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MAPÚA INSTITUTE OF TECHNOLOGY Department of Mathematics

VISION Mapua shall be among the best universities in the world. MISSION a. The Institute shall provide a learning environment in order for its students to acquire the attributes that will make them globally competitive. b. The Institute shall engage in economically viable research, development, and innovation. c. The Institute shall provide state-of-the-art solutions to problems of industries and communities BASIC STUDIES EDUCATIONAL OBJECTIVES (ELECTRICAL ENGINEERING, ELECTRONICS ENGINEERING AND COMPUTER ENGINEERING) 1. The graduates are able to apply the broad fundamental concepts in social and natural sciences, 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 a 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 society.

a

MISSION b

c

COURSE SYLLABUS 1. Course Code

:

MATH23-1

2. Course Title

:

CALCULUS 3

3. Pre-requisite

:

MATH22-1

4. Co-requisite

:

None

5. Credit / Class Schedule :

3 units

6. Course Description

A course in multivariable calculus which covers discussion in infinite series, power series, Taylor and Maclaurin Series, vectors and its application, function in two or more independent variables including limits, continuity and quadric surfaces, partial derivatives, multiple integrals and its application problems involving maxima and minima, tangent plane and normal to the surface, area and volume using multiple integrals and triple integrals in spherical and cylindrical coordinates.

:

7. Student Outcomes and Relationship to Program Educational Objectives Program Educational Objectives 1 2 3 4

Student Outcomes (a) (b) (c)

an ability to apply knowledge of mathematics, science, and engineering an ability to design and conduct experiments, as well as to analyze and interpret from data an ability to design a system, component, or process to meet desired needs

Course Title: CALCULUS 3

Date Effective: 2nd Quarter SY 2014 - 2015

Date Revised:

Prepared by:

October 2014

√

Approved by: LDSABINO Subject Chair

Committee on Calculus 3

Page 1 of 6

(d) (e) (f) (g) (h) (i) (j) (k)

(l)

8.

√

an ability to function on multidisciplinary teams an ability to identify, formulate, and solve engineering problems an understanding of professional and ethical responsibility an ability to communicate effectively the broad education necessary to understand the impact of engineering solutions in the global and societal context 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 knowledge and understanding of engineering and management principles as a member and leader in a team, to manage projects and in multidisciplinary environments

√

√ √ √ √ √ √ √

√

√

√

√

Course Outcomes (COs) and Relationship to Student Outcomes

Course Outcomes

Student Outcomes*

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

a

B

c

d

e

F

g

h

1. Apply principles gained from the D prerequisite courses. 2. Apply an appropriate test to determine the convergence or divergence of an infinite D series. 3. Interpret the dot product and cross product of vectors; evaluate vectors in plane and D I space; perform operations in vector valued functions. 4. Sketch graphs of quadric surfaces, level I curves and level surfaces and solve D I problems on functions of several variables. * Level: I- Introduced, R- Reinforced, D- Demonstrated

D

D

I

R

D

D

I

R

R

D

I

D

D

D

D

i

j

K

l

9. Course Coverage: WEEK

1

TOPIC

TLA

Orientation and Introduction to the course. Mapua’s Vision and Mision, Department’s Specific Objectives, Course Policies and Guidelines, Nature and Scope of 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 -Discovery Approach

SEQUENCES Definition and Limit of a Sequence Terminology for sequences Geometric Sequence Bounded Monotonic Sequence Course Title: CALCULUS 3

Date Effective: 2nd Quarter SY 2014 - 2015

AT

COURSE OUTCOMES

Individual / Group Presentation

- Working through Examples - Visually Guided Learning

Date Revised:

Prepared by:

October 2014

Approved by: LDSABINO Subject Chair

Committee on Calculus 3

Page 2 of 6

WEEK

TOPIC

TLA

AT

COURSE OUTCOMES

2

3

Growth Rate of Sequences INFINITE SERIES Definition Series and Convergence - Telescoping Series - Geometric Series - Divergence Test - Harmonic Series - Integral Test - p-series - Comparison Test - Limit Comparison Test - Ratio Test - Root Test - Alternating Series - Absolute and Conditional Convergence POWER SERIES Definition Approximating Functions with Polynomials - Taylor Polynomials - Maclaurin Polynomials Convergence of Power Series Interval and Radius of Convergence Combining Power Series Differentiation and Integration of Power Series Taylor Series and Maclaurin Series for a Function, Binomial Series

- Assignment 1

- Working through Examples - Technology Integration - Guided Learning

QUIZ 1

4

THREE DIMENSIONAL GEOMETRY Space Coordinates - Distance Between Two Points - Midpoint Formula PLANE AND SURFACES Plane, Cylindrical, and Quadric Surfaces VECTORS Component Form -2D, 3D

