Department of Mathematics & Statistics

Concordia University

 

 DNA

 

 

MATH 370, section A

Differential Equations

Fall 2018

 

 

 

Instructor:                  Dr. P. Gora, Office: LB 901-17 (SGW), Phone: (514) 848-2424, Ext. 3257

                                    Email: pawel.gora@concordia.ca

                                    Web: www.mathstat.concordia.ca/faculty/pgora/m370/

                            

Office Hours:          Mondays 1:15- 3:00
                               Tuesdays  11:30- 1:00
                                 or by appointment

                               I am also usually at the office: Mondays 9:45 - 11:30 , Wednesdays 9:45 - 11:30, Thursdays : 11:15 - 1:00.
                                room LB 901-17
                                 

 

Prerequisites:            MAST 214, 234, 234 or 264 or MATH 251, 252, 264 or equivalent.

 

Text:                            Elementary Differential Equations and Boundary Value Problems, 10th Edition, by William E. Boyce and Richard C. DiPrima (Wiley).

 

Assignments:             Assignments are very important; they indicate the level of difficulty of the problems that the students are expected to understand and solve.  Therefore, every effort should be made to do and understand them independently.  The assignments will be corrected and a representative sample graded (some problems may be not graded), with solution sets posted weekly.  These grades together are worth a maximum of 10%.

 

Web Resources:         Many excellent animated illustrations to the text are collected at the site www.wiley.com/college/boyce. Regular use of this resource is recommended.

 

Use of Computer  Algebra System:          It is optional but much recommended to install and use Maple or Mathematica.                    These computer tools can be used to verify and illustrate any analytical    results you get while doing your assignment problems.

 

Calculators:                Electronic communication devices (including cell phones) are not allowed in examination rooms. Only “Faculty Approved Calculators” (SHARP EL-531 or CASIO FX-300MS) are allowed in examination rooms during mid-term and final.

 

Test:                            A midterm test covering the first six weeks will be given in week 7 (or later).       

Final Grade:               The highest of the following:

-      90% final exam and 10% assignments.

-         30% midterm, 10% assignments, and 60% final exam.


 

 

 

 

Approximate schedule of topics

 

Week

Sections

Topics

1

1.1 - 1.4

Solutions of some differential equations. Classification of differential equations.

2

2.1 - 2.3

 

Linear equations; integrating factors. Separable equations; Modeling with first order equations.

3

2.4 - 2.6

Linear and Nonlinear equations. Autonomous equations; population dynamics. Exact solutions; integration factors.

4

2.7- 2.9

Numerical approximations. Existence theorems. First order equations.

5

3.1. - 3.3

Homogeneous equations, constant coefficients. Linear homogeneous equation solutions: Wronskian. Complex roots of characteristic equation.

6

 

3.4 - 3.6

Repeated roots; reduction of order. Nonhomogeneous equations;

undetermined coefficients. Variation of parameters.

7

3.7 - 3.8

Mechanical and electrical vibrations. Forced vibrations.

8

Chaps. 1 - 3

  Midterm

Midterm test, closed book

Scope: Chapt. 1 - 3 inclusive.

9

 

4.1- 4.2

 

General theory of nth order linear equations. Homogeneous equations with constant coefficients.

10

4.3- 4.4 

Method of undetermined coefficients. Variation of parameters.

11

5.1- 5.3

Review of power series,

Series solutions at an ordinary point.

12

7.4 - 7.8

Systems of First Order Linear Equations

 
Outline in pdf form.

Sample problems for Midterm
Solutions to 2017 midterm problems


The review class will be

Tuesday, December 11, 12-2 pm , room LB 921-4 .
This will be Questions and Answers only class.

A lot of first order DE problems, some very difficult.

Old finals, some with solutions             Do NOT Read The Solutions Before Trying to Solve Yourself !!!

The results of the assignments are linked at the bottom !!!

 Assignments:   #1 (due Sept. 13) ,  Solutions   , Maple        
                          #2 (due Sept. 20 ) ,  Solutions             Maple  
                            Skydiver problem: pdf , Maple
                          #3 (due Sept. 27 ), Solutions      Maple   Solution of Problem 5 changed on October 4th.
                           #4 (due October 4 ),  Solutions      Maple
                           #5 (due October 11 ) , Solutions      Maple
                          #6 (due October 18 ) ,  Solutions    Maple
                          #7 (due October 25) ,  Solutions    Maple
     No new assignment this week
Solutions of Midterm problems: There are 3 versions somewhat mixed together so find Your problems Yourself.
                                                         Sometimes Your solution method can be correct even if different from mine.
                         # 8 (due November 8 ) ,   Solutions    Maple
                         #9 (due November 15 ) , Solutions     Maple
                        #10 (due November 22 ) , Solutions  Maple
Systems we solved in class: with double eigenvalues and two with complex eigenvalues:
doublecomplex1complex2

                       # 11 (due November 29  ) ,  Solutions    Maple


MASSA has created a survey to receive feedback
about their Lunch & Learn series:
Lunch & Learn Feedback

SIAM has a web page on careers open for  math graduates:
https://www.maa.org/programs/faculty-and-departments/pic-math/solving-real-world-problems
 
 
Results of the assignments and tests

Departmental web page.