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| First order equations methods - Direct integrations and Separation of variables |
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Definition
Direct Integration: A regular integration.
[image]
Separation of Variables: Rearranging and integrating.
[image] |
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| First order equations methods - Integrating factor |
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Definition
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| First order equations methods - Equations reducible to the separable form |
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Definition
[image]
Simply a substitution of u = y/x. |
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| What are linear and homogeneous equations? |
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Definition
A linear equation is one in which the dependent variable, y, and its derivatives appear only as a linear
combination.
A homogeneous equation is one which has no functions of the
independent variable appearing on its own (or simply, ‘the
right-hand side is zero’).
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| Linear Homogeneous second order differential equations. |
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Definition
Distinct Real Roots:
[image]
Complex Roots:
[image]
Repeated Roots:
[image] |
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Term
| Non-Homogeneous Second-Order ODEs |
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Definition
[image]
Particular Integrals in Formula Book |
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Term
| When the right side of the Differential equation has the same form as part of the complementary function: |
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Definition
| Utilise a different Particular Integral from the formula booklet. |
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Term
Modelling Differential elements:
1. Draw Diagram
2. Balance forces/energy to create ODE
3. Solve ODE |
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Definition
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Term
| Homogeneous Linear Difference equations |
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Definition
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Term
| Non-Homogeneous Linear Difference equations |
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Definition
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Term
| Partial derivative with respect to x and y |
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Definition
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Term
Linearisation of partial derivatives.
What happens when the small changes in x and y tend to zero? |
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Definition
[image]
When they tend to zero you get a TOTAL DIFFERENTIAL: [image] |
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Term
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Definition
Rate of change of f when we move in the direction u = (a,b), where u is a unit vector.
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Term
| Partial Derivatives Chain Rule |
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Definition
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Term
| Normal vector to a curve/surface |
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Definition
| Not really sure what to do with this, ignore until you find a question on it or ask in a suppo. |
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