MAPÚA UNIVERSITY
Department of Mathematics
VISION
Mapua 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.
MISSION
PROGRAM EDUCATIONAL OBJECTIVES
(CIVIL ENGINEERING)
Within five years after graduation, the graduates of Civil Engineering shall have:
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.

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5. Exhibited professional behavior and attitude in engineering practice.

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6. Initiated and implemented actions toward the improvement of engineering practice.

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
COURSE SYLLABUS
1. Course Code
: MATH24-1
2. Course Title
: DIFFERENTIAL EQUATIONS
3. Pre-requisite
: Math23 -1 and Math23-1X
4. Co-requisite
: None
5. Credit
: 3 units
6. Course Description
: This course covers useful methods of solving first-order, first-degree
differential equations and higher-order, first-degree linear differential
equations that have relevant and important applications to the
sciences and engineering. It also includes methods of solving higherorder differential equations - the method of undetermined
coefficients and variation of parameters. Other topics include the
construction of differential equations as mathematical models and
introductory discussions on the Laplace Transforms.
Course Title:
DIFFERENTIAL EQUATIONS
Date Effective:
4th Quarter
SY 2016 -2017
Date Revised:
June 2, 2017
Prepared by:
Cluster V
Committee
Approved by:
LD SABINO
Subject Chair
Page 1 of 8
7. Student Outcomes and Relationship to Program Educational Objectives
Program Educational
Objectives
Student Outcomes
1
2
3
4
5
6
√

√
√
√
√
(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
√
√
√
√
√
√
(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 and societal context
√
√
√
√
√
√
(i)
a recognition of the need for, and an ability to engage in life-long
learning
√
√
√
√
√
√
(j)
a knowledge of contemporary issues
√
√
√
√
√
√
(k)
an ability to use the techniques, skills, and modern engineering tools
necessary for engineering practice
√
√
√
√
√
√
(l)
knowledge and understanding of engineering and management
principles as a member and leader in a team, to manage projects and
in multidisciplinary environments
√
√
√
√
√
√
(a)
an ability to apply knowledge of mathematics, science, and engineering
8. Course Outcomes (COs) and Relationship to Student Outcomes:
Course Outcomes
The student should be able to:
a
1. Analyze and demonstrate algebraic
quantitative manipulation of data graphically,
numerically, analytically and descriptively in
solving first order first degree differential
equations.
2. Interpret scientific and engineering
applications of first order first degree DE
through critical thinking, problem solving skills,
and integration of mathematical modeling to
real life problem situations using appropriate
algorithms and technology into mathematical
processes.
3. Communicate quantitatively mathematical
problems on higher order differential
equations and determine which numerical
technique to use to solve it logically.
b
c
Student Outcomes*
d e f
g h i
I
R
D
D
D
I
R
D
D
j
K
R
D
R
I
D
D
* Level: I- Introduced, R- Reinforced, D- Demonstrated
Course Title:
DIFFERENTIAL EQUATIONS
Date Effective:
4th Quarter
SY 2016 -2017
Date Revised:
June 2, 2017
Prepared by:
Cluster V
Committee
Approved by:
LD SABINO
Subject Chair
Page 2 of 8
l
9. Course Coverage
WEEK
DAY
1
1
2
3
4
2
5
6
7
3
4
8
9
10
11
12
13
5
14
15
16
6
17
18
19
7
20
21
22
8
23
24
25
9
10
11
:
26
27
28
29
30
TOPICS
TLA
AT
Orientation
1.1 Some Basic Mathematical Models;
Working through
Direction Fields
examples
1.2 Solutions of Some Differential
Buzz Group
Equations
1.3 Classification of Differential
Rounds
Equations
Individual Presentation
2.1 Linear Equations; Method of
Integrating Factors
Class Critique
