Department of Mathematics VISION VISION Mapua shall be among the best universities in the world.
MISSION a. The Institute shall provide a learning environment in o rder for its students to acquire the attributes that will make them globally competitive. b. The Institute shall engage in economically viable research, development, development, and innovation. c. The Institute shall provide state-of-the-art solutions to problems of industries and communities.
PROGRAM EDUCATIONAL EDUCATIONAL OBJECTIVES (ELECTRICAL ENGINEERING, ELECTRONICS ENGINEERING AND COMPUTER ENGINEERING) 1. The graduat graduates es are able able to apply apply the the broad broad fundament fundamental al concepts concepts in in social social and natural sciences, mathematics, and engineering, and the depth of knowledge gained in engineering, as professionals in their chosen careers. 2. The graduate graduatess are practicing practicing profess professional ionalss who are qualifie qualifiedd and proficie proficient nt in the use and creation of appropriate and up-to-date research and design methodologies and tools required to successfully perform their tasks in accordance with ethical norms and standards. 3. The graduates graduates demonst demonstrate rate effecti effective ve communicat communication ion skills, skills, the ability ability to work well well either individually or as part of a team, who have embraced lifelong learning values for continuous self and professional or career development. . !s professiona professionals, ls, the the graduate graduatess utili"e utili"e appropriat appropriatee knowledg knowledgee and technol technology ogy in in dealing with local and global, industrial, community, and environmental concerns for the advancement of society.
a
MISSION b
c
COURSE SYLLABUS 1.
Course Code:
MATH21 - 1
2.
Course Title:
CALCULUS 1
3.
Pre-requisite:
MATH1 ! "# MATH13 ! 1
".
Co-requisite:
$o$e
%.
Credit:
% u$its
&.
Course 'e 'es(ri)tio$:
This course course in Calculus Calculus covers covers discussio discussion n on on function functions, s, limits and continuity of functions, basic rules on differentiation of algebraic and transcendental transcendental functions, higher order and implicit differentiation, differentiation, applications applications of the derivatives which include curve tracing, equations of tangent and normal lines, applied maxima/minima and rate of change problems. This course also covers topics in Analytic Geometry that are essential in the study of Calculus. The use of the ectangular and !olar coordinate systems facilitate the thorough discussion of the fundamental concepts and theorems of Analytic Geometry and the properties and graphs of the different algebraic and polar functions.
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Stude$t Out(o+es ,$d Rel,tio$si) to Pror,+ Edu(,tio$,l O/0e(ties
Course Title:
CALCULUS
',te Ee(tie:
',te Reised:
Pre),red /4
O(t 21"
Cluster "" Committee
$d
2 Ter+ SY21"-21%
A))roed /4: #$ %A&"'( %ub)ect Chair
!age * of +
Pror,+ Edu(,tio$,l O/0e(ties 1 2 3 "
Stude$t Out(o+es abcdefghi)l-
an ability to apply nowledge of mathematics, science, and engineering an ability to design and conduct experiments, as well as to analye and interpret from data an ability to design a system, component, or process to meet desired needs an ability to function on multidisciplinary teams an ability to identify, formulate, and solve engineering problems an understanding of professional and ethical responsibility an ability to communicate effectively the broad education necessary to understand the impact of engineering solutions in the global and societal context a recognition of the need for, and an ability to engage in life0long learning a nowledge of contemporary issues an ability to use the techniques, sills, and modern engineering tools necessary for engineering practice 1nowledge and understanding of engineering and management principles as a member and leader in a team, to manage pro)ects and in multidisciplinary environments
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5. Course Out(o+es 6COs7 ,$d Rel,tio$si) to Stude$t Out(o+es Course Out(o+es After completing the course, the student must be able to2 *. Apply principles gained from the prerequisite courses 3. $iscuss comprehensively the fundamental concepts in Analytic Geometry and use them to solve application problems and problems involving lines. 4. $istinguish equations representing the circles and the conics5 use the properties of a particular geometry to setch the graph in using the rectangular or the polar coordinate system. 6urthermore, to be able to write the equation and to solve application problems involving a particular geometry. 7. $iscuss and apply comprehensively the concepts, properties and theorems of functions, limits, continuity and the derivatives in determining the derivatives of algebraic functions. 8. Analye correctly and solve properly application problems concerning the derivatives to include writing equation of tangent/normal line, curve tracing including all types of algebraic curves and cusps-, optimiation problems, rate of change and related0rates problems time0rate problems-. 8 Leel: - $trodu(ed# R- Rei$or(ed# '- 'e+o$str,ted
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. Course Coer,e Course Title:
CALCULUS
',te Ee(tie:
',te Reised:
Pre),red /4
O(t 21"
Cluster "" Committee
$d
2 Ter+ SY21"-21%
A))roed /4: #$ %A&"'( %ub)ect Chair
!age 3 of +
l
W!
