Sillaby of Differential Calculus Major Mathematics Education Semester 1 / I

Faculty                            : Mathematics and Natural Science
Study Program              : Mathematics Education
Course / Code               : Differential Calculus / MAA304
Credits                             : Theory:   2  SKS                 Practice: 1  SKS
Semester                         : 1st
Prerequisite/Code          : -
Professor                         : Wahyu Setyaningrum, M.Ed.

I.   Course Description           :

Differential  calculus  covers  the  topics  of  real  number,  plane  coordinate,  inequalities, absolute value, functions, limit, continuity, derivative functions, chain rules, maxima- minima,  high  order  derivatives, implicit  differentiation,  concavity,  and  optimization problems.

II.  Standard Competence:

Students  are  expected  to  be  able  to:  (1)  explain  the  real  number  system  and  plane coordinate, (2) determine the solution of inequalities and absolute value, (3) determine the functions, limit, and continuity of functions, (4) determine the derivative of functions, (5) apply the chain rules, (6) determine the maxima and minima of the functions, (7) determine high  order  derivatives  and  implicit  differentiation,  (8)  solve  problems  related  to  the derivative.

III. Activity

Meeting	Basic Competence	Essentials Concept	Learning Strategy	References	Character
1	Explaining            real number   system   and plane coordinate	Real     number system       and coordinate plane	Group discussion and presentation.	[A]: 4– 6 [B]: 4– 6	5 & 6
2	Determining the solution  of inequalities	Inequalities	Group discussion and presentation.	[A]: 3 – 4 [B]: 6– 10	5, 6 & 18
3 – 4	Determining          the	Absolute value	Group	[A]: 3 – 4	5, 6 & 18

	solution       of       the absolute value		discussion and presentation.	[B]: 11– 16
5	Determining          the functions	Functions	Group discussion and presentation.	[A]: 22– 45 [B]: 49– 76	5, 6 & 18
6-7	Determining the domain of the functions	Functions   and its domain	Group discussion and presentation.	[A]: 22– 45 [B]: 49– 76	5, 6 & 18
8	Graphing/sketching rational functions	Graph           of rational functions	Group discussion, investigation and presentation.	[A]: 30– 33	4, 5, 6 & 18
9-10	Determining exponential           and logarithm functions	Exponential and   logarithm functions	Group discussion and presentation.	[C]:378– 416	4, 5, 6 & 18
11	Solving       arithmetic operations of function and   determining   its domain	Arithmetic operations    of function     and its domain	Group discussion, investigation and presentation.	[C]:93 – 94	4, 5, 6 & 18
12	Solving arithmetic operations of function and determining its domain	Composite functions    and their domains	Group discussion, investigation and presentation.	[C]:94 -96 [D]:24 – 27	4, 5, 6 & 18
13-14	Determining the limit of functions	Limits	Group discussion, investigation and presentation.	[A]: 68– 74 [B]:86– 157 [D]: 27 - 29	4, 5, 6 & 18
15-16	Determining continuity                of functions	Continuity	Group discussion, investigation and presentation.	[A]: 74– 81 [D]: 29 - 32	4, 5, 6 & 18
17	Exam 1				5,  6,  13, 14
18	Determining          the derivative   of functions using the concept of limit	Limit          and derivatives	Group discussion, and presentation.	[A]: 58– 62 [A]: 83–87 [B]:176– 224 [D]: 32– 34	4, 5, 6 & 18
19	Determining the derivative   of functions using product rule and quotient rule	The derivatives	Group discussion, investigation and presentation.	[A]: 88– 92 [D]: 34 - 37	4, 5, 6 & 18
20	Determining          the derivative                of	The chain rule	Group discussion,	[A]: 92– 97 [B]:254–	4, 5, 6 & 18

	functions   using   the chain rule		investigation and presentation.	240 [D]: 37–39
21-23	Solving        problems related        to        the derivative                of exponential, logarithmic,          and trigonometric functions.	Derivatives  of exponential, logarithmic, and trigonometric functions	Group discussion, investigation and presentation.	[C]:389– 416 [D]: 39–44	4, 5, 6 & 18
24-25	Determining   implicit differentiation	Implicit differentiation	Group discussion and presentation.	[A]:102– 107 [B]:241-253	4, 5, 6 & 18
26	Determining        high order derivatives	High        order derivatives	Group discussion and presentation.	[A]:107– 114 [B]:254-260	4, 5, 6 & 18
27	Determining          the maxima  and  minima of the functions using its derivatives.	Maxima- Minima	Group discussion, investigation and presentation.	[A]:115– 117 [B]:278-288	4, 5, 6 & 18
28	Determining          the increasing/decreasing of the functions using its derivatives.	Increasing  and decreasing and the derivative test	Group discussion, investigation and presentation.	[A]:117– 119 [B]:302– 334	4, 5, 6 & 18
29	Determining the concavity of the functions using its second derivatives.	Concavity and the second derivative test	Group discussion, investigation and presentation.	[A]:120– 123	4, 5, 6 & 18
30-31	Determining          the solution of problems related   to optimization of functions	Optimization problems	Group discussion, investigation and presentation.	[A]:123– 136	4, 5, 6 & 18
32	Exam 2				5,  6,  13, 14

IV. References:

[A] Simmons, GF. (1996). Calculus with Analytic Geometry. USA: McGraw-Hill Co.
[B] Leithold, L. (1986). The Calculus with Analytic Geometry. Harper & Row Publisher.
[C] Larson & Hostetler. (1987). Brief Calculus with Applications. USA: DC Heath & Co.
[D] Setyaningrum, W. (2010). Handout: Differential Calculus. 

V.  Evaluation

No	Componen	Worth
1	Participation	15 %
2	Assignment	30 %
3	Exam 1 & 2	25%
4	Final Exam	30%
Total		100%