A First Course in Differential Equations (Undergraduate Texts in Mathematics)

This concise and up-to-date textbook is designed for the standard sophomore course in differential equations. It treats the basic ideas, models, and solution methods in a user friendly format that is accessible to engineers, scientists, economists, and mathematics majors. It emphasizes analytical, graphical, and numerical techniques, and it provides the tools needed by students to continue to the next level in applying the methods to more advanced problems. There is a strong connection to applications with motivations in mechanics and heat transfer, circuits, biology, economics, chemical reactors, and other areas. Moreover, the text contains a new, elementary chapter on systems of differential equations, both linear and nonlinear, that introduces key ideas without matrix analysis. Two subsequent chapters treat systems in a more formal way. Briefly, the topics include: First-order equations: separable, linear, autonomous, and bifurcation phenomena; Second-order linear homogeneous and non-homogeneous equations; Laplace transforms; and Linear and nonlinear systems, and phase plane properties.

J. David Logan is Willa Cather Professor of Mathematics at the University of Nebraska Lincoln. His extensive research is in the areas of theoretical ecology, hydrogeology, combustion, mathematical physics, and partial differential equations. He is the author of six textbooks on applied mathematics and its applications, including Applied Partial Differential Equations, 2nd edition (Springer 2004) and Transport Modeling in Hydrogeochemical Systems (Springer 2001).