2.2 Separable Equations
2.4 Differences Between Linear and NonStudents producing
Linear Equations
mind maps
2.4 Bernoulli’s Equation
(storyboards)
2.3 Modeling with First Order Equations
2.3 Modeling with First Order Equations
Rubric for CPR
2.5 Autonomous Equations and
Population Dynamics
LONG QUIZ 1
2.6 Exact Equations and Integrating
Case Study Analysis
Factors
Creative (Technical and
2.7 Numerical Approximation: Euler’s
Algorithmic) Writing
Method
2.8 The Existence and Uniqueness
Group Discussion
Theorems
3.1 Homogenous Equations with
Class Argumentation
Constant Coefficients; Second Order
4.2 Homogenous Equations with
Rubric for Group Work
Constant Coefficients; Higher Order
3.2 Solutions of Linear Homogenous
Rubric for Group
Equations; The Wronskian
Presentation
3.3 Complex Roots of the Characteristic
Equation
3.4 Repeated Roots; Reduction of Order
LONG QUIZ 2
3.5 Non-Homogenous Equations;
Guided Learning
Method of Undetermined Coefficients;
Second Order
Group Dynamics
4.3 The Method of Undetermined
Class Argumentation
Coefficients; Higher Order
3.6 Variation of Parameters; Second
Rubric for CPR
Order
4.4 The Method of Variation of
Parameters; Higher Order
3.7 Mechanical and Electrical Vibrations
3.8 Forced Vibrations
LONG QUIZ 3
6.1 Definition of the Laplace Transform
6.2 Solution of Initial Value Problems
31
Course Title:
DIFFERENTIAL EQUATIONS
Written Long Quiz 1(Q)
Online Homework (A)
Class work (Exr)
4th Quarter
SY 2016 -2017
Date Revised:
June 2, 2017
Prepared by:
Cluster V
Committee
CO 1
Written Long Quiz
2(Q2)
Online Homework 2
(A2)
CO 2
Design Project (Prj)
Classwork 2 (Exr 2)
Online Homework 3
(A3)
On-line Quiz 3 (Ex 3)
CO 3
Classwork 3 ( Exr 3)
CO 1 (8%)
CO 2 (9%)
CO 3 (8%)
SUMMATIVE ASSESSMENT
FINAL EXAMINATION (Written, Departmental, 25%)
Date Effective:
COURSE
OUTCOMES
Approved by:
LD SABINO
Subject Chair
Page 3 of 8
Online Homeworks
A 1 (4%)
A 2 (4%)
A 3 (4%)
ONLINE HOMEWORKS
Topics
1.1 Some Basic Mathematical Models; Direction Fields
1.2 Solutions of Some Differential Equations
1.3 Classification of Differential Equations
2.1 Linear Equations; Method of Integrating Factors
2.2 Separable Equations
2.4 Differences Between Linear and Non-Linear
Equations
2.3 Modeling with First Order Equations
2.5 Autonomous Equations and Population Dynamics
2.6 Exact Equations and Integrating Factors
2.7 Numerical Approximation: Euler’s Method
2.8 The Existence and Uniqueness Theorems
3.1 Homogenous Equations with Constant Coefficients;
Second Order
4.2 Homogenous Equations with Constant Coefficients;
Higher Order
3.2 Solutions of Linear Homogenous Equations; The
Wronskian
3.3 Complex Roots of the Characteristic Equation
3.4 Repeated Roots; Reduction of Order
3.5 Non-Homogenous Equations; Method of
Undetermined Coefficients; Second Order
4.3 The Method of Undetermined Coefficients; Higher
Order
3.6 Variation of Parameters; Second Order
4.4 The Method of Variation of Parameters; Higher
Order
3.7 Mechanical and Electrical Vibrations
3.8 Forced Vibrations
Due Date
WEEK 4 OR AS
SCHEDULED
WEEK 7 OR AS
SCHEDULED
WEEK 9 OR AS
SCHEDULED
10. Opportunities to Develop Lifelong Learning Skill
To develop lifelong learning skill, the primary learning outcome for this course is the Student’s Quantitative
Reasoning, which is to understand and apply the mathematical principles in Differential Equations that will
provide students with the needed working knowledge of advanced mathematical concepts and methods, and
an awareness of their relationship to increasingly complex world.
11. Contribution of Course to Meeting the Professional Component:
General Education:
Engineering Topics:
Basic Sciences and Mathematics:
25%
25%
50%
12. Textbook: Elementary Differential Equations and Boundary Value Problems, William E. Boyce, Richard C.
DiPrima. John Wiley & Sons, Inc. 10th ed.
