Course Name

Code

Semester

Theory
(hour/week)

Application/Laboratory
(hour/week)

Local Credits

ECTS

Calculus II

MATH 154

Fall/Spring

3

2

4

6

 

 

Prerequisites

Math153 To Have Followed The Course

 

Course Language

English

Course Type

Required

Course Level

First Cycle

Course Coordinator

·         Yrd. Doç. Dr. Sevin GÜMGÜM

Course Lecturer(s)

·         Yrd. Doç. Dr. Sevin GÜMGÜM

·         Yrd. Doç. Dr. Güvenç ARSLAN

·         Yrd. Doç. Dr. Tahsin ÖNER

·         Doç. Dr. Burak ORDİN

Course Assistants

·         Araş. Gör. Cihangir KAN

·         Araş. Gör. Demet ERSOY ÖZDEK

Course Objectives

This course is continuation of Calculus I and it aims to provide more insight to advanced mathematical techniques in engineering.

Course Learning Outcomes

The students who succeeded in this course;

·         will be able to understand the notion of a sequence, its basic properties, and the concept of a limit of a sequence.

·         will be able to distinguish between convergent and divergent sequences, calculate limits of convergent sequences and explain the meaning of an infinite series, its partial sum and compute sums of special series.

·         will be able to explain the meaning of an infinite series, its partial sum and compute sums of special series and apply correctly tests for convergence of positive numerical series.

·         will be able to understand the notions of absolute and conditional convergence and apply the alternating series test whenever appropriate and to find the radius and the interval of convergence of a power series, indicating at which points the series converges absolutelt/conditionally.

·         will be able to construct Taylor and Maclourin series for a given function, use them for approximation of functions, to use power series to calculate limits and integrals and able to understand and apply two and three dimansional Cartesian coordinate system.

·         will be able to recognize and classify the equations and shapes of quadratic surfaces, to construct the equations of lines and planes,to understand and use the concept of a function of several variables, find its domain.

·         will be able to calculate the limits of multivariable functions and prove the nonexistence of a limit, to find partial derivatives using the properties of differentiable multivariable functions and basic rules, to apply partial derivatives for finding equations of tangent planes, normal lines, and for extreme values.

·         will be able to evaluate double intagrals in Cartesian and polar coordinates and triple integrals in Cartesian, cylindrical and spherical coordinates, to apply multiple integrals for computing areas and volumes, to solve first and second order differential equations.

Course Content

Calculus II provides important tools in understanding functions of several variables and has led to the development of new areas of mathematics.

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week

Subjects

Related Preparation

1

Sequences and Convergence, Infinite Series, Convergence Tests for Positive Series

Sums and Sigma notation Finding limits of functions

2

Absolute and Conditional Convergence. Power Series

Convergence tests

3

Taylor and Maclaurin Series, Applications of Taylor and Maclaurin Series

4

Functions of Several Variables, Limits and continuity, Partial Derivatives

Finding limits and derivatives of functions of one variable

5

Gradients and Directional Derivatives MIDTERM 1

Dot and cross product of vectors

6

Extreme Values, Extreme Values of Functions Defined on Restricted Domains

Higher order derivatives

7

Lagrange Multipliers

8

Iteration of Double Integrals in Cartesian Coordinates, Polar Coordinates in Double integrals

Integration techniques

9

Triple Integrals, Change of Variables in Triple Integrals

10

Applications Using Maple MIDTERM 2

11

Classifying Differential Equations, Solving FirstOrder Equations

Antidifferentiation

12

Second Order Linear Differential Equations with Constant Coefficients

13

Differential Equations of Second Order (17.4).

14

Linear Differential Equations with Constant Coefficients

15

Review of the semester

16

Review of the semester

SOURCES

Course Notes / Textbooks

Calculus: A Complete Course Sixth Edition Adams

References

James Stewart, Calculus, Early Transcendentals 7E

EVALUATION SYSTEM

Semester Requirements

Number

Percentage of Grade

Attendance/Participation

-

-

Laboratory

-

-

Application

-

-

Field Work

-

-

Special Course Internship (Work Placement)

-

-

Quizzes/Studio Critics

5

5

Homework Assignments

-

-

Presentation/Jury

-

-

Project

-

-

Seminar/Workshop

-

-

Midterms

2

60

Final

1

35

Total

8

100

 

PERCENTAGE OF SEMESTER WORK

-

65

PERCENTAGE OF FINAL WORK

-

35

Total

0

100

COURSE CATEGORY

Course Category

Core Courses

Major Area Courses

Supportive Courses

X

Media and Managment Skills Courses

Transferable Skill Courses

THE RELATIONSHIP BETWEEN COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS

#

Program Qualifications / Outcomes

* Level of Contribution

1

2

3

4

5

1

Adequate knowledge in Mathematics, Science and Computer Engineering; ability to use theoretical and applied information in these areas to model and solve Computer Engineering problems

X

2

Ability to identify, define, formulate, and solve complex Computer Engineering problems; ability to select and apply proper analysis and modeling methods for this purpose

X

3

Ability to design a complex computer based system, process, device or product under realistic constraints and conditions, in such a way as to meet the desired result; ability to apply modern design methods for this purpose

4

Ability to devise, select, and use modern techniques and tools needed for Computer Engineering practice

5

Ability to design and conduct experiments, gather data, analyze and interpret results for investigating Computer Engineering problems

X

6

Ability to work efficiently in Computer Engineering disciplinary and multi-disciplinary teams; ability to work individually

7

<p> Ability to communicate effectively in Turkish, both orally and in writing; knowledge of a minimum of two foreign languages</p>

8

Recognition of the need for lifelong learning; ability to access information, to follow developments in science and technology, and to continue to educate him/herself

9

Awareness of professional and ethical responsibility

10

Information about business life practices such as project management, risk management, and change management; awareness of entrepreneurship, innovation, and sustainable development

11

Knowledge about contemporary issues and the global and societal effects of engineering practices on health, environment, and safety; awareness of the legal consequences of Computer Engineering solutions

*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest

ECTS / WORKLOAD TABLE

Activities

Number

Duration (Hours)

Total Workload

Course Hours (Including Exam Week: 16 x Total Hours)

16

5

80

Laboratory

-

-

-

Application

2

5

10

Special Course Internship (Work Placement)

-

-

-

Field Work

-

-

-

Study Hours Out of Class

16

3

48

Presentations / Seminar

-

-

-

Project

-

-

-

Homework Assignments

-

-

-

Quizzes

5

1

5

Midterms

2

10

20

Final

1

7

7

 

 

Total Workload

170