MAPÚA UNIVERSITY
Department of Mathematics
VISION
Mapúa shall be among the best universities in the world.
MISSION
a. The University shall provide a learning environment in order for its students to acquire the
attributes that will make them globally competitive.
b. The University shall engage in publishable and/or economically viable research, development,
and innovation.
c. The University shall provide state-of-the-art solutions to problems of industries and communities.
PROGRAM EDUCATIONAL OBJECTIVES
Within the five years after graduation, the graduates of Civil Engineering program shall have
MISSION
a b c
1. Undertaken, singly or in teams, projects that show ability to solve complex
engineering problems.
2. Had substantial involvement in projects that take into consideration safety, health,
environmental concerns and the public welfare, partly through adherence to required
codes and laws.
3. Demonstrated professional success via promotions and/or positions of increasing
responsibility.
4. Demonstrated life-long learning via progress toward completion of an advanced
degree, professional development/continuing education courses, or industrial
training courses.
✓ ✓ ✓
5. Exhibited professional behavior and attitude in engineering practice; and
✓ ✓ ✓
6. Initiated and implemented actions toward the improvement of engineering practice.
✓ ✓ ✓
✓ ✓ ✓
✓ ✓ ✓
✓ ✓ ✓
COURSE SYLLABUS
1.
Course Code:
MATH148
2.
Course Title:
CALCULUS 3
3.
Pre-requisite:
MATH147
4.
Co-requisite:
none
5.
Credit:
3 units
6.
Course Description: This course covers sequences, infinite series, power series, vectors in the plane and
in 3-dimensional space, directional derivatives and gradient, vector-valued functions, and vector fields.
Course Title:
CALCULUS 3
Date Effective:
rd
3 Quarter
SY 2018-2019
Date Revised:
Prepared by:
February 2019
Cluster III Committee
Approved by:
Dr. Mylen L. Aala-Capuno
Department Chair
Page 1 of 7
7. Student Outcomes and Relationship to Program Educational Objectives
Program Educational
Objectives
1
2
3
4
5
6
Student Outcomes
(a)
Ability to apply knowledge of mathematics, science, and engineering; ✓
✓
(b)
an ability to design and conduct experiments, as well as to analyze
and interpret from data;
✓
✓
(c)
an ability to design a system, component, or process to meet desired
needs within realistic constraints such as economic, environmental,
social, political, ethical, health and safety, manufacturability, and
sustainability, in accordance with standards;
✓
✓
✓
✓
(d)
an ability to function on multidisciplinary teams;
✓
✓
✓
✓
(e)
an ability to identify, formulate, and solve engineering problems;
✓
✓
(f)
an understanding of professional and ethical responsibility;
(g)
an ability to communicate effectively;
(h)
the broad education necessary to understand the impact of
engineering solutions in the global, economic, environmental and
societal context;
(i)
(j)
(k)
(l)
✓
✓
✓
✓
✓
✓
a recognition of the need for, and an ability to engage in life-long
learning;
a knowledge of contemporary issues;
✓
✓
✓
✓
✓
✓
an ability to use the techniques, skills, and modern engineering tools ✓
necessary for engineering practice; and
Knowledge and understanding of engineering and management
principles as a member and leader in a team, to manage projects and ✓
in multidisciplinary environment.
✓
✓
✓
✓
✓
8. Course Outcomes (COs) and Relationship to Student Outcomes
Course Outcomes
Student Outcomes*
After completing the course, the student must be able
a b c d e f g h i j
to:
1. Recall the previous concepts of the calculus courses
taken.
2. Solve with accuracy problems involving sequence,
infinite series, power series, Maclaurin and Taylor I
D D D
D D D
series, and binomial series.
3. Show patience and accuracy in solving problems
involving vectors in the plane and vectors in 3- I D
D D D D D D
dimensional space.
4. Show appreciation in other areas of calculus through
performance of the evaluative activities involving
D
D D D D D D
directional derivatives and gradients, calculus of
vector-valued functions and calculus of vector fields.