Course Title:
DIFFERENTIAL EQUATIONS
Date Effective:
4th Quarter
SY 2016 -2017
Date Revised:
June 2, 2017
Prepared by:
Cluster V
Committee
Approved by:
LD SABINO
Subject Chair
Page 4 of 8
13. Course Evaluation
Student performance will be rated based on the following:
Assessment Tasks
(All resources will be taken from wiley.plus)
CO1
CO2
CO3
Weight (%)
Online Homework 1 (A)
5
Class Work 1 (Exr)
3
Long Quiz 1 (Q) - Written
15
Online Homework 2 (A2)
5
Class Work 2 (Exr 2)
3
Design Project (Prj)
6
Long Quiz 2 (Q2) - Written
15
Online Homework 3 (A3)
5
Class Work 3 (Exr 3)
Quiz 3 (Ex 3) - Online ( 70% CO3, 30% CO1
&CO2)
Final Exam (FE)
Summative Assessment
Final Exam (FE2)
Final Examination (written)
Final Exam (FE3)
3
Minimum
Average for
Satisfactory
Performance (%)
16.1
20.3
16.1
15
8
9
17.5
8
TOTAL
100
70
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
5.00 (Fail)
13.1 Other Course Policies
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 hrs for a three-unit-course (6 meetings). Students
incurring more than 9 hours of unexcused absences automatically gets a failing grade
regardless of class standing.
b. Submission of Assessment Tasks (Student Outputs) should be on time; late submittal of
coursework’s will not be accepted. If you have a justifying circumstance, it must be discussed
and a decision made before the due date or it is due when the assignment is due. Copied
Course Title:
DIFFERENTIAL EQUATIONS
Date Effective:
4th Quarter
SY 2016 -2017
Date Revised:
June 2, 2017
Prepared by:
Cluster V
Committee
Approved by:
LD SABINO
Subject Chair
Page 5 of 8
works/tasks or any required material to be submitted in the class are strictly prohibited and
found guilty will be considered as cheating as well.
c. Major Examination (Long Quiz for both written and on-line and Final Exam) will be
administered as scheduled. No special exam will be given unless with a valid reason subject for
approval of the Chairman of the Mathematics Department. Furthermore, students of this
course are required to participate actively in the events/activities organized for this course.
d. Guidelines for Taking On-Line Exams (in-campus)
1. Students are required to bring their own computer equipments, eg, Laptop,
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
NetBook; and students must ensure that their gadgets are fully functioning and
batteries are fully charged before the exam. Tablets, such as iPads and Android
Tablets, are not recommended for use in online examinations.
Students are required to submit written solutions of their answers in the online
examination using BIG test booklet with lines.
Students are highly recommended to bring their own source of internet connection,
eg., Broadband Sticks, Portable/Pocket WiFi Connections, Mobile Hotspots. The use
of the Mapua WiFi Service might cause the student delays connecting to the
internet.
During the period of exam, a student is only allowed to use a single browser, in its
most recent updated version and as recommended by Wiley.PLUS. The student may
opt to use Mozilla Firefox, Google Chrome, Safari, Rockmelt, Internet Explorer as
his/her browser, or any internet-browsing software. Entering into private
sessions/windows and/or having multiple active sessions/tabs is strictly prohibited.
For Google Chrome users, if problems should arise, such as the failure of the loading
of exam questions and/or digital images in the WileyPlus examination, the student
may right-click-select the frame/pane of the exam question and choose the “reload
frame” option.
The use of softwares/applications other than the student's browser during the exam
is prohibited. The use of softwares/applications not categorized as browsers, such
as MS Excel, MATLab, Algebrator, Adobe Reader, PhotoViewer, and the like, is not
allowed and will be considered cheating.
Access to websites other than WileyPlus.com is not allowed. Access to online
solvers such as WolframAlpha, search engines, and third-party websites will be
considered cheating.
The use of gadgets, other than the student's computer machine, such as cellphones,
tablets, and the like, during the exam is not allowed.
Talking during the exam is not allowed. Students are to focus solely on their monitor
screens and solution papers. Clarifications should be addressed directly to the
teacher in charge.
Students are not allowed to print-screen or save the exam questions, or any
portion/part of the exam.
