Module(Course Syllabus)Catalogue 2019-2020 B_Mathematics- 1st class-2020 EVENING.pdfthat mathematics plays in the development and practice of engineering as well as motivating the

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Module(Course Syllabus)Catalogue

2019-2020

College/ Institute Erbil Polytechnic University

Department Electricity Technique

Module Name Mathematics

Module Code MAT104 Semester 1st

Credits 6

Module type Prerequisite Core Assist.

Weekly hours

Weekly hours (Theory) (2)hr Class ( 67 )hr Workload

Weekly hours (Practical) (2)hr Class ( 67 )hr Workload

Lecturer (Theory) pishtiwan K. Mahmoud

E-Mail& Mobile NO. pishtiwankamalmahmoud@ gmail.com

Lecturer (Practical) pishtiwan K. Mahmoud

E-Mail & Mobile NO. pishtiwankamalmahmoud@ gmail.com

1


Course Book

Course Description

The aim of the course is to strengthen the student's techniques in

mathematics, in particular, linear algebra, calculus and complex numbers

needed by electrical, mechanical, electronic, communications and

computer systems technicians.

Course objectives

It is aimed at broadening the students’ appreciation of the central role

that mathematics plays in the development and practice of engineering

as well as motivating the inclusion and use of essential analytical

concepts, calculus methods and linear mathematics major to

engineering. The course helps students to further develop the skill of

analysing problems in a rational (rigorous, logical) and methodical

manner. Another aim is developing the students’ ability to transfer their

mathematical understanding (and the associated methods) to diverse

engineering application areas.

Student's obligation

Late arrival to the classroom disturbs everyone; please DO NOT show up in class if you are late. Homework is a critical part of the course, and to fully understand the topics, it is essential that you work carefully on every examination and try your best to do every problem. Because after the scheduled date solutions for the homework will be given, so no homework will be accepted after the deadline. You are to submit your homework assignment every Sunday. Each week every of the submitted homework will be marked.

During the two-hour weekly theoretical part, lectures will be presented

through the projector and solutions of examples will be explained on the

white board.

Required Learning Materials

Basics of mathematics in Functions,Trigonometric functions,Exponential and logarithmic functions,Matrices,Differentiation,&Integrations.


Assessment scheme

16% Mid Term (Theory and practical) 4% Quiz 40% Assignment (report, paper, homework, seminar..) 25% final practical 15% final theory

Specific learning outcome:

1- . Determine the domain and range of a function

2-Knowing the inverse of a trigonometric function

3-Application of logarithms and exponential function.

4-Develop and use a strategy for finding limits.

5- Multiply a matrix by a scalar and multiply two matrices together

6- Differentiate by using a list of standard derivatives

Course References‌:

K.A. Stroud, Dexter J. Booth, 2001.Engineering mathematics, Industrial Press Inc, New York. K. S. Rattan,N. W. Klingbeil,2015.Introductory Mathematics for Engineering Applications,John Wiley,USA.

J. Stewart, 2012.Calculus: Early Transcendentals, Brooks/Cole, USA.

C. R. Wylie, J R.,1966.Advanced Engineering Mathematics,McGraw-Hill, UK.

J. Bird, 2007.Engineering mathematics, Elsevier Ltd., UK. L. Glasgow,2014,Applied Mathematics for Science and Engineering, John Wily,USA, G. Fiche,2008.Mathematics for Engineers, John Wiley,USA.

Course topics (Theory) Week Learning

Outcome Functions: Functions are rules but not all rules are

functions,Domain and Range,Functions and the arithmetic

operations, Inverses of functions, Inverses of functions, and

1


inverses of functions.

Exponential and logarithmic functions:Exponential

functions, Indicial equation.

2

Trigonometric functions:Rotation, Sine function, cosine

function, Tangent function, Period, Amplitude, Phase difference,

Inverse trigonometric functions.

3

Limits: The Limit of a Function, Limits of Rational Function, Limits

of Trigonometric Function.

4

Matrices: Definitions, Matrix notation, Equal matrices, Addition and

subtraction of matrices, Multiplication of matrices, Transpose of a

matrix

5

Matrices:Determinant of a square matrix,Determinant of a square

matrix

6

Solution of a set of liner equations:Cramer’s

Rule,Application of determinants.