* Level: I - Introduced, R - Reinforced, D - Demonstrated
k
✓
l
D
D
D
9. Course Coverage
WEEK
Course Title:
CALCULUS 3
TOPIC
Date Effective:
rd
3 Quarter
SY 2018-2019
TLA
Diagnostic Examination
Date Revised:
Prepared by:
February 2019
Cluster III Committee
AT
CO
CO1
Approved by:
Dr. Mylen L. Aala-Capuno
Department Chair
Page 2 of 7
WEEK
1
2
3
4
5
TOPIC
Mission and Vision of Mapúa
University
Orientation and Introduction to the
Course
Discussion on COs, TLAs, and
ATs of the course overview on
student-centered learning and
eclectic approaches to be used in
the course
I. Sequence and Infinite Series
• Sequence
• Limit of a Sequence
• Monotonic bounded sequence
• Infinite series
• Infinite sequence of constant
terms
• Infinite series of positive terms
• Tests for convergence /
divergence of infinite series
II. Power Series
• Taylor polynomials and
approximations
• Region of convergence of a
power series
• Differentiation and integration
of power series
• Maclaurin and Taylor series
• Binomial series
Long Quiz No. 1
III. Vectors in the Plane
• Properties of vectors
• Magnitude of a vector in the
plane
• Direction angle of a nonzero
vector in the plane
• Addition and scalar
multiplication
• Dot product
• Addition and scalar
multiplication
• Dot product
IV. Vectors in 3-Dimensional
Space
• Vector in 3-dimensional space
R3
• Magnitude of a vector in space
• Direction cosines and direction
angles of a nonzero vector in
space
• Addition and scalar
multiplication in space
• Dot product
• Angle between vectors
• Cross product
• Lines in space
• Coincident, parallel,
intersecting, and skew lines
Course Title:
CALCULUS 3
Date Effective:
rd
3 Quarter
SY 2018-2019
TLA
AT
CO
Visually Guided Learning
Working Through Examples
Online Readings
(Reading
Assignment)
MATLAB Activity
Blended Learning
1. //www.youtube.com/
watch?v=TrcCbdWw
CBc&list=PLSQ10a
2vh4HC5fetta6Rc5c
0wbRTx56nF7
CO2
Online Activities
(Assignment)
Written
Classworks
(Seatwork)
2. https://youtube.com/
watch?v=4ZYyg3bRvs
Working Through Examples
Technology Integrated
Learning using MATLAB
Online Readings
(Reading
Assignment)
Group Dynamics
Blended Learning
Date Revised:
1. https://www.youtube
.com/watch?v=TrcC
bdWwCBc&list=PLS
Q10a2vh4HC5fetta6
Rc5c0wbRTx56nF7
Online Activities
(Assignment)
CO3
Written
Classworks
(Seatwork)
2. https://youtube.com/
watch?v=tGVnBAHL
ApA
Prepared by:
February 2019
Cluster III Committee
Approved by:
Dr. Mylen L. Aala-Capuno
Department Chair
Page 3 of 7
WEEK
6
7
8
9
10
11
10.
TOPIC
• Distance between parallel lines
and between skew lines
• Planes in space
• Parallel planes
• Angle between planes
• Distance between a point and
a plane
• Distance between a plane and
a line parallel to that plane
Long Quiz No. 2
V. Directional Derivative and
Gradient
• Directional derivative of a
function of two variables
• Gradient of a function of two
variables
• Directional derivative of
function of three variables
• Gradient of a function of three
variables
• Tangent plane and normal line
to a surface
• Lagrange multipliers
VI. Calculus of Vector-Valued
Functions
• Vector-valued function
• Geometric representation of a
vector-valued function
• Domain of a vector-valued
function
• Limit and continuity of a
vector-valued function
• Derivative of vector-valued
functions
• Integration of vector-valued
functions
• Unit tangent vectors and unit
normal vectors
VII. Calculus of Vector Fields
• Vector fields
• Curl and divergence of a
vector field
• Line integrals
• Path independence of the line
integrals
• Green’s Theorem
• Surface integrals
• Gauss’s Divergence Theorem
• Stokes’ Theorem
Long Quiz No. 3
TLA
AT
CO
Visually Guided Learning
Blended Learning
1. https://www.youtube
.com/watch?v=TrcC
bdWwCBc&list=PLS
Q1
Online Readings
(Reading
Assignments)
2. https://youtube.com/
watch?v=tGVnBAHL
ApA
Working Through Examples
Technology Integrated
Learning Using MATLAB
CO4
Blended Learning
1. https://www.youtube
.com/watch?v=KSnt
cGOFdVc
Group Dynamics
Online Activities
(Assignment)
Written
Classworks
(Seatwork)
Blended Learning
1. https://www.youtube
.com/watch?v=iVMD
EPc2YQw
CO2,
CO3,
CO4
Final Examination
Opportunities to Develop Lifelong Learning Skill
Course Title:
CALCULUS 3
Date Effective:
rd
3 Quarter
SY 2018-2019
Date Revised:
Prepared by:
February 2019
Cluster III Committee
Approved by:
Dr. Mylen L. Aala-Capuno
Department Chair
Page 4 of 7
To help students understand and apply the mathematical principles of Calculus and Analytic Geometry and
provide them with the needed working knowledge of the different mathematical concepts and methods for
them to fully understand the relationship of Calculus with the increasingly complex world.
11.
Contribution of Course to Meeting the Professional Component
Engineering Topics
General Education
Basic Sciences and Mathematics
:
:
:
0%
0%
100%
12.
