# Chandubhai S Patel Institute of Technology, Ahmedabad

## Electronics and Communication Engineering Maths III Syllabus

CHAROTAR UNIVERSITY OF SCIENCE & TECHNOLOGY

FACULTY OF TECHNOLOGY & ENGINEERING

DEPARTMENT OF MATHAMATICS

B. TECH. (ELECTRONICS & COMMUNICATION)

2ND YEAR SEMESTER: III

MA 202: ENGINEERING MATHEMATICS – III

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Credit Hours:

Teaching Scheme Theory Practical Total

Hours/week 4 0 4

Marks 100 – 100

A. Objective of the Course:

The objectives or goals of the course are to introduce the students about various mathematical analysis like Fourier Series, Laplace Transforms, Vector Differential

Calculus which are useful to solve the complex problems of solid state electronics, network theory and other subjects.

B. Outline of the Course:

Sr. No. Title of the Unit Minimum Number of Hours

1. Fourier Series 10

2. Laplace Transforms 14

3. Roots Of Equations 06

4. Applications Of Differential Equations 10

5. Vector Differential Calculus 12

6. Vector Integral Calculus 08

Total Hours: 60

C. Detailed Syllabus:

SECTION-I

1. Fourier Series 10 Hrs 1 8 %

1.1 Periodic Functions, Trigonometric Series 3 Hrs

1.2 Euler Formulae, Fourier Series of Periodic Function of Period 2 3 Hrs

1.3 Even and Odd Functions, Half Range Series 1 Hr

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1.4 Fourier Series of Arbitrary Period 3 Hrs

2. Laplace Transforms 14 Hrs 22%

2.1 Laplace Transforms as an Improper Integral and Its Existence. Laplace Transforms of Elementary Functions, Inverse Laplace Transforms, Linearity Property

3 Hrs

2.2 First and Second Shifting Theorems, Laplace Transforms Of Derivatives and Integrals. 3 Hrs

2.3 Convolution Theorem and Its Application To Obtain Inverse Laplace Transform 3 Hrs

2.4 Laplace Transform of Periodic Functions, Unit Step Function, Unit Impulse Function (Dirac Delta Function) 3 Hrs

2.5 Application of Laplace Transforms in Solving Ordinary Differential Equations 2 Hrs

3. Roots of Equations 6 Hrs 10%

3.1 Statement of Fundamental Theorem of Algebra, Analytical Solution of Cubic Equation by Cardon’s Method 3 Hrs

3.2 Analytic Solution of Biquadratic Equations by Ferrari’s Method With their Applications. 3 Hrs

SECTION-II

4 Applications of Differential Equations 10 Hrs 15%

4.1 Applications of ODE: Mechanical Vibration System, Electrical Circuit System, Deflection of Beams. 5 Hrs

4.2 Application of PDE: Heat, Wave, Laplace Equations And Their Solution By Method of Separation of Variables And Fourier Series. 5 Hrs

5 Vector Differential Calculus 12 Hrs 20%

5.1 Revision of Concept of Vector Algebra, Scalar And Vector Fields. 03 Hrs

5.2 Gradient of A Scalar Functions, Directional Derivatives. 03 Hrs

5.3 Divergence And Curl of A Vector Field and Their Properties. 03 Hrs

5.4 Physical Interpretations of Gradient, Divergence and Curl. Irrotational, 03 Hrs

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Solenoidal and Conservative Vector Fields

6 Vector Integral Calculus 8 Hrs 15%

6.1 Line Integrals, Surface Integrals 03 Hrs

6.2 Statement and Examples of Green’s Theorem, Stoke’s And Divergence Theorem, Applications of Vector Calculus In Engineering Systems.05 Hrs

D. Instructional Method and Pedagogy:

Lectures will be taken in class room with the aid of multi-media presentations / black board or mix of both.

Assignments based on above course content will be given at the end of the chapter.

Assignment should be submitted to the respective course teacher within the given time limit.

There will be lecture for Quizzes and interaction at every 5 to 6 lecture hour.

Attendance in the lectures and laboratory is must and which is first and foremost requirement.

In the lectures and laboratory discipline and behavior will be observed strictly.

E. Student Learning Outcomes:

At the end of the course the students will be able to understand the concepts of Engineering Mathematics in broad way.

Students will able to identify, solve and analyze mathematical problems related to Technology and Engineering.

F. Recommended Study Material:

Reference Books:

1). Erwin Kreyszig: Advanced Engineering Mathematics, 8th Ed., John Wiley & Sons,

India, 1999

2). Wylie & Barrett: Advanced Engineering Mathematics, Mc graw Hill pub.

3). Greenberg M D: Advanced Engineering Mathematics, 2nd ed., Pearson Education