作者duncan2002 (Rn是小狼狗)
看板NTUCHE-02-HW
标题[工数] 胜仕班考试重点提醒 by SSW
时间Tue Oct 26 01:49:53 2010
Check list for Exam 1 of Engineering Mathematics:
Chapter 1
1.
ODE and
PDE
2.
Order, degree of ODE
3.
Linear and
nonlinear
4.
Homogeneous and
non-homogeneous
5. Types of solutions of ODEs:
general solution (G.S.),
particular solution
(P.S.),
singular solution (S.S.)
6. Singular solution and
envelop
7.
Initial Value Problem (IVP) and
boundary value problem (BVP)
8.
Separable type of ODE, separation of variables
9. Types of ODEs that can be converted into separable type of ODEs (
two lines
with intersection, or
two parallel lines)
10.
Exact ODEs: definition of exact, theorem of exact, how to solve exact ODEs
11.
Non-exact: how to
find integrating factor (I.F.), the meaning of I.F.
12.
Standard form of first order, linear ODEs: how to solve?
(3 methods)
13.How to solve
Bernoulli’s equations and
Ricatti equations
14.
Existence and uniqueness of solutions for first order ODEs
15.Modeling the
mixing tanks (conservation of mass)
Chapter 2
1.
Differential operator (D = d/dx) and its properties
2. Definition of
linear combination of functions
3. Definitions of
linearly dependent (L.D.) and
linearly independent (L.I.)
set of functions
4. Definition of
Wronskian determinant (you should also know
Cramer’s rule),
when and why do we need it?
5.
Important theorem of the solution for homogeneous ODEs (what is the
general solution?,
superposition principle)
6.
Important theorem of the solution for non-homogeneous ODEs (what is the
general solution?)
7. The general procedure of
solving any order of non-homogeneous linear ODEs.
8. How to solve the
second or higher order, linear, homogeneous ODEs with
constant coefficients? (
two distinct roots,
repeated roots,
conjugated
roots): (A) Aspect I: try
y = exp(λx) (B) Aspect II: use
differential
operator (D) and the concept from Chapter 1.
9. How many methods can we use to
find the particular solution for any order
of non-homogeneous linear ODEs? (
Undeterminded coefficients,
variation of
parameters,
inverse operator)
Good luck!!
SORRY 我排版有点乱:P
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1F：推 worldbored :胜仕的特色就是说要考什麽就会考什麽 然後一点考古题 10/26 23:31