T"#I$
T%&
&T
Mission and Vision of Mapua Institute of Technology
#eer discussion on Mission and )ision of Mapua Institute of Technology
(iagnostic *am
Orientation and Introduction to the
Course
(iscussion on $"s, T%&s, and &Ts of the course
$"
$"'
"verview on student-centered learning and eclectic approaches to be used in the c ourse.
'
&ssignment'
+undamental $oncept of &nalytic eometry ectangular $oordinate /ystem, (irected (istance, (istance +ormula (ivision of %ine /egment /lope and Inclination of a %ine &ngle 0etween %ines &rea of a Triangle1#olygon
- Working through e*amples - *ercise' - )isually uided %earning $"2
%ocus of a Moving #oint 3ormal +orm of quation of %ine (istance of #oint from %ine (istance between #arallel %ines &ngle 0isector 2
45I6 '
$"2 -Working through e*amples
*ercise 2
$I$%/ and the $"3I$/ 7
#roperties and &pplication Involving t he $ircles, #arabola, llipse and 8yperbola9 with )erte*1 $enter at any point 9 with 8ori:ontal1)ertical1 "blique &*is
- &ssignment 2 -
)isually uided %earning
$"7 ; #olar $urves and #arametric $urves9 /ketching a nd Transformation to ectangular forms of equations
45I6 2 =>?@ written, 7?@ on-lineA
$"7
< - &ssignment7 %imits
(efinition and $oncepts Theorems "ne-/ided %imits %imits of +unctions Infinite %imits and %imits at Infinity valuation &nd Interpretation /quee:e Theorem %imits of *pression Involving Transcendental +unctions
$ontinuity (efinition and Theorem Types of (iscontinuity9 elationship between limits and (iscontinuity B
Course Title:
CALCULUS
The (erivative and (ifferentiability of a +unction (efinition and concept valuation of the (erivative of a + unction based on (efinition =Increment Method or +our-/tep ule MethodA
',te Ee(tie:
- *ercise 7
- )isually ,uided %earning
- roup (ynamics
- Technology ,uided %earning CO4
',te Reised:
Pre),red /4
O(t 21"
Cluster "" Committee
$d
2 Ter+ SY21"-21%
- Working through e*amples
A))roed /4: #$ %A&"'( %ub)ect Chair
!age 4 of +
(erivatives of &lgebraic +unctions 5sing the 0asic Theorems of (ifferentiation and the $hain ule 8igher "rder and Implicit (ifferentiation
> (erivatives of the *ponential and %ogarithmic +unctions with &pplications
$";
45I6 7 &pplications quations of Tangent and 3ormal %ines C
- Working through e*ample
&ssignment ; *ercise ;
&pplication of the $oncepts of the (erivative and $ontinuity on $urve Tracing = Include all types of the &lgebraic curves, cuspsA
- )isually uided learning
#roDect
E
"ptimi:ation #roblems &pplied Ma*ima1Minima #roblems
CO5
ate of $hange #roblems9 elated-ate #roblems =Time-ate #roblemsA '?
QUI 4 Su!!ati"e
$"<
#ssess!ent
$IN#% &'#MIN#TION
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CO() CO*) CO4+ CO5
1. O))ortu$ities to 'eelo) Lielo$ Le,r$i$ S9ill To help students understand and apply the mathematical principles of Calculus and Analytic Geometry and provide them with the needed woring nowledge of the different mathematical concepts and methods for them to fully understand the relationship of Calculus with the increasingly complex world. 11. Co$tri/utio$ o Course to Meeti$ te Proessio$,l Co+)o$e$t 9ngineering Topics General 9ducation &asic %ciences and
2 2 2
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12. Te;t/oo9: College Algebra and Trigonometry by Aufmann, et.al. th Calculus 9arly Transcendentals *: ed by Anton, &ivens and $avis 13. Course E,lu,tio$ Course Title:
CALCULUS
',te Ee(tie:
',te Reised:
Pre),red /4
O(t 21"
Cluster "" Committee
$d
2 Ter+ SY21"-21%
A))roed /4: #$ %A&"'( %ub)ect Chair
!age 7 of +
%tudent performance will be rated based on the following2 Assess+e$t T,s9s
CO , CO (
CO *
Mi$i+u+ Aer,e 3or S,tis3,(tor4 Peror+,$(e 6=7
&.ercise ,
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Qui1 ,
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-iagnostic &.a!ination #ssign!ent,
&.ercise ( */2On3line Qui1 ( 0/2ritten
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#ssign!ent *
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Su!!ati"e #ssess!ent7 $inal &.a!ination
TOT#%
The final grades will correspond to the weighted average scores shown below2
Final Average 96 ≤ x < 100 93 ≤ x < 96 90 ≤ x < 93 86 ≤ x < 90 83 ≤ x < 86 80 ≤ x < 83 76 ≤ x < 80 73 ≤ x < 76 70 ≤ x < 73 Below 70
*4.*.
