Sillaby of Calculus of Integral Major International Programme for Science Education Semester 3 / III

Faculty                                 : Mathematics and Natural Science

Study Program                     : International Programme for Science Education

Course/Code                       : Calculus of Integral/MAA 307

Credit                                 : Teory = 3 (three) SKS Semester                             : 3 (three) Prerequisite/Code                : -

Professor                             : Nikenasih Binatari, M.Si

I. Course Description

This course study about definite and indefinite integral, fundamental theorem of integral, the application of definite integral, transendent function, integration technique, indefinite form and improper integral.

II. Standard of Competence

Upon completing this course, students should understand the general theory of integral calculus and the basic techniques for solving calculus of integrals. At this end of this course, students should understand which theory and method of calculus of integral 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
1st week	Students  know  the  motivation to study integral calculus and its connection with differential calculus	Sillaby, motivation and differentiation rules	Discussion, Exercise	[A], [C]	Curiousity
2nd week		Sigma Notation å n, ån 2 , ån3	Lecturing, Discussion, Exercise	[A], [B]	Understand
3rd week	Students understand the idea to determine the approximation of several problems	Area under a curve	Lecturing, Exercise	[A], [B],[C]	Understand,
4th week		Volume of a solid of revolution	Lecturing, Discussion, Exercise,	[A], [B],[C]	Understand
5th week		Arc Length	Lecturing, Discussion, Exercise,	[B], [A]	Understand
6th week		Surface area of a solid of revolution	Lecturing, Discussion, Exercise,	[B]	Understand
7th week		Work and Momen of Inersia	Lecturing, Discussion, Exercise,	[B]	Understand
8th week	Students  understand  the  basic theory of integral calculus	Definition   of   Antiderivative,   its rules, its linearity properties.	Lecturing, Discussion, Exercise,	[A], [B]	Understand, Reasonable
9th week		Riemann Sum, Definition of definite integral,      Computing      definite integral	Lecturing, Discussion, Exercise,	[A], [B]	Understand, reasonable
10th week		Fundamental Theorem of Calculus, Properties of Definite Integral	Lecturing, Discussion, Exercise,	[A], [B]	Understand, reasonable
11st week	Students   able   to   solve   the problems    before    using    the theory of integral	The   application   of   integral   on counting the area under a curve, volume of a solid of revolution, etc	Lecturing, Discussion, Exercise,	[A], [B]	Understand, Applicative

12nd week	Midterm Exam and
13rd week	Students understand several method to solve integration problems.	Substitution   method,   rasionalize subtitution method	Lecturing, Discussion, Exercise,	[A], [B]	Understand, Creative
14th week		Partial Method	Lecturing, Discussion, Exercise,	[A], [B]	Understand, Creative
15th week		Integral of rasional function	Lecturing, Discussion, Exercise,	[A], [B]	Understand, Creative
16th week		Integral    of    indefinite    function, Improper Integral	Lecturing, Discussion, Exercise,	[A], [B]	Understand, Creative

IV. Reference

Compulsory :

[A]   Passow, Eli, Ph.D. Schaum’s Outline of Theory and Problems of Understanding Calculus Concepts. 1996. McGraw-Hill Companies. USA.

[B]   Varberg, Dale. Purcell, Edwin J. Calculus. 2001.

Additional :

[C]   Ryan, Mark. Calculus for dummies. 2003. Wiley Publishing Inc.