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Mathematics-II

PÎRî REİS UNIVERSITY

MARITIME FACULTY

Marine Engineering Programme

 

Course catalog Form

Issue date: 01.10.2019

 

Revision date: 01.10.2019

 

Revision No: 00

 

DF Board Decision No: -

 

Course Name : Mathematics-II

Degree:  Bachelor

 

Code

 

 

Year/Semester

 

Local Credits

 

ECTS Credits

 

Course Implementation, Hours/Week

Course

Tutorial

Laboratory

MATH 121

1/2 (spring)

4

6

3

2

-

Department

Maritime Transportation and Management Engineering

Marine Engineering

Instructors

 

 

Contact Information

 

Office Hours

 

Web page

http://www.pirireis.edu.tr

Course Type

 Compulsory

Course Language

English

Course Prerequisites

  MATH 111

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

14

3

42

Midterm

1

15

15

Quiz

5

3

15

Homework

10

2

20

Term Paper/Project

 

 

 

Laboratory Work

 

 

 

Practices

2

14

28

Tutorial

 

 

 

Seminar

 

 

 

Presentation

 

 

 

Field Study

 

 

 

Final Exam

1

20

20

Total Workload

 

 

140

Total Workload/25

 

 

140/25

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

 

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

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

Midterm

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

 

 

Relationship between the Course and the Programme Curriculum

 

 

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

X

 

 

g

An ability to communicate effectively

X

 

 

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 legal, societal and environmental knowledge in maritime transport and in all respective modes of transport operations.

 

X

 

m

An ability to interpret and analysis of the data regarding maritime management and operations, recognition and solution of problems for decision making process.

 

 

X

 

 

         1: Small, 2: Partial, 3: Full

 

Programme Outcomes & Course Outcomes Connectivity Matrix

Course

Outcomes

I

II

III

IV

V

VI

Programme Outcomes

 

a

X

X

X

X

X

X

b

X

X

 

 

 

 

c

 

 

 

 

 

 

d

X

 

 

 

 

 

e

X

X

X

X

X

X

f

 

 

 

 

 

 

g

 

 

 

 

 

 

h

 

X

 

 

 

 

 

i

 

 

 

 

 

 

j

X

 

 

 

 

 

 

k

 

X

 

 

 

 

l

 

X

 

 

 

 

m