7

Vectors:Introduction: scalar and vector quantities, Vector

representation, Components of a given vector,

8

Vectors: Vectors in space, Direction cosines, Scalar product of two

vectors, Vector product of two vectors, Vector product of two vectors,

Direction ratios.

9

Differentiation: Standard derivatives, Derivative of Trigonometric

function,

10

Differentiation: Logarithmic differentiation, Implicit function,

Parametric equation.

11

Differentiation Application: Equation of a straight line,

Differentiate the inverse trigonometric functions.

12

Differentiation Application: Differentiate the inverse

hyperbolic functions, Maximum and minimum value.

13

Integrations: Standard integrals, Functions of a liner function of X 14


Integrations: Integration by part, Integration by partial fraction,

Integration of Trigonometrical functions

15

Integrations Application: Definite integrals, Area under curves, 16

Practical Topics Week Learning

Outcome Home work of Functions: Functions are rules but not all rules

are functions,Domain and Range,Functions and the arithmetic

operations, Inverses of functions, Inverses of functions, and

inverses of functions.

1

Home work of Exponential and logarithmic

functions:Exponential functions, Indicial equation.

2

Home work of Trigonometric functions:Rotation, Sine

function, cosine function, Tangent function, Period, Amplitude, Phase

difference, Inverse trigonometric functions.

3

Home work of Limits: The Limit of a Function, Limits of Rational

Function, Limits of Trigonometric Function.

4

Home work of Matrices: Definitions, Matrix notation, Equal

matrices, Addition and subtraction of matrices, Multiplication of

matrices, Transpose of a matrix

5

Home work of Matrices:Determinant of a square

matrix,Determinant of a square matrix

6

Home work of Solution of a set of liner equations:Cramer’s

Rule,Application of determinants.

7

Home work of Vectors:Introduction: scalar and vector quantities,

Vector representation, Components of a given vector,

8

Home work of Vectors: Vectors in space, Direction cosines, Scalar

product of two vectors, Vector product of two vectors, Vector product

of two vectors, Direction ratios.

9

Home work of Differentiation: Standard derivatives, Derivative

of Trigonometric function,

10


Home work of Differentiation: Logarithmic differentiation,

Implicit function, Parametric equation.

11

Home work of Differentiation Application: Equation of a

straight line, Differentiate the inverse trigonometric functions.

12

Home work of Differentiation Application: Differentiate the

inverse hyperbolic functions, Maximum and minimum value.

13

Home work of Integrations: Standard integrals, Functions of a

liner function of X

14

Home work of Integrations: Integration by part, Integration by

partial fraction, Integration of Trigonometrical functions

15

Home work of Integrations Application: Definite integrals,

Area under curves,

16

Questions Example Design 1-Calculate:( Answer only 4 )

𝑎)𝑙𝑖𝑚𝑥→4

𝑥 − 4

𝑥2−𝑥−12 𝑏)𝑙𝑖𝑚

𝑥→2 (2x + 3) 𝑐)𝑙𝑖𝑚

𝑡→0

𝑠𝑖𝑛 (2𝑡)

𝑡

d)limx→2

(5x) 𝑒) 𝑙𝑖𝑚𝑡→0

sin (𝑡2)−1

𝑡𝑓) 𝑙𝑖𝑚

𝑥→4 (25 − 𝑥2)2

2-A- Write an equation for the line that passes through poin:

a) P (−2 , 3) with slope m = −2 .

b) P1 (3 , −2) and P2 ( 1 , 4 ).

B- Find the missing angles α , ( β ) in the below graphic

Extra notes: The one-hour weekly tutorials will be used primarily to assist you with the assignments. You will get

some hints and tips, and see some similar problems worked through. You may also see some extra

examples of problems related to the topics discussed in recent classes.

In addition to the textbook, lectures, and office hours where are other resources accessible that might


be of use for you during the course. You can get lectures in two ways, first on my faculty website all of my lectures and homework sheets will be posted. Second, you can get a hard copy of them directly in the class.

External Evaluator

Documents

Module(Course Syllabus)Catalogue 2019-2020 B_Mathematics- 1st class-2020 EVENING.pdfthat mathematics plays in the development and practice of engineering as well as motivating the