Course Title:

CALCULUS 2

Date Effective:

4th

Term SY 2013-2014

Date Revised:

April 2014

Prepared by:

Cluster III Committee

Approved by:

LD SABINO Subject Chair

Page 1 of 7

MAPA INSTITUTE OF TECHNOLOGY

Department of Mathematics

COURSE SYLLABUS

1. Course Code: MATH 22-1

2. Course Title: Calculus 2 3. Pre-requisite: MATH 21-1

4. Co-requisite: None

5. Credit: 5 units

6. Course Description: This course in Calculus covers topics on the discussion of the limits of indeterminate forms, application of the differential, definite and indefinite

integrals of algebraic and transcendental functions and techniques of integration,

applications of integration such as plane areas, area of regions bounded by polar curves, volume of solids of revolution, centroids of plane regions and volume of

solids with known cross section, length of curves, work, surface of revolution,

improper integrals and its applications, and force due to liquid pressure, the basic and advance integration of algebraic and transcendental functions, and techniques

VISION

The Mapua Institute of Technology shall be a global center of excellence in education by providing instructions that are current in content and state-of-the-art in delivery; by engaging in cutting-edge, high impact research; and by aggressively taking on present-day global concerns.

MISSION

a. The Mapua Institute of Technology disseminates, generates, preserves and applies knowledge in various fields of study.

b. The Institute, using the most effective and efficient means, provides its students with highly relevant professional and advanced education in preparation for and furtherance of global practice.

c. The Institute engages in research with high socio-economic impact and reports on the results of such inquiries.

d. The Institute brings to bear humanitys vast store of knowledge on the problems of industry and community in order to make the Philippines and the world a better place.

PROGRAM EDUCATIONAL OBJECTIVES (ELECTRICAL ENGINEERING, ELECTRONICS ENGINEERING AND COMPUTER

ENGINEERING )

MISSION

a b c d

1. The graduates are able to apply the broad fundamental concepts in social and natural science, mathematics and engineering, and the depth

of knowledge gained in engineering, as professionals in their chosen

careers.

2. The graduates are practicing professionals who are qualified and

proficient 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 demonstrate effective communication skills, the ability

to work well either individually or as part of a team, who have

embraced lifelong learning values for continuous self and professional or career development.

4. As professionals, the graduates utilize appropriate knowledge and

technology in dealing with local and global, industrial, community,

and environmental concerns for the advancement of the society.

Course Title:

CALCULUS 2

Date Effective:

4th

Term SY 2013-2014

Date Revised:

April 2014

Prepared by:

Cluster III Committee

Approved by:

LD SABINO Subject Chair

Page 2 of 7

of integration that will be utilized in solving many application problems involving

integrals.

7. Student Outcomes and Relationship to Basic Studies Educational Objectives

Student Outcomes Basic Studies Educational Objectives

1 2 3 4

(a) an 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

(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

8. Course Outcomes (COs) and Relationship to Student Outcomes

Course Outcomes

After completing the course, the student must be able to: Student Outcomes*

A b c d E F g h I j K

1. Solve problems involving the derivative of a function, as well as problems on different planar and space geometries by applying

concepts and principles learned in the prerequisites. D R R R

2. Solve the limits of indeterminate forms and the differentials. Solve definite and indefinite integrals using basic integration formulas,

simple substitution, absolute value function and the mean value for

integrals.

I

D

D

D

D

D

D

D

3. Solve integrals of logarithmic and exponential functions, basic trigonometric integration formulas, transformation of six

trigonometric functions and using powers and product, integrals

yielding inverse trigonometric functions, integration of hyperbolic functions, and integrals yielding inverse hyperbolic functions.

