revised syllabus math22-1 2014 mapua

Course Title:

CALCULUS 2

Date Effective:

4th Quarter SY 2013 - 2014

Date Revised:

July 2014

Prepared by:

Committee on Calculus 3

Approved by:

LDSABINO Subject Chair

of 8

MAPÚA 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 starts with discussions on derivatives of

trigonometric and hyperbolic functions, as well as their inverses, limits of

indeterminate forms, the differentials and its application. It progresses to

the discussion of the basic and advance integration of algebraic and

transcendental functions. The definite integral is used extensively in

solving application problems involving area of regions bounded by

algebraic/polar curves, volume of solids of revolution and of solids with

known cross-section, centroids of plane regions and of solid of revolution,

length of curves, surface area of revolution, force due to liquid pressure

and work. And lastly, this course also deals with the application of

improper integrals.

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 humanity’s 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 (BIOLOGICAL ENGINEERING, CHEMICAL ENGINEERING, CIVIL ENGINEERING, ENVIRONMENTAL AND SANITARY ENGINEERING, INDUSTRIAL ENGINEERING,

MECHANICAL ENGINEERING AND MANUFACTURING ENGINEERING))

MISSION

a b c d

1. To enable our graduates to practice as successful engineers for the advancement of society.

2. To promote professionalism in the engineering practice.

Course Title:

CALCULUS 2

Date Effective:


Date Revised:

July 2014

Prepared by:


Approved by:


of 8

7. Student Outcomes and Relationship to Program Educational Objective

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 l

1. Solve problems involving the derivative of algebraic,

exponential and logarithmic functions, 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 problems involving derivatives of the other

transcendental functions, evaluate limits of

indeterminate forms and solve problems concerning the

differentials.

I

D

D

D

D

D

D

D

3. Solve definite and indefinite integrals using basic

integration formulas. Use simple substitution to

transform integrals to forms yielding any of the

transcendental functions.

I D D D D D D D

4. Solve definite and indefinite integrals using appropriate

integration technique. I D D D D D D D D

Student Outcomes Program Educational Objectives

1 2

(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 √ √

(l)

knowledge and understanding of engineering and

management principles as member and leader, to manage

projects and in multidisciplinary environments.

√ √

Course Title:

CALCULUS 2

Date Effective:


Date Revised:

July 2014

Prepared by:


Approved by:


of 8

5. Solve, by integration, application problems concerning

length of an arc, area under the curve and between

curves, volume of solids of revolution, centroid of the

area and solid of revolution, surface area of revolution,

force to liquid pressure, work. Use Pappus’ Theorem in

solving problems of volume and surface area of

revolution

D D D D D D D D

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

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

E

x

a

m

CO1

Derivatives of Trigonometric

and Inverse Trigonometric

Functions

2

Derivatives of Hyperbolic and

Inverse of Hyperbolic Functions

- Visually guided

Learning

- Working

through

Examples

Class Produced

R

e

v

i

e

w

e

r

1

CO2

INDETERMINATE FORMS:

L’Hopital’s Rule

0/0, /

- , 0*

00,

, 1

THE DIFFERENTIALS

Differential of the Dependent

Variable

Derivatives of Parametric

Equations

3

Application

- Approximate Formula (nth

root, volume of shells and

others)

Differential of Length of an Arc

Radius of Curvature

Course Title:

CALCULUS 2

Date Effective:


Date Revised:

July 2014

Prepared by:


Approved by:


of 8

3

LONG QUIZ 1

ANTIDERIVATIVES

Indeterminate Integrals and

Basic Integration Formula

Class Produced

R

e

v

i

e

w

e

r

2

Class Produced

Reviewer 2

CO3

CO3

Generalized Power Formula

Integration by Simple

Substitution

THE DEFINITE INTEGRALS

Properties of the Definite

Integral

Integrals of Odd and Even

Functions

Integration of Absolute Value

Function

Average Value of a Function

Mean Value Theorems for

Integrals

Simple U-substitution

4

TRANSCENDENTAL

FUNCTIONS

Integrals Yielding the Natural

Logarithmic Functions

- Visually guided

Learning

-Working through

examples

Integration of Exponential

Function

Integral Forms Leading to the

Trigonometric / Inverse

Trigonometric Functions

Transformations of

Trigonometric Function

– Powers of Sine and

Cosine

5

– Product of Sine

and Cosine

-Walli’s Formula

– Powers and

Product of Tangent and Secant

– Powers and

Product of Cotangent and Cosecant

Integrals Yielding Inverse

Trigonometric Functions

Integration of Hyperbolic

Functions

Integrals Yielding Inverse

Hyperbolic Function

LONG QUIZ 2

TECHNIQUES OF INTEGRATION

Integration by Parts

-Visually guided

Class Produced

Integration by Algebraic

Substitution

Course Title:

