Apollonius of Perga
Apollonius of Perga
Apollonius was a great mathematician, known by his contempories as " The
Great
Geometer, " whose treatise Conics is one of the greatest scientific works from
the ancient world.
Most of his other treatise were lost,
Carl Friedrich Gauss was a German mathematician and researcher who
overwhelmed the scientific group amid and after his lifetime. His
exceptional work incorporates the disclosure of the technique for minimum squares,
the revelation of non-Euclidean geom
MA2001N Differential Equations
Lecture Notes for Weeks 7 and 8
[7. Series solutions of 2nd order,
linear, homogeneous odes]
7.
Series solutions of 2nd order, linear, homogeneous odes
Up to now, we have been able to obtain the complete form of certain gene
MA2001N Differential Equations
Lecture Notes for Week 2
[3. 2nd order, linear odes, reducible
to 1st order form]
[4. 2nd order odes with constant
coefficients]
3.
2nd order, linear odes, reducible to 1st order form
3.1
The general solution
Consider the 2n
MA2001N Differential Equations
Lecture Notes for Week 2
[3. 2nd order, linear odes, reducible
to 1st order form]
[4. 2nd order odes with constant
coefficients]
3.
2nd order, linear odes, reducible to 1st order form
3.1
The general solution
Consider the 2n
MA2001N Differential Equations
Lecture Notes for Weeks 9, 10 and 11
[8. Laplace Transforms]
8.
Laplace Transforms
Ordinary differential equations can be solved by using the Laplace Transform
method.
The method works by transforming from the domain of the
MA2001N Differential Equations
Lecture Notes for Weeks 3, 4 and 5
[5.
General 2nd order, linear odes
(including)
5.2 Solution by the general method
of Reduction of Order]
5.
General 2nd order, linear odes
The most general form for a 2nd order, linear ode
MA2001N Differential Equations
Lecture Notes for Week 6
[6. Eulers Equation]
6.
Eulers Equation
Eulers equation takes the following form
x 2 y x y y 0 ,
x0 ,
(76)
where and are constants.
Equation (76) suggests a solution of the form
y xr ,
(77)
where the
MA2001N Differential Equations
Lecture Notes for Week 1
[1. Revision of terminology]
[2. Revision of the solution
of 1st order odes]
1.
Revision of terminology
1.1
What is an Ordinary Differential Equation (or ODE)?
An ordinary differential equation (ode)