DIFEQNS.pdf

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HOLY ANGEL UNIVERSITY College of Engineering & Architecture Department of Computer Engineering

University Vision, Mission, Goals and Objectives:

Mission Statement (VMG)

We, the academic community of Holy Angel University, declare ourselves to be a Catholic University. We dedicate ourselves to our core purpose, which is to provide accessible quality education that transforms students into persons of conscience, competence, and compassion. We commit ourselves to our vision of the University as a role-model catalyst for countryside development and one of the most influential, best managed Catholic universities in the Asia-Pacific region. We will be guided by our core values of Christ-

centeredness, integrity, excellence, community, and societal responsibility. All these we shall do for the greater glory of God. LAUS DEO SEMPER!

College Vision, Goals and Objectives:

Vision

A center of excellence in engineering and architecture education imbued with Catholic mission and identity serving as a role- model catalyst for countryside development

Mission

To provide accessible quality engineering and architecture education leading to the development of conscientious, competent and compassionate professionals who continually contribute to the advancement of technology, preserve the environment, and improve life for countryside development.

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Goals

The College of Engineering and Architecture is known for its curricular programs and services, research undertakings, and community involvement that are geared to produce competitive graduates:

- who are equipped with high impact educational practices for global employability and technopreneurial opportunities;

- whose performance in national licensure examinations and certifications is consistently above national passing rates and that falls within the 75^th to 90^th percentile ranks; and,

- who qualify for international licensure examinations, certifications, and professional recognitions;

Objectives

In its pursuit for academic excellence and to become an authentic instrument for countryside development, the College of Engineering and Architecture aims to achieve the following objectives:

1. To provide students with fundamental knowledge and skills in the technical and social disciplines so that they may develop a sound perspective for competent engineering and architecture practice;

2. To inculcate in the students the values and discipline necessary in developing them into socially responsible and globally competitive professionals;

3. To instill in the students a sense of social commitment through involvement in meaningful community projects and services;

4. To promote the development of a sustainable environment and the improvement of the quality of life by designing technology solutions beneficial to a dynamic world;

5. To adopt a faculty development program that is responsive to the continuing development and engagement of faculty in research, technopreneurship, community service and professional development activities both in the local and international context;

6. To implement a facility development program that promotes a continuing acquisition of state of the art facilities that are at par with leading engineering and architecture schools in the Asia Pacific region; and,

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7. To sustain a strong partnership and linkage with institutions, industries, and professional organizations in both national and international levels.

Relationship of the Program Educational Objectives to the Vision-Mission of the University and the College of Engineering &

Architecture:

General Engineering Educational Outcomes (PEOs):

Within a few years after graduation, our

graduates of engineering program are expected to have:

Vision-Mission

Christ-

Centeredness Integrity Excellence Community Societal Responsibility

1. Practiced their profession √ √ √ √ √

2. Shown a commitment to life-long learning √ √ √ √ √

3. Manifested faithful stewardship √ √ √ √ √

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Relationship of the Engineering Program Outcomes to the Program Educational Objectives:

General Engineering Student Outcomes (SOs):

At the time of graduation, engineering program graduates should be able to:

PEOs

1 2 3

a) Apply knowledge of mathematics, physical sciences, engineering sciences to the practice of engineering √ √ √

b) Design and conduct experiments; as well as analyze and interpret data √ √ √

c) 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) Function on multidisciplinary teams √ √ √

e) Identify, formulate and solve engineering problems √ √ √

f) Understand professional and ethical responsibility √ √ √

g) Demonstrate and master the ability to listen, comprehend, speak, write and convey ideas clearly and

effectively, in person and through electronic media to all audiences. √ √ √

h) Modernize education necessary to understand the impact of engineering solutions in a global, economic,

environmental, and societal context √ √ √

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i) Recognize the need for, and engage in life-long learning and keep current of the development in the field √ √ √

j) Respond to contemporary issues √ √ √

k) Use the techniques, skills, and modern engineering tools necessary for engineering practice. √ √ √ l) Apply engineering and management principles as a member and leader in a team; manage projects in

multidisciplinary environments √ √ √

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COURSE SYLLABUS

DIFEQNS

FINALS

PRELIMS MIDTERMS

1. Definitions and Terminology 1.1. Definition and

Classification of Differential Equations (by type, by order, by degree, by linearity)

