1 Model problem 1.1 Poisson Equation in 1D Boundary Value Problem(BVP) (x)=∫(x) (0,1),u(0)=(1)=0,f Describes many simple physical phenomena(e.g) Deformation of an elastic bar Deformation of a string under tension Temperature distribution in a bar The Poisson equation in one dimension is in fact an ordinary differ tion. When dealing with ordinary differential equations we Poisson equation will be used here to illastrate numerical techniques for elliptic PDE's in multi-dimensions. Other techniques specialized for ordinary differen tial equations could be used if we were only interested in the one dimension

Overview: As you may discover, growing single crystals takes patience as well as an artful hand Crystallizations can be very sensitive to temperature and minor disturbances. Therefore, you will be encouraged to try several different temperatures using otherwise identical conditions, and to always find a quiet undisturbed location to promote crystal growth. Here are some tried and true tips to get

Anything that can be learned from direct experience can also be learned by indirect or vicarious experience

Substitutivity of Equivalence Let A,M and N be wffs and let AMN be the result of replacing M by N at zero or more occurrences (henceforth called designate occurrences) of M in A. 1. AMN is a wff. 2. If |= M ≡ N then |= A ≡ AMN

According to a survey and my own observation young people today are more consumeristic and less idealistic. The college students'major objective \is to be financially well off.\ Less important than ever is developing a meaningful philosophy of life. It is true that we need to be financially comfortable, but we also need to feel we have perspective on the world beyond the confines of our occupation It is the duty of educational institutions to help people get a better understanding

Introduction A primary goal of your efforts in this course will be to gather empirical data so as to prove(or disprove) your hypothesis Typically the data that you gather will not directly satisfy this goal Rather, it will be necessary to \reduce\the data. to put it into an appropriate form, so that you can

The surplus amino acids in animals can be completely oxidized or converted to other storable fuels Amino acids in excess (from diet, protein turnover) can neither be stored, nor excreted, but oxidized to release energy or converted to fatty acids or glucose. Animals also utilize amino acid for energy generation during starvation or in diabetes mellitus

DEFINITION OF A HYPOTHESIS Hypothesis A tentative explanation that accounts for facts and can be tested by further investigation; a theory Something taken to be true for the purpose of argument or investigation; an assumption .Experiment test under controlled conditions that is made to demonstrate

Rank deficiencies Ranks deficiencies are combinations of parameters that can not be separately estimated In GPs. there are several rank deficiencies UTl, Longitudes of all the stations and the nodes of the satellite orbits, effectively can not be separated In theory, orbit perturbations by the moon/sun on the GPs

Class expectations This is a graduate level class. There is no final exam Grading in the class is based on homework (75%) and on a final written report(25%) The report will be revised during semester and should be 2000-3000 words(8-10 double spaced pages)