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%

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