1.2. General and Particular Solution

2. Solution of Some 1st Order, 1st Degree D.E.

2.1. Exact Differential Equations, Method of Grouping, and

Integrating Factor 2.2. Variable Separable 2.3 .Homogeneous

Equations

2.4.Linear D.E. and its solution

2.5.Bernoulli Equations 2.6.Special Transformations

3. Applications of 1st Order D.E.

3.2. Rate of Growth and Decay

3.3. Population Growth 3.4. Newton’s Law of

Cooling

3.5. Mixture Problems 3.6. Problems in

Mechanics

5. Solution of Higher Order Linear Differential Equations 5.1. Homogeneous Linear

D.E. with Constant Coefficients

5.2. Non-Homogeneous Differential Equation 5.2.1. Method of

Undetermined Coefficients 5.2.2. Variation Of

Parameters 6. Application of 2^nd Order

Linear Differential Equations with Constant Coefficients 6.1. Electrical Circuits

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Course Title: Differential Equations Subject Code:DIFEQNS

Course Credit: 3 units Year Level: 3^rdYear

Pre-requisites: INTECAL Course Calendar: 1^stSemester

Course Description:

Differentiation and integration in solving first order, first-degree differential equations, and linear differential equations of order n; and applications involving differential equations.

Course Outcomes/Objectives (CO):

After completing the course, the student must be able to:

PO Code Link(s)

a b c d e f g h i j k l m n 1. Define and Identify different classifications of differential

equations I I I I I I I

2. Perform engineering calculations using appropriate mathematical

principles and solutions in differential equations. I I I I I I I Values Objectives:

1. Explain the relevance of Differential Equations in our everyday life.

2. Display a keen sense of analytical thinking and technical approach to problem solving.

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COURSE ORGANIZATION

Time

Frame Hours

CO Code

Link

Course Outline Teaching & Learning Activities Assessment Tools

(Outcomes-Based) Resources Week

1-2

6 CO 1

CO 2

1. Definitions and Terminology 1.1. Definition and Classification of Differential Equations (by type, by order, by degree, by linearity)

1.2. General and Particular Solution

2. Solution of Some 1st Order,

1st Degree D.E.

2.1. Exact Differential Equations

 Group/class discussion

 Define and Classify Differential Equations by type, by order, by degree, and by linearity

 Solve the general solution of DE.

 Solve the particular solution of DE.

 Obtain the solution of 1^st order, 1^st degree DE when the equation is Exact.

 Problem set

 Recitation/Board work (Individual Participation)

 A1, combined with other course references

Week 3-4

6 CO 1

CO 2

Method of

Grouping, and Integrating Factor

 Obtain the solution of 1^st order, 1^st degree DE by Method of grouping

 Obtain the solution of 1^st order, 1^st degree DE by finding the

Integrating Factor (IF)

 Examination (Written)

 Problem Set

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Week 5-6

6 CO 1

CO 2

2.2. Variable Separable 2.3 .Homogeneous Equations

2.4 Linear D.E. and its solution.

 Obtain the general and particular solution of DE by separating the variables.

 Obtain the general and particular solution of homogeneous DE.

 Discuss the linear equation of order one and obtain the solution of linear DE

 Problem Set

PRELIMINARY EXAMINATION

Week 7-8

6 CO 1

CO 2

2.5.Bernoulli Equations 2.6.Special Transformations

 Discuss the Bernoulli Equation and obtain the solution of Bernoulli equation.

 Obtain the solution of DE using special transformation

 Problem set

Week 9-10

6 CO 1

CO 2

3. Applications of 1^st Order D.E.

3.1. Rate of Growth and Decay 3.2. Population Growth

3.3. Newton’s Law of Cooling

 Discuss the applications of 1^st order DE and solve problems involving growth and decay.

 Discuss and solve problems involving Population growth and Newton’s law of cooling.

