Prerequisite: MATH 231, or equivalent, with grade C- or better

Course Topics:

• First order ordinary differential equations
• Second order differential equations
• Higher order differential equations
• Series solutions of linear differential equations with non-constant coefficients
• Laplace transforms

Course Learning Outcomes: By the end of this course students will be able to:

• Learn to identify and solve different types of first order ODE’s, including linear, separable, Bernoulli, homogeneous and exact.
• Use direction field plots to analyse the qualitative behavior of the solution curves of first order ODE’s.
• Study modeling with first order ODE’s, including Newton’s law of cooling, mixing problems, Newtons second law of motion, etc.
• Solve homogeneous second and higher order linear ODE’s with constant coefficients.
• Solve second order ODE’s, for which one solution is known/given, by using reduction of order.
• Solve non-homogeneous second and higher order linear ODE’s with constant coefficients using the method of undetermined coefficients.
• Solve non- homogeneous second and higher order ODE’s using the method of variation of parameters.
• Study modeling with second order ODE’s, including mass-spring systems and RLC circuits.
• Use Laplace transforms to solve homogeneous second and higher order linear ODE’s.
• Use Laplace transforms to solve non-homogeneous second and higher order linear ODE’s, in which the forcing functions involve continuous functions, piecewise continuous functions, delta functions, etc
• Solve second order linear ODE’s with non-constant coefficients using series solution methods, centered at an ordinary point.
• Learn how to classify ordinary and singular points for ODE’s with non constant coefficients.
• Solve Cauchy-Euler ODE’s.
• Solve second order linear ODE’s with non-constant coefficients using series solution methods, centered at a regular singular point: the Frobenius method.
• Solve ODE’s, such as Bessel’s equation, in which the indicial equation has a repeated root - or roots that differ by an integer.

Program Learning Outcomes and Mission Statement of the Department of Mathematics

Course Requirements

• Textbook (required): W. E. Boyce and R. C. DiPrima, Elementary Differential Equations and Boundary Value Problems, 9th ed, Wiley, 2009
• Lecture Notes
• Goals and Objectives of the Course: The purpose of this course is to study the elementary theory of ordinary differential equations with emphasis on methods of solution and applications.
• Class Procedures: The majority of each class period will be lecture oriented. You are expected to: You are expected to: attend the lectures and to take your own lecture notes, read the textbook and work out problems from that section covered in class, do the homework problems.
• Attendance Requirements: It is important that you attend every class scheduled for this course. You are responsible for all announcements and material covered in this class as well as material from the textbook which is assigned but not covered in class.
• Computers: Any electronic devices such as laptops, tablets and cell phones cannot be used during the class. Please set your cell phones on vibrate. Calculators will be allowed on the tests, but you have to show your work in detail.

Grading

• Homework: There will be weekly homework assignments that will count for 25% of the grade.
• Tests: There will be two midterms tests and a final exam. Each test will count for 25% of the total grade.
• Make-ups: Make-up exams will be given only in cases of extremely properly documented emergencies. Late homework will not be accepted.
• Evaluation: Grades will be determined on a 100 point scale. Those point totals near cutoff will be individually considered for the next higher grade. I do reserve the right to add some extra points depending on the class participation and outstanding exam performance.

Changes: The course plan may be modified during the semester. Such modifications will be announced in advance during class periods. You are responsible for keeping abreast of such changes.

Remarks: This course is cumulative and it is assumed that all earlier parts covered are liable for any exam. It is strongly advised that you start working on this course from the very beginning. The course moves at a fast place, so it is very hard to catch up if you get behind.

Counseling and Disability Services. Reasonable Accommodations: New Mexico Tech is committed to protecting the rights of individuals with disabilities. Qualified individuals who require reasonable accommodations are invited to make their needs known to the Office of Counseling and Disability Services (OCDS) as soon as possible. In addition, New Mexico Tech offers mental health and substance abuse counseling through the Office of Counseling and Disability Services. The confidential services are provided free of charge by licensed professionals. To schedule an appointment, please call 835-6619.