Final Grade 1.0 1.2 1.5 1.7 2.0 2.2 2.5 2.7 3.0 5.00 (Fail)
(ther Course !olicies a. Attendance According to C=9$ policy, total number of absences by the students should not be more than 3:; of the total number of meetings or > hrs for a three0unit0course. %tudents incurring more than > hours of unexcused absences automatically gets a failing grade regardless of class standing. b. %ubmission of Assessment Tass
Course Title:
CALCULUS
',te Ee(tie:
',te Reised:
Pre),red /4
O(t 21"
Cluster "" Committee
$d
2 Ter+ SY21"-21%
A))roed /4: #$ %A&"'( %ub)ect Chair
!age 8 of +
%tudent output should be submitted on time. #ate submission of course wors will not be accepted. c. ?ritten 9xamination #ong quies and final examination will be administered per schedule. 'o special exam will be given unless with a valid reason sub)ect to approval of the $epartment Chairman. d. Course !ortfolio Course portfolio will be collected at the end of the quarter. e. #anguage of "nstruction #ectures, discussion, and documentation will be in 9nglish. ?ritten and spoen wor may receive a lower mar if it is, in the opinion of the instructor, deficient in 9nglish. f.
=onor, $ress and Grooming Codes All of us have been instructed on the $ress and Grooming Codes of the "nstitute. ?e have all committed to obey and sustain these codes. "t will be expected in this class that each of us will honor the commitments that we have made. 6or this course the =onor Code is that there will be no plagiariing on written wor and no cheating on exams. !roper citation must be given to authors whose wors were used in the process of developing instructional materials and learning in this course. "f a student is caught cheating on an exam, he or she will be given ero mar for the exam. "f a student is caught cheating twice, the student will be referred to the !refect of %tudent Affairs and be given a failing grade.
g. Consultation %chedule Consultation schedules with the !rofessor are posted outside the faculty room and in the $epartment@s web0page http2//mat h.mapua.edu.ph -. "t is recommended that the student first set an appointment to confirm the instructor@s availability.
1". Oter Reere$(es *7.*.
*7.3
&oos a. TC?AG by #ouis #eithold, "nternational 9dition 3::*. b. %chaumm@s (utline %eries, $ifferential and "ntegral. c. $ifferential and "ntegral Calculus by #ove and ainville d. Calculus e by 9dwards and !enny th e. CA#CB#B% (ne and %everal variables- *: 9d by %alas, =ille and 9tgen f. Bniversity Calculus by =ass, et al th g. Calculus 9arly Transcendental 6unctions 8 ed. &y on #arson and &ruce 9dwards h. Analytic Geometry by 6uller and Tarwater i. Analytic Geometry by iddle ). Analytic Geometry by
?ebsites ?iley!lus 9nhanced ?eb Assign
15. Course Materials Made Available Course schedules for lectures and quies %amples of assignment/!roblem sets of students %amples of written examinations of students 9nd0of0course self0assessment 16. Committee Members: Course Cluster Chair CQI Cluster Chair Course Title:
CALCULUS
',te Ee(tie:
: Reynaldo anu!a ',te Reised:
Pre),red /4
O(t 21"
Cluster "" Committee
$d
2 Ter+ SY21"-21%
: Maria Rosario C. Exconde
A))roed /4: #$ %A&"'( %ub)ect Chair
!age of +
Members
Course Title:
',te Ee(tie:
CALCULUS
2$d Ter+ SY21"-21%
: Morris Martin "aballas #erardo #. $sita Alberto C. %illalu!
',te Reised:
Pre),red /4
O(t 21"
Cluster "" Committee
A))roed /4: #$ %A&"'( %ub)ect Chair
!age + of +
