Differential Equations I

Catalog description

The course will include coverage of solution methods, existence and uniqueness of solutions and approximation methods. Applicability of differential equations to a variety of physical phenomena will be explored. After completing this course, students should be able to (1) Identify and classify various types of differential equations. (2) Find general and particular solutions of first-order linear differential equations by various methods, including integrating factors, separation of variables and Bernoulli methods. (3) Find general and particular solutions of second-order linear differential equations by various methods, including reduction of order, undetermined coefficients, variation of parameters and solution by series. (4) Use Laplace transforms to solve differential equations. (5) Use differential equations to model physical phenomena. (6) Solve systems of first-order linear equations using various methods, including finding eigenvalues and eigenvectors. (7) Use technology to analytically and numerically solve differential equations.