Course Name : Mathematics-II

Degree:  Bachelor

Code

Year/Semester

Local Credits

ECTS Credits

Course Implementation, Hours/Week

Course

Tutorial

Laboratory

MATH122

1/2 (spring)

4

6

3

2

-

Department

Naval Architecture and Marine Engineering

Instructors

Instr. Serap Herdem

Contact Information

Piri Reis University, Faculty of  Engineering Tuzla-Istanbul

Phone: +90 216 5810050

Ext:1628

E-mail: skaya@pirireis.edu.tr

Office Hours

Web page

http://www.pirireis.edu.tr

Course Type

 Compulsory

Course Language

English

Course Prerequisites

  MATH 112

Course Category by Content, %

Basic Sciences

Engineering Science

Engineering Design

Humanities

100

Course Description

Improper integrals, Infinite sequences and series, Vectors in Space, Vector-Valued Functions, Functions of  Several Variables and Partial Derivatives , Multiple Integrals.

Course Objectives

1.To provide the concepts and applications of the convergence of improper integrals, sequences and infinite series

2.To provide the knowledge of applications of partial differentiation and multiple integrals

3.To give an ability to apply knowledge of mathematics on engineering problems

Course Learning Outcomes

Upon successful completion of the course, students should be able to

1. recognize improper integrals and test if  they converge
2. use various convergence tests (geometric series test,  nth term test, integral test, comparison tests, alternating series tests, ratio test, and root test) to determine convergence or divergence of series
3. represent some functions as power series; apply the ratio and root tests to find the radius of convergence for a power series.
4. write the equations of lines and planes using appropriate information
5. have the knowledge about  limits and continuity of functions of several variables ,  partial differentiation, total differential,  maxima and minima (with/without constraints) , the Hessian test for local extrema, the method of Lagrange multipliers
6. evaluate double and triple iterated integrals, express areas and volumes as double and triple integrals

Instructional Methods and Techniques

Lecture, problem solving

Tutorial Place

Co-term Condition

Textbook

Thomas’ Calculus, 12th Edition, Pearson, Global Edition, George B. Thomas, Jr , Maurice D. Weir,  Joel Hass, 2010.
 

Other References

1. Calculus: A Complete Course, 7th Edition, Robert A. Adams and Christopher Essex, Pearson, Canada, 2010.
2. Calculus: A New Horizon, Howard Anton, 6th Edition; John Wiley & Sons, 1999.
3. Calculus: Concepts and Contexts, James Stewart, 4th Edition, Brooks/Cole Pub., 2008.

Homework & Projects

Laboratory Work

Computer Use

Other Activities

Assessment Criteria

Activities

Quantity

Effects on Grading, %

Attendance

Midterm

1

40

Quiz

5

10

Homework

Term Paper/Project

Laboratory Work

Practices

Tutorial

Seminar

Presentation

Field Study

Final Exam

1

50

TOTAL

100

Effects of Midterm on Grading, %

50

Effects of Final on Grading, %

50

TOTAL

100

ECTS/

WORKLOAD TABLE

Activities

Count

Hours

Total

Workload

Lecture

13

3

39

Midterm

1

14

14

Quiz

5

       2

10

Homework

10

2

20

Term Paper/Project

Laboratory Work

Practices

14

2

                   28

Tutorial

Seminar

Presentation

Field Study

Final Exam

1

28

28

Total Workload

139

Total Workload/25

139/25

Course ECTS Credits

6

Week

Topics

Course Outcomes

1

Improper Integrals , Sequences, Infinite Series 

I

2

 The Integral Test, Comparison Tests, The Ratio and Root Tests

II

3

Alternating Series, Absolute and Conditional Convergence, Power Series

II

4

Taylor and Maclaurin Series, Convergence of Taylor Series, The Binomial Series and Applications of Taylor Series

III

5

Parameterizations of  Plane Curves , Calculus with Parametric Curves, Polar Coordinates, Graphing in Polar Coordinates

IV

6

Areas and Lengths in Polar Coordinates, Three-Dimensional Coordinate Systems, Vectors

IV

7

The Dot Product, The Cross Product, Lines and Planes in Space , Midterm

IV

8

Curves in Space and Their Tangents, Integrals of Vector Functions; Projectile Motion,  Arc Length in Space,  Curvature and Normal Vectors of a Curve, Tangential and Normal Components of Acceleration, Velocity and Acceleration in Polar Coordinates

IV

9

Functions of Several Variables, Limits and Continuity in Higher Dimensions, Partial Derivatives, The Chain Rule

V

10

Directional Derivatives and Gradient Vectors, Tangent Planes and Differentials

V

11

Extreme Values and Saddle Points, Lagrange Multipliers

V

12

Double and Iterated Integrals over Rectangles, Double Integrals over General Regions  

VI

13

Area by Double Integration, Double Integrals in Polar Form

VI

14

 Triple Integrals in Rectangular Coordinates, Triple Integrals in Cylindrical and Spherical Coordinates

VI

Program Outcomes

Level of Contribution

1

2

3

a

An ability to apply knowledge of mathematics, science, and engineering

X

b

An  ability to design and conduct experiments, as well as to analyze and interpret data

X

c

An ability to design a system, component or process to meet desired needs

X

d

Ability to function on multi-disciplinary teams

X

e

An ability to identify, formulate, and solve engineering problems

X

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 a global and societal context

X

i

A recognition of the need for, and an ability to engage in life-long learning

X

j

A knowledge of contemporary issues

X

k

An ability to use the techniques, skills and modern engineering tools necessary for engineering practice

X

l

An ability to apply engineering knowledge in fluid mechanics, structural mechanics, material selection and energy/propulsion systems in the context of marine vehicles and offshore structures.

X

Course Outcomes

I

II

III

IV

V

VI

Programme

outcomes

a

X

X

X

X

X

X

b

X

X

c

X

d

e

X

X

X

X

f

g

h

X

X

X

X

i

X

X

j

X

X

k

X

X

X

X

X

X

l

X

X

X

X

X

X

Prepared by

Instr. Serap Herdem

Date

Signature