 Examination (written)

 Problem Set

 Group Sharing

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Week 11-12

6 CO 1

CO 2

3.4. Mixture Problems 3.5. Problems in Mechanics

 Discuss and solve problems involving mixture problems.

 Discuss and solve problems involving problems in mechanics.

 Problem Set

MIDTERM EXAMINATION

Week 13-15

9 CO 1

CO 2

4.1 Solution of Higher Order Linear Differential Equations 4.1. Homogeneous Linear D.E.

with Constant Coefficients

 Discuss higher order DE like homogeneous linear DE with constant coefficient and solve problems involving homogeneous linear DE.

 Problem Set

Week 16-17

6 CO 1

CO 2

4.2 Non-Homogeneous Differential Equation 4.2.1 Method of

Undetermined Coefficients 4.2.2 Variation Of

Parameters

 Discuss non-homogeneous DE by the method of undetermined coefficient and solve problems related to it.

 Problem Set

Week 18

6 CO 1

CO 2

5. Application of 2^nd Order Linear Differential Equations with Constant Coefficients

 Discuss applications of 2^nd order linear DE with constant coefficient

 Problem Set

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5.1. Electrical Circuits And solve problems in electrical circuits.

FINAL EXAMINATION

Course References:

A. Basic Readings: (Text Book)

1. Rainville et al. (2014). Elementary Differential Equation (8^th Ed.). Pearson Education Limited B. Extended Readings ( Books, Journals):

1. Brannan, J. R. (2011). Differential Equations with Boundary Value Problems: Modern Methods and Applications. New Jersey: John Wiley 2. Edwards, H. C. (2008). Differential Equations: Computing and Modeling (4^th Ed.). New Jersey: Pearson Education

3. Zill, D. G. (2009). Differential Equations with Boundary-Value Problems (7th Ed.) Australia: Brooks/Cole 4. Zill, D.G. et al. (2013). Succeeding with Differential Equations (8^th Ed.). Cengage Learning Asia Pte. Ltd.

C. Web References

1. http://www.intmath.com/Differential-equations/1_Solving-DEs.php

2. http://www.tutorvista.com/content/math/calculus/differential-equations/differential-equation-applications.php

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Course Requirements and Policies

1. 3 Major Examinations (PRELIMS, MIDTERMS, FINALS) 2. 6 Quizzes (Minimum)

3. Maximum Allowable Absences: 10 (held 3 times a week); 7 (held 2 times a week) Aside from academic deficiency, other grounds for failing grade are:

1. Grave misconduct and/or cheating during examinations.

2. A failing academic standing and failure to take graded exams.

3. Unexcused absences of more than the maximum allowable absences per term.

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Grading System

Class Standing/Quizzes (60%) 3 Major Exams (40%)

TOTAL (100%) Passing Grade (50%)

CAMPUS++ COLLEGE ONLINE GRADING SYSTEM Legend: (All Items in Percent)

CSA Class Standing Average for All Performance Items (Cumulative) P Prelim Examination Score

M Midterm Examination Score F Final Examination Score MEA Major Exam Average PCA Prelim Computed Average MCA Midterm Computed Average FCA Final Computed Average

Note: For purposes of illustration, the sharing between CSA and MEA is shown below as 70% and 30%, respectively, when

computing the Computed Average for each Grading Period. Depending on the grading parameters set for a subject the sharing may be 65%- 35%, 60%-40%, or other possible combinations.

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Computation of Prelim Computed Average (PCA) CSA =

MEA = P

PCA = (60%)(CSA) + (40%)(MEA)

Computation of Midterm Computed Average (MCA) CSA =

MEA =

MCA = (60%)(CSA) + (40%)(MEA)

Computation of Final Computed Average (FCA) CSA =

MEA =

FCA = (60%)(CSA) + (40%)(MEA)

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Date Revised: Date Effectivity: Prepared By: Checked By: Approved By:

June 3, 2016

Schuvert C. Frigillana Filipina I. De Guzman Maria Doris C. Bacamante Note: A student's Computed Average is a consolidation of Class Standing Percent Average and Major Exam Percent Average.

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