Calculus Cheat Sheet
Calculus Cheat Sheet
Limits
Definitions Precise Definition : We say lim f ( x ) = L if Limit at Infinity : We say lim f ( x ) = L if we
x a x
for every e > 0 there is a d > 0 such that whenever 0 < x - a < d then f ( x ) - L < e . Wo
Systems of Differential Equations
S. Bonnot
S. Bonnot
Systems of Differential Equations
Examples coming from physics
Goal: Physical systems where separate parts interact on each other create automatically systems of differential equations. Example: a syst
Suggested Problems for Week 1 and 2
1 First Order equations
1. Solve the equation y = 6y on (, +) 2. Solve y = 5y with the initial condition y (0) = 12. 3. Make a change of variables in order to solve y + 17y = 0. 4. The population of a city grows at a ra
MAT 212 - Midterm Exam
February 23, 2010.
Name: Student Id:
1.
(15) If a, b and c are > 0, show that every solution y (t) of ay + by + cy = 0 is such that limt+ y (t) = 0 (5) Give one example of a linear second order equation for which y (t) = 0 (constan
Method of Variation of parameters
S. Bonnot
February 15, 2011
S. Bonnot
Method of Variation of parameters
Setting of the method
Goal: Find a particular solution for y + p(t ).y + q (t ).y = g (t ) where the right-hand side can be an arbitrary continuous f