By J. David Logan (auth.)
The 3rd variation of this concise, renowned textbook on trouble-free differential equations offers teachers a substitute for the various voluminous texts out there. It provides an intensive remedy of the normal subject matters in an available, easy-to-read, layout. The overarching point of view of the textual content conveys that differential equations are approximately applications. This e-book illuminates the mathematical idea within the textual content with a large choice of purposes that might attract scholars in physics, engineering, the biosciences, economics and arithmetic. teachers tend to locate that the 1st 4 or 5 chapters are compatible for a primary direction within the subject.
This version features a fit elevate over previous versions within the variety of labored examples and routines, fairly these regimen in nature. appendices contain a overview with perform difficulties, and a MATLAB® complement that offers easy 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 suggestions. ideas to even-numbered difficulties can be found on springer.com.
From the studies of the second one edition:
“The assurance of linear structures within the aircraft is well exact and illustrated. …Simple numerical equipment are illustrated and using Maple and MATLAB is inspired. …select Dave Logan’s new and more suitable 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 tools, and an advent to modeling. …The ebook that effects bargains a concise advent to the topic for college kids of arithmetic, technological know-how and engineering who've accomplished the introductory calculus series. …This e-book is worthy a cautious glance as a candidate textual content for the subsequent differential equations path you teach.”
—William J. Satzer, MAA Reviews, January, 2011
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Extra resources for A First Course in Differential Equations
Which one seems to best ﬁt the human population? A ﬁsh population? 10. (Reactors) A chemical ﬂows into a reactor at concentration Cin with volumetric ﬂow rate q. While in the reactor it chemically reacts according to C + C → Products. The mixture ﬂows out at the same rate q. 7) (V C) = qCin − qC − kV C 2 . Initially, take C(0) = C0 and assume Cin = 0. Show that this is a Bernoulli equation and solve it. 11. (Parasite infections) One study on the eﬀect of a parasitic infection on an animal’s immune system was carried out with the intestinal nematode parasite Heligmosoides polygyrus and a ﬁxed number of laboratory mice.
16) is called the source term or forcing term. 16), has a very nice property: the left side of the equation can be multiplied by a function μ = μ(t) that transforms it into a total derivative. In other words, there is a function μ = μ(t) such that μ(t) (x + p(t)x) = (μ(t)x) . The function μ(t) is called an integrating factor and it is given by μ(t) = e p(t) dt = eP (t) , where P (t) = p(t) dt; P (t) is the antiderivative of p(t). By the product rule and the chain rule it is easy to check that it works: (μ(t)x) = eP (t) x = eP (t) x + eP (t) p(t)x (because P (t) = p(t)) = μ(t)x + μ(t)p(t)x = μ(t)(x + p(t)x), which is our claim.
Q (f) Q = . 4 + Q2 x = e−2x . 2 y = 1 + y2. 1 . (d) u = 5 − 2u (g) x = ex . (c) (h) y = r(a − y). 2. Solve y = r(a − y), where r and a are constants. 3. In Exercises 1(a)–(b) ﬁnd the solution to the resulting IVP when x(0) = 1. 4. Find the general solution: (a) x = 2x . t+1 t2 + 1 sec θ. (b) θ =t (c) (2u + 1)u − (t + 1) = 0, (d) R = (t + 1)(R2 + 1). (e) y +y+ (f) (t + 1)x + x2 = 0, 1 = 0. y 5. Solve the initial value problem and ﬁnd the interval of existence. dy 1 = , dt 2y + 1 y(0) = 1. 6. Find the interval of existence for the initial value problem dx = (4t − x)2 , dt x(0) = 1.
A First Course in Differential Equations by J. David Logan (auth.)