Instructor: Dr. James Wilson
Office, phone, email: Carver 396D, 515 294 9816, jawilson@iastate.edu
Office hours: Mon, Fri 10:00 - 10:50; Tues, Wed, Thurs 2:10 - 3:00. You are also welcome to make appointments.

Regular class meetings: Mon, Tues, Thurs, Fri, January 8 - April 27 in Carver 202, 9:00 - 9:50
Exceptions and additional meeting times: Holidays Monday, January 15 and Monday - Friday, March 12 - 16. Final exam, in exam week, Monday, April 30, 7:30 - 9:30 AM

Text and syllabus: Boyce & DiPrima, Elementary Differential Equations and Boundary Value Problems, eight edition, Wiley.

Recommended preparation for quizzes:
Meaning and examples of:
differential operator, differential equation, initial condition, initial value problem, mathematical modeling, direction field, solution, general solution, integral curve, linear process, linear operator, linear d.e., ordinary or partial d.e., order of a d.e., system of d.e., homogeneous linear d.e., use of linearity to find more solutions of homogeneous linear d.e., use of initial condition to determine constants in solutions, integration technique for linear and separable first order d.e., existence and uniqueness theorem for first order linear d.e.

mixing problem applications, gravitation, existence and uniqueness theorem for first order d.e. (linear or not), use of direction field for autonomous first order d.e., equilibrium solutions, stable and unstable, population models, exact differentials and d.e., recognizing and solving exact d.e., solving second order homogeneous constant-coefficient equations and initial value problems (real, complex, or repeated characteristic roots), existence and uniqueness theorem for second order linear differential equations, fundamental set of solutions, linear independence, Wronskian determinant test

method of reduction of order (even applied to nonhomogeneous equations), form of general solution of nonhomogeneous second order linear equations: particular solution plus complementary solution, existence and uniqueness theorem for second order linear initial value problems, methods of variation of parameters and undetermined coefficients, mass and spring systems and electric circuit loop applications

(review: power series, radius of convergence, ratio test, Taylor series, geometric series), operations on power series, power series solutions (options 1: solution to initial value problem, 2: first few terms of two lin. indep. solutions, 3: formulas for all coefficients, and possibly formulas for the solutions in familiar terms), functions analytic at a point, existence theorem for power series solutions, ordinary and singular points, radius of convergence for power series of rational functions

(Review improper integrals, partial fractions) Laplace transform definition, convergence, table, use in solving linear second order init. value problems with constant coefficients, especially problems involving discontinuous functions and impulse functions, convolution integrals: formula and use in connection with Laplace transforms

systems of differential equations, reduction to equivalent first order systems, distinguishing homogeneous from nonhomogeneous, linear from nonlinear, algebra of vectors and matrices, invertibility, Gaussian elimination, eigenvalues, eigenvectors, expression of systems of differential equations by means of matrices and vectors, form of the general solution for homogeneous and nonhomogeneous systems, solution of homogeneous systems and initial value problems by use of eigenvectors, calculation and use of fundamental matrices, the matrix exponential and its use as a fundamental matrix, diagonalization (change of variable using eigenvectors), dealing with multiple (repeated) eigenvalues, solution of constant coefficient nonhomogeneous systems by diagonalization

phase portraits, trajectories, and stability for constant coefficient two dimensional homogeneous problems with eigenvalues nonzero

Grading: There will be a final exam worth 150 points, 7 quizzes worth 50 points each, and one point for each day of attendance on other days. There will be about 50 days attendance, but fewer if I forget to pass the attendance sheet. (So, it will help your grade if you remind me.) Quizzes will be during every second week of class, beginning week two. A tentative grading scale is 0-40% F, 40-53.33% D, 53.33-66.67% C, 66.67%-80% B, 80-100% A.

Disabilities: If you have a disability and require accommodations, please see me early in the semester so that your learning needs may be appropriately met. Also, show documentation of your disability at the Disability Resources office, Student Services Building 1076, 515-294-6624.