Course Name : Mathematics-I

Degree:  Bachelor

Code

Year/Semester

Local Credits

ECTS Credits

Course Implementation, Hours/Week

Course

Tutorial

Laboratory

MATH112

1/1 (fall)

4

6

3

2

-

Department

Industrial 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/pruonline

Course Type

 Compulsory

Course Language

English

Course Prerequisites

  -

Course Category by Content, %

Basic Sciences

Engineering Science

Engineering Design

Humanities

100

Course Description

Functions, Limits and Continuity, Differentiation, Applications of Derivatives, Integration, Applications of Definite Integrals, Transcendental Functions, Techniques of Integration

Course Objectives

1. To introduce  the concepts of function, limit, continuity, differentiation and integration

2. To acquire skills to apply the knowledge of mathematics on engineering

problems

Course Learning Outcomes

Upon  successful completion of the course students should be able to

1. describe a function,  and  determine the domain and range of functions, find the sum, difference, product, quotient and composition of functions
2. sketch the graph of functions by using reflection, translation and scaling of graphs of functions
3. compute limits and find derivatives of functions
4. use differentiation in sketching  the graphs and in finding extreme values of functions
5. evaluate integrals and  apply integration to compute area, volume of revolution and arc length
6. integrate various functions by using techniques of integration        

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

Functions and Their Graphs, Combining Functions; Shifting and

Scaling Graphs

I-II

2

 Rates of Change and Tangents to Curves , Limit of a Function and Limit Laws, The Precise Definition of a Limit

I-III

3

One-Sided Limits, Continuity, Limits Involving Infinity; Asymptotes of Graphs

I-III

4

Tangents and the Derivative at a Point, The Derivative as a Function, Differentiation Rules, The Derivative as a Rate of Change

III-IV

5

Derivatives of Trigonometric Functions, The Chain Rule,  Implicit Differentiation

IV

6

Related Rates, Linearization and Differentials

III-IV

7

Extreme Values of Functions, The Mean Value Theorem, Monotonic Functions and the First Derivative Test, Midterm

IV

8

Concavity and Curve Sketching, Applied Optimization, Newton's Method, Antiderivatives

I-IV

9

Area and Estimating with Finite Sums, Sigma Notation and Limits of Finite Sums, The Definite Integral

III

10

The Fundamental Theorem of Calculus, Indefinite Integrals and the Substitution Method, Substitution and Area Between Curves

IV-V

11

Volumes Using Cross-Sections, Volumes Using Cylindrical Shells

 Arc Length, Areas of Surfaces of Revolution

IV-V

12

Inverse Functions and Their Derivatives, Natural Logarithms, Exponential Functions

 Indeterminate Forms and L’Hopital's Rule,

III-IV

13

Inverse Trigonometric Functions, Hyperbolic Functions, Integration by Parts

I-V

14

Trigonometric Integrals, Trigonometric Substitutions, Integration of Rational Functions by Partial Fractions

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

Application of administrative skills and knowledge in the business world

X

Course

Outcomes

I

II

III

IV

V

VI

Programme Outcomes

a

X

X

X

X

X

X

b

X

X

X

c

X

d

e

X

X

X

X

f

g

h

X

X

X

X

i

X

X

X

j

X

k

X

X

X

X

l

X

X

X

X

X

Prepared by

Instr. Serap Herdem

Date

Signature