5

6

Cross Product Lines and Planes in Space VECTOR-VALUED FUNCTIONS Limits and Continuity Derivatives Integrals Length of Curves, Curvature

Course Title: CALCULUS 3

Date Effective: 2nd Quarter SY 2014 - 2015

CO2

- Technology Integration - Guided Learning

Dot Product

CO 2

- Working through Examples - Technology Integration - Guided Learning

Date Revised:

- Assignment 2

Prepared by:

October 2014

Approved by: LDSABINO Subject Chair

Committee on Calculus 3

CO3

Page 3 of 6

WEEK

TOPIC

TLA

AT

QUIZ 2

COURSE OUTCOMES CO3

FUNCTION OF SEVERAL VARIABLES Domain and Range Level Curves Level Surfaces Limits and Continuity Partial Derivatives Higher Order Partials

7

8

Directional Derivatives and the Gradient Tangent Planes and Normal to the Surfaces Extrema of Functions of Two variables Maxima and Minima Problems

Multiple Integrals Evaluation of Double Integrals Evaluation of Triple Integrals Change of Variables Application - Area and Volume by Double Integral Volume by Triple Integral Triple Integrals in Cylindrical and Spherical Coordinates

9

10

- Working through Examples - Technology Integration - Guided Learning

- Assignment 3 CO4

QUIZ 3 (70% written / 30% on-line) 11

SUMMATIVE ASSESSMENT

10.

/

FINAL EXAMINATION

CO4 CO2, CO3, CO4

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 the maximization of mathematical principles in Multivariate 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: General Education : Engineering Topics : Basic Sciences and Mathematics:

0% 25% 75%

12. Textbook CALCULUS EARLY TRANCENDENTAL 10ed. By Howard Anton, Irl Bivens, and Stephen Davis

Course Title: CALCULUS 3

Date Effective: 2nd Quarter SY 2014 - 2015

Date Revised:

Prepared by:

October 2014

Approved by: LDSABINO Subject Chair

Committee on Calculus 3

Page 4 of 6

13.

Course Evaluation Student performance will be rated based on the following:

Weight (%)

Minimum Average for Satisfactory Performance (%)

Diagnostic Examination

10.00

7.00

Quiz 1

13.00

Exercise 1

3.00

Assignment 1

3.20

Quiz 2

13.00

Exercise 2

3.00

Assignment 2

3.20

Assessment Tasks CO 1

CO 2

CO 3

Quiz 3 (written/on-line) CO 4

13.44

13.44

9.80 / 4.20

Exercise 3

4.00

Assignment 3

3.60

18.62

5.00

PROJECT Summative Assessment: - Final Examination (CO2, CO3, CO4) TOTAL

25.00

17.50

100.00

70.00

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

GRADING SYSTEM 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 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. 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. c. Written Major Examination (Long Quiz and Final Exams) will be administered as scheduled. No special exam will be given unless with a valid reason subject to approval by the Chairman of the Mathematics Department. d. Course Portfolio will be collected at the end of the quarter. Course Title: CALCULUS 3

Date Effective: 2nd Quarter SY 2014 - 2015

Date Revised:

Prepared by:

October 2014

Approved by: LDSABINO Subject Chair

Committee on Calculus 3

Page 5 of 6

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 Book a. Calculus, 9th Ed., by George B. Thomas, Jr. and Ross L. Finnez. b. The Calculus, 7th Ed., Louis Leithold c. Calculus 8th Ed., by Dales Vasberg, Edwin J. Purcell and Steve Rigdon. d. Calculus of Several Variables, by Earl W. Swokoski, Michael Olinick, Dennis Pence e. Calculus, 7th Ed., Howard Anton, Irl Bivens and Stephen Davis. f. Calculus, 6th Ed., Edward and Penney 14.2 Websites www.sosmath.com www.hmc.com www.intmath.com www.hivepc.com

15. Course Materials Made Available: a. b. c. d.

Course schedules for lectures and quizzes Sample of assignments/problem sets of students Sample of written examination of students End-of-course self assessment

16. Committee Members: Course Cluster Chair : Prof. Rosario S. Lazaro CQI Cluster Chair : Prof. Robert P. Domingo Members : Prof. Juanito E. Bautista Prof. Robert M. Dadigan Prof. Francis Anthony G. Llacuna

Course Title: CALCULUS 3

Date Effective: 2nd Quarter SY 2014 - 2015

Date Revised:

Prepared by:

