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.