Diffusion: Read Plummer Chap. 7, sections 7.1-7.4,, 7.53, 7.5.8 Show that c(zt) Wroexpfzla)I,with a=2VDf, is a solution to Fick's second law of diffusion. ac(z, t) dc(zt) 2. a) What is the intrinsic carrier concentration in Si at 1100 C? b) Calculate the effective diffusivity (including first-order, charged-vacancy corrections)for As impurities in Si at 1100 C for two cases: 1)CAs=10 cm and ii)

Introduction to Probability Probability is the last topic in this course and perhaps the most important. Many Igorithms rely on randomization. Investigating their correctness and performance re- quires probability theory. Moreover, many aspects of computer systems, such as memory

Guessing a particular solution. Recall that a general linear recurrence has the form: f(n)=a1f(n-1)+a2f(n-2)+…+aaf(n-d)+g(n) As explained in lecture, one step in solving this recurrence is finding a particular solu- tion; i.e., a function f(n)that satisfies the recurrence, but may not be consistent with the boundary conditions. Here's a recipe to help you guess a particular solution:

Problem set 2 Solutions Due: Monday, February 14 at 9 PM Problem 1. Use induction to prove that n/n for alln olution. The proof is by induction on n. Let P(n) be the proposition that the equation Base case. P(2 )is true because Inductive step. Assume P(n)is true. Then we can prove P(n +1)is also true as follows

Vitamins are organic chemicals required by the body in trace amounts but which cannot be synthesized by the body. The vitamins required for growth and maintenance of health differ between species; compounds regarded as vitamins for one species may be synthesized at adequate rates by other species. For example, only primates and the guinea-pig require ascorbic acid (vitamin C; section 6.4) from their diet; other species possess the enzyme gluconolactone oxidase which is necessary for the synthesis of vitamin C from D-glucose or D-galactose

Like all other foods of plant or animal origin, milk contains several indigenous enzymes which are constituents of the milk as secreted. The principal constituents of milk (lactose, lipids and proteins) can be modified by exogenous enzymes, added to induce specific changes. Exogenous en- zymes may also be used to analyse for certain constituents in milk. In addition, milk and most dairy products

Bob, a student taking 7.012, looks at a long-standing puddle outside his dorm window Curious as to what was growing in the cloudy water, he takes a sample to his TA, Brad Student. He wanted to know whether the organisms in the sample were prokaryotic or eukaryotic

Types of market efficiency The weak-form of efficiency: price accurately reflect all information that can be derived by examining market trading data such as past prices, trading volume, short interest rate, etc

Introduction The consumption-based model as a complete answer to most asset pricing question in principle, does not work well in practice; This observation motivates effects to tie the discount factor m to other data; Linear factor pricing models are most popular models of this sort in finance; They dominate discrete-time empirical work

Number theory is regarded as a beautiful but largely useless in the past a Today number-theoretic algorithms are used videly