I D D D D D D D

4. Solve rational function by partial fraction, and techniques of

integration. I D D D D D D D D

5. Use integration formulas in computing the length of an arc and solve problems involving area under the curve and between curves,

volume of solids of revolution, centroid of the area and solid of

revolution

D D D D D D D D

6. Solve improper integrals, Pappuss theorem and work and force due to liquid pressure.

R R

R

R R R R R

* Level: I- Introduced, R- Reinforced, D- Demonstrated

Course Title:

CALCULUS 2

Date Effective:

4th

Term SY 2013-2014

Date Revised:

April 2014

Prepared by:

Cluster III Committee

Approved by:

LD SABINO Subject Chair

Page 3 of 7

9. Course Coverage

Week TOPICS TLA AT COURSE

OUTCOMES

1

Mission and Vision of Mapua

Institute of Technology

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

Peer discussion on

Mission and Vision

of Mapua Institute of

Technology

Diagnostic Exam

CO1

INDETERMINATE FORMS:

LHopitals Rule

0/0, /

- Visually guided

learning

- Working through

examples

Class Produced Reviewer 1

CO2

- , 0* 00, , 1

THE DIFFERENTIALS Differential of the Dependent

Variable

Derivatives of Parametric Equations

Application - Approximate Formula (nth

root, volume of shells and

others)

2

Differential of Length of an Arc

Radius of Curvature ANTIDERIVATIVES

Indefinite Integrals and Basic Integration Formula

Generalized Power Formula

Integration by Simple Substitution

THE DEFINITE INTEGRALS

Properties of the Definite Integral

Integrals of Odd and Even Functions

3

Integration of Absolute Value Function

Average Value of a Function

Mean Value Theorems for Integrals

LONG QUIZ NO. 1 CO2

TRANSCENDENTAL

FUNCTIONS

Integrals Yielding the Natural Logarithmic Functions

- Visually guided

learning

- Working through examples

Class Produced Reviewer 2

CO3

Integration of Exponential Function

4

Basic Trigonometric Integration Formulas

Transformations of Trigonometric Function Powers of Sine and Cosine

Product of Sine and Cosine -Wallis Formula

Powers and Product of Tangent and Secant

Course Title:

CALCULUS 2

Date Effective:

4th

Term SY 2013-2014

Date Revised:

April 2014

Prepared by:

Cluster III Committee

Approved by:

LD SABINO Subject Chair

Page 4 of 7

Week TOPICS TLA AT COURSE

OUTCOMES

Powers and Product of Cotangent and Cosecant

5

Integrals Yielding Inverse Trigonometric Functions

Integration of Hyperbolic Functions

Integrals Yielding Inverse Hyperbolic Function

LONG QUIZ NO. 2 CO3

TECHNIQUES OF INTEGRATION

Integration by Parts

- Visually guided learning

- Working through examples

Class Produced Reviewer 3

CO4

6

Integration by Algebraic Substitution

Integration by Trigonometric Substitution

Half-Angle Substitution / Reciprocal Substitution

Partial Fraction - Linear Factors - Repeated Linear Factors - Quadratic Factors - Repeated Quadratic

Factors

Integration of Rational Function by Partial Fraction

- Linear Factors - Repeated Linear Factors

7

- Quadratic Factors - Repeated Quadratic

Factors

LONG QUIZ NO. 3 CO4

PLANE AREAS

Differential of Area

Fundamental Theorem of Integral Calculus

- Visually guided

learning

- Working through

examples

- Guided Learningproach-

Class Produced Reviewer 4

CO5

Area Under the Curve

Area Between Curves

8

VOLUME OF REVOLUTION

Disk Method

Circular Ring or Washer Method

Cylindrical Shell Method

Solids with Known Cross-Section

CENTROID

Centroid of a Region

9

Centroid of Volume of Revolution

Length of Curves

Surface Area of Revolution

LONG QUIZ NO. 4 CO5

IMPROPER INTEGRALS

Infinite Intervals

- Visually guided learning

- Working through examples

Class Produced Reviewer 5

Project

CO6

Unbounded Integrands

10

Application of Improper Integrals

Pappuss Theorem Surface Area

Volume

Force Due to Liquid Pressure

Work

LONG QUIZ NO. 5 CO6

Course Title:

