howto:hambasics:sections:test
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howto:hambasics:sections:test [2021/01/04 22:00] – [Differential Equations] va7fi | howto:hambasics:sections:test [2021/01/06 20:47] – [Differential Equations] va7fi | ||
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<WRAP center round info 80%> | <WRAP center round info 80%> | ||
- | A differential equation is an equation that relates a function to its derivatives in some ways and the question is: given some information about the system, what's the function (or family of functions) that satisfy the differential equation. | + | * A differential equation is an equation that relates a function to its derivatives in some ways and the question is: given some information about the system, what's the function (or family of functions) that satisfy the differential equation. |
- | In physics we often use a dot above the function to indicate a derivative with respect to time, where as in math, we'll often use an apostrophe. | + | * In physics we often use a dot above the function to indicate a derivative with respect to time, where as in math, we'll often use an apostrophe. |
\$$ \dot{x}(t) = x'(t) = \frac{dx}{dt} \quad \text{and} \quad \ddot{x}(t) = x'' | \$$ \dot{x}(t) = x'(t) = \frac{dx}{dt} \quad \text{and} \quad \ddot{x}(t) = x'' | ||
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\$r\$ then: | \$r\$ then: | ||
- | \$$ r = \left\{ \begin{array}{rl} -\alpha \pm \beta & \text{if } b^2 - 4ac > 0,\\ | + | \$$ r = \left\{ \begin{array}{ll} -\alpha \pm \beta & \text{if } b^2 - 4ac > 0,\\ |
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howto/hambasics/sections/test.txt · Last modified: 2021/02/13 19:14 by va7fi