Textbook:
CALCULUS: EARLY TRANSCENDENTALS 11e by Anton
13.
Course Evaluation
Student performance will be rated based on the following:
Weight
(%)
Assessment Tasks
CO1
CO2
CO3
CO4
Diagnostic Exam
Assignment 1
Exercise 1
Quiz 1
Assignment 2
Exercise 2
Quiz 2
Assignment 3
Exercise 3
Quiz 3 Written
Quiz 3 Online
Project
Summative Test: Final Examination
Total
10.00
5.00
4.00
11.00
5.00
4.00
11.00
5.00
4.00
7.00
4.00
5.00
25.00
CO2 - 9.00
CO3 - 9.00
CO4 - 7.00
100.00
Minimum Average for
Satisfactory
Performance (%)
7.00
3.50
2.80
7.70
3.50
2.80
7.70
3.50
2.80
4.90
2.80
3.50
17.50
CO2 - 6.30
CO3 - 6.30
CO4 - 4.90
70.00
The final grades will correspond to the weighted average scores shown below:
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
Final Grade
1.00
1.25
1.50
1.75
2.00
2.25
2.50
2.75
3.00
5.0 Fail)
13.1 Other Course Policies
Course Title:
CALCULUS 3
Date Effective:
rd
3 Quarter
SY 2018-2019
Date Revised:
Prepared by:
February 2019
Cluster III Committee
Approved by:
Dr. Mylen L. Aala-Capuno
Department Chair
Page 5 of 7
a. Attendance
According to CHED policy, total number of absences by the students should not be more than
20% of the total number of meetings or 9 hours for a three-unit-course. Students incurring more
than 9 hours of unexcused absences automatically gets a failing grade regardless of class
standing.
b. Submission of Assessment Tasks
Student output should be submitted on time. Late submission of course works will not be accepted.
c. Written Examination
Long quizzes and final examination will be administered per schedule. No special exam will be
given unless with a valid reason subject to approval of the Department Chairman.
d. Course Portfolio
Course portfolio will be collected at the end of the quarter.
e. Language of Instruction
Lectures, discussion, and documentation will be in English. Written and spoken work may receive
a lower mark if it is, in the opinion of the instructor, deficient in English.
f.
Honor, Dress, and Grooming Codes
All of us have been instructed on the Dress and Grooming Codes of the University. We have all
committed to obey and sustain these codes. It will be expected in this class that each of us will
honor the commitments that we have made.
For this course the Honor Code is that there will be no plagiarizing on written work and no cheating
on exams. Proper citation must be given to authors whose works were used in the process of
developing instructional materials and learning in this course. If a student is caught cheating on
an exam, he or she will be given zero mark for the exam. If a student is caught cheating twice,
the student will be referred to the Prefect of Student Affairs and be given a failing grade.
g. Consultation Schedule
Consultation schedules with the Professor are posted outside the faculty room and in the
Department’s web-page (http://math.mapua.edu.ph). It is recommended that the student first set
an appointment to confirm the instructor’s availability.
14.
Other References
14.1 e-Books
Calculus Single and Multivariable, 7e by Hughes-Hallett, 2016
Calculus AP Edition by Hughes-Hallett
Applied Calculus 6 edition by Hughes-Hallett
Calculus of a Single Variable by Larson and Edwards, 2018
Applied Calculus by Waner and Constenoble, 2018
Calculus: An Applied Approach by Larson, 2017
Calculus Early Transcendental by Stewart, 2016
Applied Calculus for Managerial, Life and the Social Sciences by Tan, 2017
14.2 Websites
https://mapua.blackboard.com
www.sosmath.com
www.intmath.com
www.hivepc.com
https://www.mathworks.com/
https://matlab.mathworks.com/
15.
Course Materials Made Available
Course schedules for lectures and quizzes
Course Title:
CALCULUS 3
Date Effective:
rd
3 Quarter
SY 2018-2019
Date Revised:
Prepared by:
February 2019
Cluster III Committee
Approved by:
Dr. Mylen L. Aala-Capuno
Department Chair
Page 6 of 7
Samples of assignment/Problem sets of students
Samples of written examinations of students
End-of-course self-assessment
16.
Committee Members:
Course Cluster Chair
CQI Cluster Chair
Members
Course Title:
CALCULUS 3
Date Effective:
rd
3 Quarter
SY 2018-2019
: Rosario S. Lazaro
: Floro Deogracias G. Llacuna
: Juanito E. Bautista
: Francis Anthony G. Llacuna
Date Revised:
Prepared by:
February 2019
Cluster III Committee
Approved by:
Dr. Mylen L. Aala-Capuno
Department Chair
Page 7 of 7