Differential Equations: A Visual Introduction for Beginners, Paperback/Dan Umbarger

Differential Equations: A Visual Introduction for Beginners is written by a high school mathematics teacher who learned how to sequence and present ideas over a 30-year career of teaching grade-school mathematics. It is intended to serve as a bridge for beginning differential-equations students to study independently in preparation for a traditional differential-equations class or as supplemental material for students currently in such a class. It is highly visual with dozens of cartoon illustrations, dozens of MatLab graphs, dozens of tables, and dozens of other images throughout its 310 color pages as well as many correlative applets found on the internet that can be used to supplement the text. Comprehension and understanding of ideas is emphasized over symbol manipulation, although the latter is covered. Topics covered include definitions; Euler's method; separable, logistic, linear, exact, Bernoulli, and homogenous equations; slope fields; eigenvalues, eigenvectors, and eigenlines; solving systems of differential equations; Laplace transforms; and more.