In this chapter we will extend the concepts which have been presented in the preceding chapter so as to develop general methods of phasor analysis for circuits which are under conditions of sinusoidal steady-state excitation. The methods are very similar to those for resistance circuits which were presented in Chap.2

In this chapter we introduce a circuit element that is very important in circuit design, the operational amplifier.This element will be used extensively in the studies of future chapters. Here we consider its use with resistors only to perform the algebraic functions of multiplication, addition and subtraction

Augmented loop matrix +1when branch b; is in loop lk and has the same orientation; B. =]; ={-1 when branch b; is in loop lk and has the opposite orientation; when branch; is not in loop lk

The operational amplifier (hereafter OP-AMP)is developed in the 1940s primarily for use in analog computers, made cheaply and readily available in the late 1960s through integrated-circuit technology. The actual construction of a modern OP-AMP is indeed very complex, involving many transistors, diodes, resistors and capacitors

One of the CLRM assumptions is: there is no perfect multicollinearity-no exact linear relationships among explanatory variables, Xs, in a multiple regression. In practice, one rarely encounters perfect multicollinearity, but cases of near or very high multicollinearity where explanatory variables are approximately linearly related frequently arise in many applications

The models we discussed are models that are linear in parameters; variables Y and Xs do not necessarily have to be linear The price elasticity of demand~the log-linear models The rate of growth~semilog model Functional forms of regression models which are linear in parameters, but not necessarily linear in variables:

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

Plant nitrogen 1.1 Uptake of N 1. N is required by plants in large amounts Most plant material contains 2-4%N and 40%C. 2. N is usually the limiting nutrient in unfertilized systems 3. Most n is taken up from the soil in the form of nht or no a small amount of NH3 can be absorbed through the leaves N2 can be used by legume plant via biological nitrogen fiXation

Soil fertil Soil fertility is the characteristics of soil that enables it to Provide nutrients in adequate amounts in adequate time In appropriate balance for growth of particular plant(s)

In lecture D9, we saw the principle of impulse and momentum applied to particle motion. This principle was of particular importance when the applied forces were functions of time and when interactions between particles occurred over very short times, such as with impact forces. In this lecture, we extend these principles to two dimensional rigid body dynamics. Impulse and Momentum Equations Linear Momentum In lecture D18, we introduced the equations of motion for a two dimensional rigid body. The linear momen- tum for a system of particles is defined