# A Treatise on Differential Equations by A. R. Forsyth

By A. R. Forsyth

Vintage 19th-century paintings certainly one of the best remedies of the subject. Differential equations of the 1st order, basic linear equations with consistent coefficients, integration in sequence, hypergeometric sequence, resolution by way of yes integrals, many different issues. Over 800 examples. Index.

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50 per hour plus \$2 for each unit produced per hour. 32 for each mile traveled. (d) A computer that was purchased for \$750 depreciates \$100 per year. com. S. 4 FUNCTIONS What you should learn • Determine whether relations between two variables are functions. • Use function notation and evaluate functions. • Find the domains of functions. • Use functions to model and solve real-life problems. • Evaluate difference quotients. Introduction to Functions Many everyday phenomena involve two quantities that are related to each other by some rule of correspondence.

COLLEGE ENROLLMENT The Pennsylvania State University had enrollments of 40,571 students in 2000 and 44,112 students in 2008 at its main campus in University Park, Pennsylvania. (Source: Penn State Fact Book) (a) Assuming the enrollment growth is linear, find a linear model that gives the enrollment in terms of the year t, where t ϭ 0 corresponds to 2000. (b) Use your model from part (a) to predict the enrollments in 2010 and 2015. (c) What is the slope of your model? Explain its meaning in the context of the situation.

The input value 2 is matched with two different y-values. c. 48 does describe y as a function of x. Each input value is matched with exactly one output value. Now try Exercise 11. Representing functions by sets of ordered pairs is common in discrete mathematics. In algebra, however, it is more common to represent functions by equations or formulas involving two variables. For instance, the equation y ϭ x2 y is a function of x. represents the variable y as a function of the variable x. 4 HISTORICAL NOTE © Bettmann/Corbis 41 the independent variable and y is the dependent variable.