CALCULUS 2

Date Effective:


Date Revised:

July 2014

Prepared by:


Approved by:


of 8

10. Opportunities to Develop Lifelong Learning Skill The primary learning outcome for this course to develop lifelong learning skill is the student’s

capability to exhibit critical and logical reasoning in different areas of learning specifically with

6

Integration by Trigonometric

Substitution learning

-Working through

examples

Reviewer 3

Class Produced

Reviewer 3

CO4

CO4

Half-Angle Substitution /

Reciprocal Substitution

7

Partial Fraction

- Linear Factors

- Repeated Linear Factors

- Quadratic Factors

- Repeated Quadratic Factors

Integration of Rational

Function by Partial Fraction

- Linear Factors

- Repeated Linear Factors

- Quadratic Factors

- Repeated Quadratic Factors

8

Improper Integrals

LONG QUIZ NO. 3 (70% written, 30% on-line)

PLANE AREAS

Differential of Area

Fundamental Theorem of

Integral Calculus

-Visually guided

learning

-Working through

examples

- Guided Learningproach-

Class Produced

R

e

v

i

e

w

e

r

4

Project

CO5

Area Under the Curve

Area Between Curves

VOLUME OF REVOLUTION

Disk Method

9

Circular Ring or Washer

Method

Cylindrical Shell Method

Solids with Known Cross-Section

CENTROID

Centroid of a Region

Centroid of Volume of

Revolution

Length of Curves

Surface Area of Revolution

10

Pappus’s Theorem: Preposition 1 and

2 -Visually guided

learning

-Working through

Examples

Force Due to Liquid Pressure

Work

LONG QUIZ 4

11 SUMMATIVE ASSESSMENT

FINAL EXAMINATION

CO2, CO3,

CO4, CO5

Course Title:

CALCULUS 2

Date Effective:


Date Revised:

July 2014

Prepared by:


Approved by:


of 8

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 : 0 %

General Education : 0 %

Basic Sciences and Mathematics : 100%

12. Textbook:

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

13. Course Evaluation

Student performance will be evaluated 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

Assessment Tasks

Weight (%)

Minimum

Average for

Satisfactory

Performance (%)

CO1 Diagnostic Examination 10 7

CO2

Long Quiz 1 10 7

Classwork 1 3 2.1

Class Produced Reviewer 1 2 1.4

CO3

Long Quiz 2 10 7

Classwork 2 3 2.1


CO4

Long Quiz 3 10 7

Classwork 3 3 2.1


CO5

Long Quiz 4 10 7

Classwork 4 3 2.1


Project 5 3.5

Summative Assessment Final Examination 25.00 17.50

TOTAL 100 70

Course Title:

CALCULUS 2

Date Effective:


Date Revised:

July 2014

Prepared by:


Approved by:


of 8

80 X < 83 2.25

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 (Student Outputs) should be on time; late submittal will

not be accepted.

c. Written Examination (Long Quiz and Final Examination) will be administered as

scheduled. No special examination will be given unless valid reason is presented like

medical certificate / other acceptable documents and will be subject to approval by the

Chairman of the Mathematics Department.

d. Course Portfolio will be collected at the end of the term.

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

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 Books

http://math.mapua.edu.ph/

Course Title:

CALCULUS 2

Date Effective:


Date Revised:

July 2014

Prepared by:


Approved by:


of 8

a. Calculus, 6th

ed., Edwards and Penney

b. The Calculus, 7th

ed., by Louis Leithold

c. Differential and Integral Calculus by Schaum’s Outline Series

d. Differential and Integral Calculus by Love and Rainville

s and quizzes

14.2.1 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

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

CQI Cluster Chair: Robert P, Domingo

Members: Robert M. Dadigan

Rosario S. Lazaro

Francis Anthony G. Llacuna

http://www.sosmath.com/

http://www.hmc.com/

http://www.intmath.com/

http://www.hivepc.com/

revised syllabus math22-1 2014 mapua

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