October 2014

Approved by: LDSABINO Subject Chair

Committee on Calculus 3

Page 6 of 6

View more...
VISION Mapua shall be among the best universities in the world. MISSION a. The Institute shall provide a learning environment in order for its students to acquire the attributes that will make them globally competitive. b. The Institute shall engage in economically viable research, development, and innovation. c. The Institute shall provide state-of-the-art solutions to problems of industries and communities BASIC STUDIES EDUCATIONAL OBJECTIVES (ELECTRICAL ENGINEERING, ELECTRONICS ENGINEERING AND COMPUTER ENGINEERING) 1. The graduates are able to apply the broad fundamental concepts in social and natural sciences, 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 a 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 society.

a

MISSION b

c

COURSE SYLLABUS 1. Course Code

:

MATH23-1

2. Course Title

:

CALCULUS 3

3. Pre-requisite

:

MATH22-1

4. Co-requisite

:

None

5. Credit / Class Schedule :

3 units

6. Course Description

A course in multivariable calculus which covers discussion in infinite series, power series, Taylor and Maclaurin Series, vectors and its application, function in two or more independent variables including limits, continuity and quadric surfaces, partial derivatives, multiple integrals and its application problems involving maxima and minima, tangent plane and normal to the surface, area and volume using multiple integrals and triple integrals in spherical and cylindrical coordinates.

:

7. Student Outcomes and Relationship to Program Educational Objectives Program Educational Objectives 1 2 3 4

Student Outcomes (a) (b) (c)

an ability to apply knowledge of mathematics, science, and engineering an ability to design and conduct experiments, as well as to analyze and interpret from data an ability to design a system, component, or process to meet desired needs

Course Title: CALCULUS 3

Date Effective: 2nd Quarter SY 2014 - 2015

Date Revised:

Prepared by:

October 2014

√

Approved by: LDSABINO Subject Chair

Committee on Calculus 3

Page 1 of 6

(d) (e) (f) (g) (h) (i) (j) (k)

(l)

8.

√

an ability to function on multidisciplinary teams an ability to identify, formulate, and solve engineering problems an understanding of professional and ethical responsibility an ability to communicate effectively the broad education necessary to understand the impact of engineering solutions in the global and societal context 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 knowledge and understanding of engineering and management principles as a member and leader in a team, to manage projects and in multidisciplinary environments

√

√ √ √ √ √ √ √

√

√

√

√

Course Outcomes (COs) and Relationship to Student Outcomes

Course Outcomes

Student Outcomes*

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

a

B

c

d

e

F

g

h

1. Apply principles gained from the D prerequisite courses. 2. Apply an appropriate test to determine the convergence or divergence of an infinite D series. 3. Interpret the dot product and cross product of vectors; evaluate vectors in plane and D I space; perform operations in vector valued functions. 4. Sketch graphs of quadric surfaces, level I curves and level surfaces and solve D I problems on functions of several variables. * Level: I- Introduced, R- Reinforced, D- Demonstrated

D

D

I

R

D

D

I

R

R

D

I

D

D

D

D

i

j

K

l

9. Course Coverage: WEEK

1

TOPIC

TLA

Orientation and Introduction to the course. Mapua’s Vision and Mision, Department’s Specific Objectives, Course Policies and Guidelines, Nature and Scope of 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 -Discovery Approach

SEQUENCES Definition and Limit of a Sequence Terminology for sequences Geometric Sequence Bounded Monotonic Sequence Course Title: CALCULUS 3

Date Effective: 2nd Quarter SY 2014 - 2015

AT

COURSE OUTCOMES

Individual / Group Presentation

- Working through Examples - Visually Guided Learning

Date Revised:

Prepared by:

October 2014

Approved by: LDSABINO Subject Chair

Committee on Calculus 3

Page 2 of 6

WEEK

TOPIC

TLA

AT

COURSE OUTCOMES

2

3

Growth Rate of Sequences INFINITE SERIES Definition Series and Convergence - Telescoping Series - Geometric Series - Divergence Test - Harmonic Series - Integral Test - p-series - Comparison Test - Limit Comparison Test - Ratio Test - Root Test - Alternating Series - Absolute and Conditional Convergence POWER SERIES Definition Approximating Functions with Polynomials - Taylor Polynomials - Maclaurin Polynomials Convergence of Power Series Interval and Radius of Convergence Combining Power Series Differentiation and Integration of Power Series Taylor Series and Maclaurin Series for a Function, Binomial Series

- Assignment 1

- Working through Examples - Technology Integration - Guided Learning

QUIZ 1

4

THREE DIMENSIONAL GEOMETRY Space Coordinates - Distance Between Two Points - Midpoint Formula PLANE AND SURFACES Plane, Cylindrical, and Quadric Surfaces VECTORS Component Form -2D, 3D

