Math III – Engineering Mathematics I

The course includes a discussion of sequences, series, and differential equations. It includes discussions on Convergence Tests, Power series, Taylor series, and Fourier series. The differential equations portion of the course begins with classification, followed by a discussion of ordinary differential equations (ODEs), starting with first order ODEs. The concepts of direction fields, boundary, and initial value problems are introduced. Several methods of solution of first order ODEs are considered. It is emphasized that each method applies to a certain subclass of equations. The topics covered include methods of solving linear equations, separable equations, homogeneous and exact equations, Bernoulli, and autonomous equations. The main methods under discussion are the method of integrating factors, variation of parameters, and the method of separation of variables. The idea of approximating a solution by numerical computation is introduced in the discussion of Euler’s method. The course continues with a discussion of the general theory and methods of solution of second and n-th order ordinary differential equations. Conditions for the existence and uniqueness of the solution are analyzed. Substantial attention is given to methods of solution of second order differential equations with constant coefficients. Methods under discussion are the method of reduction of order, the method of undetermined coefficients, the variation of parameters method, the method of series solutions, and the method of Laplace transform. The course concludes with a discussion of partial differential equations, Fourier series, and the method of separation of variables as a method for solving partial differential equations. Throughout the course, applications of differential equations to simple physical problems are thoroughly discussed. The class meets three hours per week in the first semester.