Lecture4-3

III.DynamicProgramming:MethodandApplications

Nowweworkwithmodelswhereagentsliveforever(infiniteplanninghorizon).

Anexample:infinitely-livedrepresentativehousehold

max∞󰀆

t=0βtu(c

t)

s.t.c

t+k

t+1=y

t=kα

t∀t,k

0given

DynamicProgramming(DP)isusefultosolvethissortof“recursiveproblem”.

Defineaperiodicreturnfunction:r

t(x

t,u

t).

•r

t(−)isconcave

•x

t:vectorofstatevariables

–statevariablescharacterizetheeconomicsystem’scurrentposition

–statevariablesareoutofthecontrolofanagent(cannotchangeinperiodt)

–statevariablescanbeexogenousvariablesorendogenousvariables

–statevariablesusuallyincludeinformationvariablesthathelppredictthe

future

•u

t:vectorofcontrolvariables(choicevariables)

–controlvariablesareundercontrolofanagent(canchangeinperiodt)

Defineatransitionfunction:g

t(x

t,u

t).

•atransitionfunctionmapsthestateofthemodeltodayintothestatetomorrow

语言学笔记

陈银 2014/3/28

Lecture 4

Pretest

 1. What is phonetics?

 2. Phonetics can be further divided into three main areas, what are they? What do they

study respectively?

 3. What do phonology study? What‟s similarity of and the difference between phonetics

and phonology?

Answer

 1. Phonetics studies how speech sounds are produced, transmitted, and perceived.

 2. They are articulatory, accoustic and auditory phonetics.

 ARTICULATORY PHONETICS studies the production of speech sounds

 ACOUSTIC PHNETICS studies physical properties of sounds produced in speech

 AUDITORY PHONETIC studies perception of speech sounds

 3. Phonology studies the sound patterns and sound systems of languages.

 Similarity: concerned with the speech sounds.

 Differences: Phonetics is strictly physical while phonology also pays attention to the

1 Assignment for Word Skill

1. List as many words you can that make each of the words in the list below

more specific.

go:

walk:

frighten

clothes

beautiful

…

2. Read the following anecdote and answer the questions below it. You may

look up some of the verbs in the dictionary.

A shriveled-up, bowlegged, bent old man requested tree-cutting work from the

foreman.

“Nope,” snapped the foreman.

“But, please,” the old man rattled.

“Go on, get out of here,” the foreman grunted.

“But give me a chance,” the old man whined. His request was so pathetic that

the foreman at last gave in.

“Cut that little tree over there，” he smiled, pointing to a sapling.

He did so at once. “Not so bad,” the burly foreman admitted, “but it’s only a

sapling. Now cut that big one.”

The giant spruce was felled in no time.

1

ECE 303 –Fall 2006 –Farhan Rana –Cornell UniversityLecture 4

Electric Potential

In this lecture you will learn:

•Electric Scalar Potential

•Laplace’s and Poisson’s Equation

•Potential of Some Simple Charge Distributions

ECE 303 –Fall 2006 –Farhan Rana –Cornell UniversityConservative or IrrotationalFields

Irrotationalor Conservative Fields:

Vector fields for which are called “irrotational”or “conservative”fields

Fr0=×∇Fr

•This implies that the line integral of around any closed loop is zeroFr

0.=

∫sdFrr

Equations of Electrostatics:

Recall the equations of electrostatics from a previous lecture:

ρε

=∇E

or

.

0 =×∇Er

⇒In electrostatics or electroquasistatics, the E-field is conservative or irrotational

(But this is not true in electrodynamics)

2

ECE 303 –Fall 2006 –Farhan Rana –Cornell UniversityConservative or IrrotationalFields