12-267/Topic List: Difference between revisions
No edit summary |
(Added some links, improved formatting) |
||
| Line 1: | Line 1: | ||
Here is a (incomplete) list of subjects covered in MAT267 this semester. |
Here is a (incomplete) list of subjects covered in MAT267 this semester. |
||
| ⚫ | |||
| ⚫ | |||
[http://imgur.com/a/OSx1U#0 Solution techniques] |
|||
| ⚫ | |||
| ⚫ | |||
Separable equations |
Separable equations |
||
| Line 18: | Line 20: | ||
[http://drorbn.net/index.php?title=12-267/Existence_And_Uniqueness_Theorem Fundamental Theorem and proof] |
[http://drorbn.net/index.php?title=12-267/Existence_And_Uniqueness_Theorem Fundamental Theorem and proof] |
||
==Calculus of Variations== |
|||
Chain law |
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 |
|||
Variational problems |
|||
Euler-Lagrange, derivation and reductions |
|||
Lagrange multipliers |
Lagrange multipliers |
||
| Line 29: | Line 31: | ||
Isoperimetric Inequality |
Isoperimetric Inequality |
||
==Numerical methods== |
|||
[http://drorbn.net/index.php?title=Numerical_Methods Examples] and derivations |
|||
Evaluating local error |
Evaluating local error |
||
Higher |
==Higher Order Constant Coefficient Homogeneous Linear ODEs== |
||
Multiple roots |
Multiple roots |
||
| Line 41: | Line 45: | ||
Method of Undetermined Coefficients |
Method of Undetermined Coefficients |
||
Systems of |
==Systems of First-Order Linear Equations== |
||
[http://i.imgur.com/uTugV.jpg Solution techniques] |
|||
Matrix exponetiation |
Matrix exponetiation |
||
| Line 49: | Line 55: | ||
Non-homogeneous systems |
Non-homogeneous systems |
||
Power-series solutions |
==Power-series solutions== |
||
[http://imgur.com/a/sZSYx#0 Quick guide] |
|||
Global existence for linear ODEs |
Global existence for linear ODEs |
||
| Line 58: | Line 66: | ||
Radius of convergence |
Radius of convergence |
||
==Qualitative Analysis== |
|||
Airy's equation |
Airy's equation |
||
Revision as of 21:03, 10 December 2012
Here is a (incomplete) list of subjects covered in MAT267 this semester.
First-order linear equations
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
Calculus of Variations
Chain law
Euler-Lagrange, derivation (alternate) and reductions
Lagrange multipliers
Isoperimetric Inequality
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
Matrix exponetiation
Phase portraits
Non-homogeneous systems
Power-series solutions
Global existence for linear ODEs
Wronskian
Series solutions for y' = f(x,y)
Radius of convergence
Qualitative Analysis
Airy's equation
Fuch's Theorem
Regular singular points
Frobenius series and Frobenius Method
The basic oscillation theorem
Non-oscillation theorem
Sturm comparison theorem
Changing the independent variable
Amplitudes of oscillations
