By J. David Logan (auth.)
The 3rd variation of this concise, well known textbook on simple differential equations supplies teachers an alternative choice to the numerous voluminous texts out there. It provides a radical therapy of the traditional issues in an available, easy-to-read, layout. The overarching point of view of the textual content conveys that differential equations are approximately applications. This booklet illuminates the mathematical conception within the textual content with a wide selection of functions that would attract scholars in physics, engineering, the biosciences, economics and arithmetic. teachers are inclined to locate that the 1st 4 or 5 chapters are compatible for a primary path within the subject.
This version includes a fit bring up over prior variants within the variety of labored examples and workouts, really these regimen in nature. appendices contain a assessment with perform difficulties, and a MATLAB® complement that provides uncomplicated codes and instructions for fixing differential equations. MATLAB® isn't required; scholars are inspired to make use of on hand software program to plan a lot of their ideas. suggestions to even-numbered difficulties can be found on springer.com.
From the experiences of the second one edition:
“The assurance of linear structures within the aircraft is well precise and illustrated. …Simple numerical tools are illustrated and using Maple and MATLAB is inspired. …select Dave Logan’s new and more advantageous textual content for my course.”
—Robert E. O’Malley, Jr., SIAM Review, Vol. fifty three (2), 2011
“Aims to supply fabric for a one-semester path that emphasizes the elemental rules, resolution equipment, and an advent to modeling. …The publication that effects bargains a concise creation to the topic for college kids of arithmetic, technology and engineering who've accomplished the introductory calculus series. …This booklet is worthy a cautious glance as a candidate textual content for the following differential equations direction you teach.”
—William J. Satzer, MAA Reviews, January, 2011
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Extra resources for A First Course in Differential Equations
28. Write the solution to the initial value problem 2 dy = −y 2 e−t , dt y(0) = 1 2 in terms of the erf function. 29. (Demography) Let N0 be the number of individuals in a cohort at time t = 0 and N = N (t) be the number of those individuals that are still alive at time t. If m is the constant per capita mortality rate, then N /N = −m, which gives N (t) = N0 e−mt . The survivorship function is deﬁned by S(t) = N (t)/N0 , and S(t) therefore gives the probability of an individual living to age t.
Dt (b) dx √ = 2t + x + 3. dt 23. Solve the initial value problem for x = x(t): d xe2t = e−t , dt Hint: Integrate both sides. x(0) = 3. 30 1. First-Order Diﬀerential Equations 24. Find the general solution x = x(t) of the DE 1 d (tx (t)) = −2. t dt 25. (Epidemiology) A population of u0 individuals all have HIV, but none has the symptoms of AIDS. Let u(t) denote the number that does not have AIDS at time t > 0. If r(t) is the per capita rate of individuals showing AIDS symptoms (the conversion rate from HIV to AIDS), then u /u = −r(t).
6. Find the interval of existence for the initial value problem dx = (4t − x)2 , dt x(0) = 1. Hint: Change the dependent variable to y = y(t) where y = 4t − x. 7. Determine the maximum interval of existence of the solution x = x(t) to x = 2tx2 , x(0) = 1. 3 Separable Equations 27 8. Find the solution to the initial value problem x = t2 e−x , x(0) = ln 2, and determine the interval of existence. 9. Solve x = x(4 + x) subject to the initial condition x(0) = 1. Hint: It is helpful to use a partial fractions expansion a b 1 = + , x(4 + x) x 4+x where a and b are to be determined.
A First Course in Differential Equations by J. David Logan (auth.)