5

6

Cross Product Lines and Planes in Space VECTOR-VALUED FUNCTIONS Limits and Continuity Derivatives Integrals Length of Curves, Curvature

Course Title: CALCULUS 3

Date Effective: 2nd Quarter SY 2014 - 2015

CO2

- Technology Integration - Guided Learning

Dot Product

CO 2

- Working through Examples - Technology Integration - Guided Learning

Date Revised:

- Assignment 2

Prepared by:

October 2014

Approved by: LDSABINO Subject Chair

Committee on Calculus 3

CO3

Page 3 of 6

WEEK

TOPIC

TLA

AT

QUIZ 2

COURSE OUTCOMES CO3

FUNCTION OF SEVERAL VARIABLES Domain and Range Level Curves Level Surfaces Limits and Continuity Partial Derivatives Higher Order Partials

7

8

Directional Derivatives and the Gradient Tangent Planes and Normal to the Surfaces Extrema of Functions of Two variables Maxima and Minima Problems

Multiple Integrals Evaluation of Double Integrals Evaluation of Triple Integrals Change of Variables Application - Area and Volume by Double Integral Volume by Triple Integral Triple Integrals in Cylindrical and Spherical Coordinates

9

10

- Working through Examples - Technology Integration - Guided Learning

- Assignment 3 CO4

QUIZ 3 (70% written / 30% on-line) 11

SUMMATIVE ASSESSMENT

10.

/

FINAL EXAMINATION

CO4 CO2, CO3, CO4

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 the maximization of mathematical principles in Multivariate 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: General Education : Engineering Topics : Basic Sciences and Mathematics:

0% 25% 75%

12. Textbook CALCULUS EARLY TRANCENDENTAL 10ed. By Howard Anton, Irl Bivens, and Stephen Davis

Course Title: CALCULUS 3

Date Effective: 2nd Quarter SY 2014 - 2015

Date Revised:

Prepared by:

October 2014

Approved by: LDSABINO Subject Chair

Committee on Calculus 3

Page 4 of 6

13.

Course Evaluation Student performance will be rated based on the following:

Weight (%)

Minimum Average for Satisfactory Performance (%)

Diagnostic Examination

10.00

7.00

Quiz 1

13.00

Exercise 1

3.00

Assignment 1

3.20

Quiz 2

13.00

Exercise 2

3.00

Assignment 2

3.20

Assessment Tasks CO 1

CO 2

CO 3

Quiz 3 (written/on-line) CO 4

13.44

13.44

9.80 / 4.20

Exercise 3

4.00

Assignment 3

3.60

18.62

5.00

PROJECT Summative Assessment: - Final Examination (CO2, CO3, CO4) TOTAL

25.00

17.50

100.00

70.00

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

GRADING SYSTEM 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 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. 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. c. Written Major Examination (Long Quiz and Final Exams) will be administered as scheduled. No special exam will be given unless with a valid reason subject to approval by the Chairman of the Mathematics Department. d. Course Portfolio will be collected at the end of the quarter. Course Title: CALCULUS 3

Date Effective: 2nd Quarter SY 2014 - 2015

Date Revised:

Prepared by:

October 2014

Approved by: LDSABINO Subject Chair

Committee on Calculus 3

Page 5 of 6

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 Book a. Calculus, 9th Ed., by George B. Thomas, Jr. and Ross L. Finnez. b. The Calculus, 7th Ed., Louis Leithold c. Calculus 8th Ed., by Dales Vasberg, Edwin J. Purcell and Steve Rigdon. d. Calculus of Several Variables, by Earl W. Swokoski, Michael Olinick, Dennis Pence e. Calculus, 7th Ed., Howard Anton, Irl Bivens and Stephen Davis. f. Calculus, 6th Ed., Edward and Penney 14.2 Websites www.sosmath.com www.hmc.com www.intmath.com www.hivepc.com

15. Course Materials Made Available: a. b. c. d.

Course schedules for lectures and quizzes Sample of assignments/problem sets of students Sample of written examination of students End-of-course self assessment

16. Committee Members: Course Cluster Chair : Prof. Rosario S. Lazaro CQI Cluster Chair : Prof. Robert P. Domingo Members : Prof. Juanito E. Bautista Prof. Robert M. Dadigan Prof. Francis Anthony G. Llacuna

Course Title: CALCULUS 3

Date Effective: 2nd Quarter SY 2014 - 2015

Date Revised:

Prepared by:

October 2014

Approved by: LDSABINO Subject Chair

Committee on Calculus 3

Page 6 of 6

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