Syllabus

DIFFERENTIAL EQUATIONS / MA523

SPRING SEMESTER  2007

 

 

INSTRUCTOR:       Mazhar Jamil

 

Office:                   Room #101(Class in 208)            Phone:  357-3174 ext. 129        e-mail: MJamil@lsmsa.edu

 

TEXT:                   1)  Elementary Differential Equations; 7th edition by Earl D. Rainville & Phillips E. Bedient

2)  The Ultimate ODE Power Tool (ODE Architect  Compaion) CODEE by John Wiley & Sons Inc.

 

COURSE               This course is a study of ordinary differential equations, including linear equations, systems

DESCRIPTION:     of equations, equations with uniqueness of solutions, methods, boundary value problems, and

                             applications.

 

COURSE               In order to demonstrate that a student is in the process of achieving the major course objectives, the 

REQUIREMENT:    student must be able to work problems on major tests and quizzes similar to those problems

                             regularly assigned as homework.  5% of the grades are taken from homework assignments,

                             homework is an integral part of the course and provides the means by which the student can learn

                             mathematical concepts.  It is doubtful that the student will be able to pass the course without working

                             the homework assignments.

 

ATTENDANCE:     Students are expected to be present and on time to every class.  Attendance, including tardiness, will

                             be recorded and turned in daily.  Students should note that absence from class, excused or

                             unexcused, does not automatically give students the right to postpone quizzes or tests that follow.

                             Unexcused absences and Tardiness will negatively affect the final grade.

 

RULES FOR         1.  If any student has legitimate reason for being unable to take a test on any of the

TEST TAKING:      scheduled test dates, that student must notify Mr. Jamil at least 2 days before the exam  unless

                             excused by the school.

 

                             2.If a student fails to take an exam or quiz on the scheduled test date without previously notifying Mr.

Jamil, 10% points will be taken off of that student's test grade, and NO bonus points will be available for that student.

 

GRADING             There will be five tests and a final.  Pop quizzes and assignments will be administered throughout the 

PROCEDURE:      the course.  One test and a quiz will be dropped before the final grade is given. Any test may be

                            cumulative.  The final exam will be comprehensive.  The break-up is as follows:

 

         Tests                                                                          60%

Pop quizzes                                                               10%

Assignments & class participation                                10%                  

Final                                                                           20%

 

OFFICE HOURS:        M         10:00 – 11:00,                                          T          9:30 – 11:30, 2:00 – 2:30 & 3:30 – 4:30

                                 W         10:00 – 11:00                                           R          10:30   12:00              

                                 F          10:00 – 11:00                                           By appointment only:  T  1:30, W  8:00 & R   2:00

 

 

GUIDED STUDY:        Mondays            4:00 – 5:30 pm                           

 

 

DIFFERENTIAL EQUATIONS (MA523) / SPRING SEMESTER  2005

 

WEEK     DATE                          TOPIC                                                                                IN TEXT

 

 1            1 – 8 – 2007                 Introduction, Definitions, and review of integrals                    1-2/pg. 1-3

                                                 The elimination of arbitrary constant                                      3/pg. 6

                                                 Families of curves & The isoclines of an equation                 4-5/pg. 17

 2            1 – 15                          (Read the Existence Theorem), Separation of variables        7/pg. 21

                                                 Homogeneous functions                                                      8/pg. 26

 3            1 – 22                          Equations with homogeneous coefficients                            9/pg. 28

1 – 24 – 2007               TEST  # 1

 4            1 – 29                          Exact equations                                                                  10/pg 32

                                                 The linear equation of order one                                          11/37

                                                 The general solution of a linear equation, Applications          12/pg. 41, 47  

 

  5           2 – 5                            Integrating factor found by inspection                                    18/pg. 63

                                                 The determination of integrating factor                                   19/pg. 67

  6           2 – 12                          Substitution suggested by the equation                                20/pg. 67

2 – 15 – 2007               TEST # 2

  7           2 – 19 – 2007               Mardi Gras Holidays

  8           2 -  26                          Bernoulli's equation                                                             21/pg. 74

                                                 Coefficients linear in the two variables                                  22/pg. 77

  9           3 – 5                            The general linear equation & An existence and

uniqueness Theorem                                                           24-25/pg. 87-89

  10          3 – 12                          Linear independence & The Wronskian                                26-27/pg. 90-91

                                                 General solution of homogeneous equation                          28/pg. 94

               3 – 15 – 2005               TEST # 3

 11          3 – 19                          General solution of nonhomogeneous equation                    29/pg. 96

                                                 Differential Operators & The fundamental laws of operation    31/pg. 100

                                                 Some properties of differential operators                              32/pg. 102

 12          3 – 26                          The auxiliary equation; distinct roots                                     34/pg. 105

The auxiliary roots; repeated roots                                       35/pg. 108

A definition of exp z for imaginary z                                      36/pg. 112

  13          4 – 2                            The auxiliary equation; imaginary roots & Hyperbolic funs.     37-38/pg. 114-116

                                                 Construction of a homogeneous equation from a                   39/pg. 121

                                                 specified solution                                                               

               4 – 5 – 2007                 TEST # 4

  14          4 – 9 – 2007                 Spring Break

  15         4 – 16                          Solution of a non homogeneous equation                             40/pg. 124

                                                 The method of undetermined coefficients                             41/pg. 126

                                                 Solution by inspection                                                         42/pg. 132

                                                 Introduction & Reduction of order                                         43-44/pg.139

  16          4 – 23                          Variation of parameters                                                        45 / pg. 143

                                                 Solution of  y'' + y = f(x)                                                       46 / pg. 148

                                                  The exponential shift                                                            47 / pg. 152

               4 – 26 – 2007               TEST # 5

                                                 The inverse differential operator, 1 / f(D)                               48 / pg. 156

                                                 Evaluation of [ 1 / f(D) ] eax                                                   49 / pg. 157

                                                  Evaluation of (D2+ a2 ) -1sinax  &  (D2+ a2 ) -1cosax                 50 / pg. 158

Laplace transformation                                                         60 / pg. 185

  17          4 – 30                          Inverse Laplace transformation                                             70 / pg. 209

                                                 Catch Up – Numerical solution will be added if the time permit

  18         5 – 7 – 2007               Finals

 

The Instructor reserves the right to change any portion of this class guide by announcing the change during a scheduled class meeting.

J