Strict checking of attendance will be done before and after the exam. Students who
send another person (ringer) in lieu of their presence will be considered cheating.
Thus, students should take the exam on his/her assigned classroom not anywhere
else.
Students are required to come on time in their respective classes for the exam will
open exactly during their respective class periods and close automatically at the end
of the class period. It is suggested to finish the exam at least 5 minutes earlier to
ensure that the exams will be sent to Wiley.PLUS administrators before the due
time.
Course Title:
DIFFERENTIAL EQUATIONS
Date Effective:
4th Quarter
SY 2016 -2017
Date Revised:
June 2, 2017
Prepared by:
Cluster V
Committee
Approved by:
LD SABINO
Subject Chair
Page 6 of 8
13. Lastly, the professor will not be held responsible if technical problems should arise,
such as loss of internet connection, machine malfunction, loss of battery charge and
others.
e. Course Portfolio will be collected at the end of the quarter. Lost documents will not be
given due credit.
f. 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.
g. Honor, Dress and Grooming Codes
All of us have been instructed on the Dress and Grooming Codes of the Institute. 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/class produced
reviewers/design projects/video clips and learning in this course. If a student is caught
cheating on an exam by his instructor or substitute teacher, he or she will be given
zero mark for the exam. If a student is caught cheating twice on the same course, the
student will be referred to the Prefect of Student Affairs and be given a failing grade.
Grave misconduct other than cheating will likewise be given a failing grade. Disrespect
to your teacher or to others in the classroom will not be tolerated in the least.
Argument is great but bullying, fighting, mocking, and demeaning the teacher or other
students will not be allowed. Come to class on time, there can be mitigating
circumstances from time to time but if it becomes a chronic behavior you may lose
points or credit for the class.
h. Consultation Schedule
Consultation schedules with the Professor are posted outside the Math Faculty room
and in the School’s web-page (http://che-chm.mapua.edu.ph). It is recommended that
the student first set an appointment to confirm the instructor’s availability.
14. Other References
14.1 Books
a) A First Course in Differential Equations with Modern Applications by Dennis Zill, 7th ed., 2000
b) Fundamentals of Differential Equations, Pearson International Edition by Nagle, R. Kent, 7th
ed, 2008
c) Elementary Differential Equations by Boyce and Richard C. Diprima, 1997
d) Elementary Differential Equations by William Derrich and Stanley Grossman, 1997
14.2 Websites
a) S.O.S Differential Equations http://www.sosmath.com/diffeq/diffeq.html
b) Paul’s Online Math Notes http://tutorial.math.lamar.edu/Classes/DE/DE.aspx
c) MIT Open Courseware http://ocw.mit.edu/courses/mathematics/18-03sc-differentialequations-fall-2011/
d) Differential Equations Interactive Mathematics http://www.intmath.com/differentialequations/des-intro.php
e) http://demonstrations.wolfram.com/topic.html?topic=Differential+Equations
These are interactive explorations of differential equations topics that can run in a free
player. Boyce 10e WileyPLUS course includes some which are specifically associated with the
textbook.
Course Title:
DIFFERENTIAL EQUATIONS
Date Effective:
4th Quarter
SY 2016 -2017
Date Revised:
June 2, 2017
Prepared by:
Cluster V
Committee
Approved by:
LD SABINO
Subject Chair
Page 7 of 8
f)
http://odetoolkit.hmc.edu/
A Java program that helps users calculate, visualize, and explore solutions to differential
equations, by the creators of the ODE Toolkit software.
15. Course Materials Made Available:
Course Calendar
Samples of Coursework’s /Design Projects/Video Presentations/Class Produced Reviewers
Samples of written examinations of students
End-of-course self-assessment
16. Committee Members (Cluster V):
Course Cluster Chair: Dr. Dante L. Silva
CQI Cluster Chair: Engr. Ma. Christina A, Valerio
Members: Engr. Ronald L. Arciaga
Engr. Gerardo Usita
Course Title:
DIFFERENTIAL EQUATIONS
Date Effective:
4th Quarter
SY 2016 -2017
Date Revised:
June 2, 2017
Prepared by:
Cluster V
Committee
Approved by:
LD SABINO
Subject Chair
Page 8 of 8