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%