Download PDF by J. David Logan: A First Course in Differential Equations (Undergraduate

By J. David Logan

ISBN-10: 0387299300

ISBN-13: 9780387299303

This article is designed for a standard post-calculus direction in easy differential equations. it's a short, one-semester therapy of the fundamental principles, types, and resolution equipment. The e-book, which serves in its place to current texts for teachers who wish extra concise assurance, emphasizes graphical, analytical, and numerical methods, and is written with transparent language in a simple structure. It presents scholars with the instruments to proceed directly to the subsequent point in making use of differential equations to difficulties in engineering, technological know-how, and utilized mathematics.

The subject matters include:
* separable and linear first-order equations;
* self reliant equations;
* moment order linear homogeneous and nonhomogeneous equations;
* Laplace transforms;
* linear and nonlinear platforms within the section plane.

Many workouts are supplied, as well as examples from engineering, ecology, physics, economics, and different parts. An increased part at the required linear algebra is gifted, and an appendix includes templates of Maple and MATLAB instructions and courses that are priceless in differential equations.

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Extra info for A First Course in Differential Equations (Undergraduate Texts in Mathematics)

Example text

10 Plots of the logistics model of population growth. The left plot shows the per capita growth rate vs. population, and the right plot shows the growth rate vs. population. Both plots give important interpretations of the model. 11). ) But, there are qualitative properties of solutions that can be exposed without actually finding the solution. Often, all we may want are qualitative features of a model. 11), p(t) = 0 and p(t) = K, corresponding to no animals (extinction) and to the number of animals represented by the carrying capacity, respectively.

Scientific exactness is sometimes sacrificed for mathematical tractability. Model predictions depend strongly on the assumptions, and changing the assumptions changes the model. If some assumptions are less critical than others, we say the model is robust to those assumptions. The best strategy to learn modeling is to begin with simple examples and then graduate to more difficult ones. The reader is already familiar with some models. In an elementary science or calculus course we learn that Newton’s second law, force equals mass times acceleration, governs mechanical systems such as falling bodies; Newton’s inverse-square law of gravitation describes the motion of the planets; Ohm’s law in circuit theory dictates the voltage drop across a resistor in terms of the current; or the law of mass action in chemistry describes how fast chemical reactions occur.

14) where populations are measured relative to the carrying capacity and time is measured relative to how fast the population is growing. For example, if the carrying capacity is K = 300, 000, and the dimensioned p varies between 0 < p < 300, 000, it is much simpler to have dimensionless populations P with 0 < P < 1. 14) it is easy to see that the equilibria are P = 0 and P = 1, the latter corresponding to the carrying capacity p = K. We have pointed out that an autonomous model can be easily analyzed qualitatively without ever finding the solution.

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A First Course in Differential Equations (Undergraduate Texts in Mathematics) by J. David Logan

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