Sillaby Differential Equation Major International Mathematics Education Semester 3 / III

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%