Faculty                                 : Mathematics and Natural Science Study Program                             : International Mathematics Education Course/Code                       : Differential Equation
Credit                                 : Teory = 2 (two) SKS, Practise = 1 (one) SKS Semester                             : 3 (three)
Prerequisite/Code                : Differential Calculus
Professor                             : Nikenasih Binatari, M.Si

I. Course Description

The subject of differential equation constitutes a large and very important branch of modern mathematics. From the early days of the calculus, the subject has been an area of great theoretical research and practical applications, and it continuous to be so in our day. Therefore, differential equation is an essential subject to be known for all mathematicians. This course will discuss about three major aspects of the subject: theory, method and application.

II. Standard of Competence

Upon  completing  this  course,  students  should  understand  the  general  theory  of  differential  equations  and  the  basic techniques for solving differential equations involving one unknown function and one independent variable. At this end of this course, students should understand which theory and method of differential equation may be applied to solve numerous problems, be able to solve it and interpret the solution in the origin problems.

III. Activity Plan

Meeting
Basic Competence
Essential Concept
Learning
Strategies
Referencee
Character


1



Students should understand the motivation of differential equation arise from the real problem. Next, the students should understand the concepts and classification of differential equation and its general solution.
I.   Introduction to Differential
Equations
-   Some Basic Mathematical Models
-   Definitions and Terminology
Lecturing
[B] p.1
[C] p.2
Curiousity


2
-   Classification of Differential
Equations
-   Initial Value Problems
-   Boundary Value Problems
Lecturing
[A]
Understand
3
-   Autonomous Equation
Lecturing      and
Exercise
[B] p.74
Reasonable
4
-   Definition of Differential Equations
Solution
Lecturing,
Discussions
[B]
Careful


5










Students  should  be  able  to recognize  various  types  of   first order    differential   equation   for which exact solutions may be obtained by definite procedures and to understand how to solve it.
II.  First  Order  Equations  for  Which
Exact Solutions are obtainable
-   Standard  forms  of   First  Order
Differential Equations
-   Exact Equation
Lecturing,
Discussion    and
Exercise
[A] p.25 - 31
Creative

6
-   Solution    of    Exact    Differential
Equations
Lecturing,
Discussion    and
Exercise
[A] p.31 - 38
Creative

7
-   Method of Grouping
-   Integrating Factor
Lecturing,
Discussion    and
Exercise
[A] p.35 - 36
Creative

8
-   Separable Differential Equations
Lecturing,
Discussion    and
Exercise
[A] p.39
[C] p.31
Creative

9
-   Homogeneous              Differential
Equations
Lecturing,
Discussion    and
Exercise
[D]
Creative

10
-   Linear Differential Equations
Lecturing,
Discussion    and
Exercise
[A] p.49 - 53

Creative

11

-   Bernoulli Differential Equations
Lecturing,
Discussion    and
Exercise
[A] p.54 – 61
[D]
Creative

12,13

-   Special Integrating Factor
-   Special Transformation
Lecturing,
Discussion    and
Exercise
[A] p.61

14

First Mid Term Exam
Examination

[A], [B], [C]
Sportsmanship
15
Review of the First Midterm Exam

[A], [B], [C]


16


Students should be able to interpret the solution in terms of the quantities involved in the original problem
III. Applications     of     First     Order
Equations
-   Orthogonal Trajectories
Lecturing,
Discussion    and
Exercise
[A] p.70 – 74
Tough

17
-   Oblique Trajectories
Lecturing,
Discussion    and
Exercise
[A] p.74 – 77
Tough
18,19
-   Application in Mechanics Problems
and Rate Problems
Presentation
[A]
Applicative
Innovative
20

Second Mid Term Exam
Examination

[A], [B], [C]

21
Review of the Second Midterm Exam

[A], [B], [C]



22,23





Students  should  be  able  to recognize higher order linear differential equation and to understand the explicit methods of solving them.
IV. Explicit Methods of Solving Higher
Order Linear Differential Equations
-   Basic Theory of Linear Differential
Equations
Lecturing,
Discussion    and
Exercise
[A], [E],
Creative

24,25,26
-   The Homogeneous Linear Equation
with Constant Coefficients
Lecturing,
Discussion    and
Exercise
[A] p.135,
[E]
Creative
27
28
-   The   Method   of   Undetermined
Coefficients
Lecturing,
Discussion    and
Exercise
[A] p.152,
[E]
Creative
29
30
-   Variation of Parameters
Lecturing      and
Exercise,
Discussion
[A] p.152,
[E]
Creative
31
Practises
Exercise
[A]

32
Final Exam

IV. Reference

Compulsory :
[A]   Ross, S.L, Differential Equations, 1984, J. Willey, New York
[B]  Boyce, W.E., and Diprima, R.C. Elementary Differential Equations and Boundary Value Problems, 1992, J. Willey, New York. 

Additional :
[C]  Zill,  Dennis  G.,  Cullen,  Michael  R.  1997.  Differential  Equations  with  Boundary-value Problems.  Fourth  Edition.  USA  : Brooks/Cole Publishing Company.
[D]   http://tutorial.math.lamar.edu/Classes/DE/DE.aspx
[E]    http://www.sosmath.com/diffeq/diffeq.html

V. Evaluation

Component
Worth
Individual Assignment
10%
Group Assignment
15%
First Midterm Exam
20%
Second Midterm Exam
20%
Final Exam
35%
Total
100%

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