CALCULUS 2

Date Effective:

4th

Term SY 2013-2014

Date Revised:

April 2014

Prepared by:

Cluster III Committee

Approved by:

LD SABINO Subject Chair

Page 5 of 7

Week TOPICS TLA AT COURSE

OUTCOMES

11 SUMMATIVE ASSESSMENT

FINAL EXAMINATION

CO2, CO3,

CO4, CO5, CO6

10. Opportunities to Develop Lifelong Learning Skill

The primary learning outcome for this course to develop lifelong learning skill is the students capability to exhibit critical and logical reasoning in different areas of learning specifically with the maximization of mathematical principles in Integral Calculus, and the value integration of this course will equip the takers to respond to different societal challenges.

11. Contribution of Course to Meeting the Professional Component

Engineering Topics : 25 % General Education : 25 % Basic Sciences and Mathematics : 50%

12. Textbook:

Calculus Early Transcendental Functions by Ron Larson and Bruce H. Edwards. 5th edition 13. Course Evaluation

Student performance will be rated based on the following:

The final grades will correspond to the weighted average scores shown below:

Final Average Final Grade

96 X < 100 1.00 93 X < 96 1.25 90 X < 93 1.50 86 X < 90 1.75 83 X < 86 2.00 80 X < 83 2.25

Assessment Tasks

Weight (%)

Minimum Average for Satisfactory

Performance (%) CO1 Diagnostic Examination 10 7

CO2 Long Quiz 1 8 5.6

Classwork 1 2 1.4

Class Produced Reviewer 1 2 1.4

CO3

Long Quiz 2 8 5.6

Classwork 2 2 1.4

Class Produced Reviewer 2 2 1.4

CO4

Long Quiz 3 8 5.6

Classwork 3 2 1.4 Class Produced Reviewer 3 2 1.4

CO5

Long Quiz 4 8 5.6

Classwork 4 2 1.4

Class Produced Reviewer 4 2 1.4

CO6

Long Quiz 5 8 5.6

Classwork 5 2 1.4

Class Produced Reviewer 5 2 1.4

Project 5 3.5

Summative Assessment Final Examination 25.00 17.50

TOTAL 100 70

Course Title:

CALCULUS 2

Date Effective:

4th

Term SY 2013-2014

Date Revised:

April 2014

Prepared by:

Cluster III Committee

Approved by:

LD SABINO Subject Chair

Page 6 of 7

76 X < 80 2.50 73 X < 76 2.75 70 X < 73 3.00

Below 70 5.0 (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 15 hrs for a five-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

c. Written Examination

d. Course Portfolio 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 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 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 Departments web-page ( http://math.mapua.edu.ph ). It is recommended that the student first set an appointment to confirm the instructors availability.

14. Other References 14.1 Books a. Calculus, 6th ed., Edwards and Penney

b. The Calculus, 7th ed., by Louis Leithold

c. Differential and Integral Calculus by Schaums Outline Series d. Differential and Integral Calculus by Love and Rainville

s and quizzes

14.2 Websites www.sosmath.com www.hmc.com www.intmath.com www.hivepc.com

15. Course Materials Made Available

a. Course schedules for lectures and quizzes b. Samples of assignment / Problem sets of students c. Samples of written examinations of students

d. End-of-course self-assessment

Course Title:

CALCULUS 2

Date Effective:

4th

Term SY 2013-2014

Date Revised:

April 2014

Prepared by:

Cluster III Committee

Approved by:

LD SABINO Subject Chair

Page 7 of 7

16. Committee Members: Course Cluster Chair: Juanito E. Bautista

CQI Cluster Chair: Robert P, Domingo Members: Robert M. Dadigan

Ernarnie C. De Guzman

Rosario S. Lazaro

Francis Anthony G. Llacuna