Applied Mathematics 2270A/B Lecture 1: 1.1 Lecture
28 Sep 2018
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Department
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Def: A differential equation D.E is an equation including an unknown function and it's derivatives
Two types:
Ordinary DE
(ODE)
All derivatives are with respect to a single independent variable
Partial DE (PDE)
Derivatives in the equations are with respect to more than one independent
variable
Definition: The order of a DE is determined by the highest derivative of the unknown function in
the equation
Definition: We can have linear and non-linear ODE's (PDE's as well, but that's next year).
Linear ODE's are linear (power of 1) in the unkonwn function and it's derivative with no cross
terms.
1.1 Lecture
September 10, 2018
9:35 AM
Lecture Notes Page 1
Document Summary
Def: a differential equation d. e is an equation including an unknown function and it"s derivatives. All derivatives are with respect to a single independent variable. Derivatives in the equations are with respect to more than one independent variable. Definition: the order of a de is determined by the highest derivative of the unknown function in the equation. Definition: we can have linear and non-linear ode"s (pde"s as well, but that"s next year). Linear ode"s are linear (power of 1) in the unkonwn function and it"s derivative with no cross terms. So basically, as long as all the unknown functions are to the first power The rest of the function does not matter. In this case the independent variable is not to the first. Because the unknown functions are of order of max 1. Cross terms: it"s when you multiply the function by it"s derivative.
