differential equations

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differential equations by Mind Map: differential equations

1. applications

2. applications

2.1. misc.

2.2. PDEs in Slime mould

2.3. Chaos, fractals and statistics (Working in the age of Big Data)

3. PDE

4. ODE

4.1. first order linear differential equations

4.1.1. standard linear form y' + p(x)y = q(x)

4.1.2. determine the integrating factor e^(int[p(x)]dx)

4.1.2.1. integrating factor

4.1.3. multiply BOTH sides by integrating factor

4.1.4. integrate

4.2. second order non-homogeneous constant coefficient differential equations

4.2.1. Vocab

4.2.2. roots of the characteristic equation

4.2.2.1. Real roots

4.2.2.2. Repeated roots

4.2.2.3. Complex roots

4.2.3. for non-homogenous... let the RHS have a coefficient and call it Y. To find this coefficient substitute Y into the originial differential (You will need to find Y' and Y''.)

4.2.3.1. sines and cosines

4.2.3.2. exponential

4.2.3.3. polynomial

4.2.3.4. Superposition principle IF Y has sum of these functions, then solve separately and sum them up

4.2.3.4.1. Product principle Write down all the general entities. Then multiply them to find all terms. Then add a coefficient for each.

4.2.4. we can use the polynomial y and its derivative y' to find the constant coefficients (A and B) if we know initial conditions.

5. systems of diffrential equations

5.1. homogenous linear systems

5.2. inhomogenous systems

5.2.1. ...?

5.2.1.1. same method (of undetermined coefficients)?

6. Bernoulli's equation