The University of Massachusetts Boston

Department of Mathematics

MA270 Applied Ordinary Differential Equations, Fall 2021

nstructor: Prof. Alfred Noël

Office : 3-154-14 Wheatley

Phone : (617)-287-6458

Email : alfred.noel@umb.edu

Url : http://www.math.umb.edu/~anoel

Class hours : TTh 5:30 PM - 6:45 PM Wheatley 1-44

Office hours: T: 2:00 PM – 3:50 PM Th: 2:50 PM – 3:50 PM https://umassboston.zoom.us/j/96541633195

Text : Fundamentals of Differential Equations Eigth edition by Nagle Saff and Snider Pbl. Pearson Addison Wesley

Course Info: This is an introductory course in the theory of Ordinary Differential Equations, one of the most fundamental tools in Mathematics and Science. The students are expected to be mathematically mature enough to start dealing with concepts beyond Calculus and Linear Algebra. The goal of this course is to give to students a set of mathematical tools that they will need in order to pursue advanced studies in Mathematics, Physics, Chemistry, Engineering in particular and Science in general. Students who are concerned about their mathematical background should speak to me as soon as possible for advising. Students who have taken Calculus I, II, III and Linear Algebra should, in principle, be able to take this course. However, regardless of your background you will find the course to be very challenging. Consequently, you should not collaborate on homework and you should participate in class discussions. Also I strongly advise students to form discussions groups that meet outside of the class-room.

 

Topics:

Chapter 1:

1.1 Motivational background.
1.2 Solutions; initial value problems.
1.3 Direction fields.
1.4 Euler's approximation method.

Chapter 2:

2.2 Separable Equations.
2.3 Linear Equations.
2.6 Substitutions and Transformations.

Chapter 4:

4.1 Introduction to the Mass-Spring Oscillator.
4.2 Homogeneous Linear Equations: General Solution.
4.3 Auxiliary Equations with Complex Roots.
4.4 Nonhomogeneous Equations: Undetermined Coefficients.
4.5 Superposition Principle using undetermined Coefficients.

Chapter 5:

5.2 Constant Coefficients Systems: Elimination Methods.
5.4 Phases Plan introduction.

Chapter 6:

6.2 Homogeneous Linear Equation with Constant Coefficients.

Chapter 7:

7.2 Laplace Transform: Definition.
7.3 Laplace Transform: Properties.
7.4 Inverse Laplace Transform.
7.5 Solving Initial Value Problems.
7.6 Transforms of Discontinuous & Periodic Functions.

7.7 Convolution

7.8 Impulses and the Dirac Delta function

7.9  Solving Linear Systems with Laplace Transforms.

Chapter 8:

8.1 Taylor Polynomial Approximations.
8.2 Power Series and Analytic Functions.
8.3 Power Series solution of Linear Differential Equations.
8.4 Differential Equations with Analytic Coefficients.
8.5 Cauchy-Euler (Equidimensional) Differential Equations.
8.6 Frobenius Method at Regular Singular Points.

 

Exams: There will be 4 one-hour exams and a cumulative final exam:

Exam I: Thursday, September 30

Exam II: Thursday, October 21

Exam III: Thursday, November, 18

Exam IV: Thursday, December, 9

 

Grading Procedures: Exam 1: 15%, Exam 2: 15%, Exam 3: 20%, Exam 4: 20%; Final exam: 30%.

 

 

THERE WILL BE NO MAKEUP EXAMS.

STUDENTS ARE RESPONSIBLE FOR MATERIAL COVERED IN CLASS.