View source for 12-267/Topic List

Here is a (incomplete) list of subjects covered in MAT267 this semester.

==First-order linear equations==

[http://imgur.com/a/OSx1U#0 Solution techniques]

The brachistochrone

Separable equations

Escape velocities

Changing source and target coordinates

Homogeneous equations

Reverse-engineering separable and exact equations

Solving exact equations with and without integration factors

[http://drorbn.net/index.php?title=12-267/Existence_And_Uniqueness_Theorem Fundamental Theorem and proof]

==Calculus of Variations==

Chain law

Euler-Lagrange, [http://drorbn.net/index.php?title=12-267/Derivation_of_Euler-Lagrange derivation] ([http://graphics.ethz.ch/teaching/former/vc_master_06/Downloads/viscomp-varcalc_6.pdf alternate]) and reductions

Lagrange multipliers

Isoperimetric Inequality

==Numerical methods==

[http://drorbn.net/index.php?title=Numerical_Methods Examples] and derivations

Evaluating local error

==Higher Order Constant Coefficient Homogeneous Linear ODEs==

Multiple roots

Reduction of order

Method of Undetermined Coefficients

==Systems of First-Order Linear Equations==

[http://i.imgur.com/uTugV.jpg Solution techniques]

Matrix exponetiation

Phase portraits

Non-homogeneous systems

==Power-series solutions==

[http://imgur.com/a/sZSYx#0 Quick guide]

Global existence for linear ODEs

Wronskian

Series solutions for y' = f(x,y)

Radius of convergence

==Qualitative Analysis==

[http://drorbn.net/AcademicPensieve/Classes/12-267/QualitativeAnalysis/QualitativeAnalysis.pdf Handout]

Airy's equation

Fuch's Theorem

Regular singular points

[http://drorbn.net/images/0/03/12-267-Frobenius.pdf Frobenius series and Frobenius Method]

The basic oscillation theorem

Non-oscillation theorem

Sturm comparison theorem

Changing the independent variable

Amplitudes of oscillations