}\) | inverse Laplace transform | Paragraph |
| \(u_c(t)\) | shifted unit step function | Paragraph |
| \(\vec{X}\) | state vector of a linear system | Paragraph |
| \(A\) | coefficient matrix of a linear system | Paragraph |
| \(\vec{v}\) | eigenvector of the coefficient matrix | Paragraph |
| \(f(x,y)\) | right-hand side of the first equation of a system | 📙 Definition 316 |
| \(g(x,y)\) | right-hand side of the second equation of a system | 📙 Definition 316 |
| \((x^*, y^*)\) | equilibrium point of a system | 📙 Definition 317 |
| \(J\) | Jacobian matrix of a nonlinear system | 📙 Definition 325 |
- DE implies ODE
-
Since this text only covers ordinary differential equations, any use of DE will always imply ODE.
- Derivative Notation
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We will use the following notations for derivatives:
Derivative Order 1st 2nd 3rd 4th \(...\) nth Prime \(y^\prime\) \(y^{\prime\prime}\) \(y^{\prime\prime\prime}\) \(y^{(4)}\) \(...\) \(y^{(n)}\) Leibniz \(\ds\frac{dy}{dx}\) \(\ds\frac{d^2y}{dx^2}\) \(\ds\frac{d^3y}{dx^3}\) \(\ds\frac{d^4y}{dx^4}\) \(...\) \(\ds\frac{d^ny}{dx^n}\)
