# CHARUSAT Mathematics IV Syllabus

CHAROTAR UNIVERSITY OF SCIENCE & TECHNOLOGY

FACULTY OF TECHNOLOGY AND ENGINNERING

DEPARTMENT OF MATHAMETICS

B. TECH. (ELECTRONICS & COMMUNICATION)

2ND YEAR SEMESTER: IV

MA 203: ENGINEERING MATHEMATICS – IV

_______________________________________________________________________

Credit Hours:

Teaching Scheme

Theory

Practical

Total

Hours/Week

4

0

4

Marks

100

–

100

A. Objective of The Course:

The purposes or objectives of the course are to prepare the students for mathematical analysis which is very useful to solve the problems related to (I) Antenna Theory (II) Electromagnetic Theory (III) Digital Signal Processing (IV) Fiber Optics and related subjects of the higher semester of B. Tech. (EC).

B. Out Line of The Course:

Sr No.

Title of The Unit

Minimum Number of Hours

1.

Fourier Transforms

09

2.

Function of Complex Variable-I

11

3.

Function of Complex Variable-Ii

10

4.

Z-Transforms

12

5.

Numerical Methods

10

6.

Solution of Equations

08

Total Hours: 60hrs

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C. Detailed Syllabus:

SECTION-I

1.

Fourier Transforms 09 Hrs

15%

1.1

Fourier Transform of A Real Valued Function, Fourier Sine and Cosine Transforms.

3 Hrs

1.2

Discrete and Continuous Signals and Their Representation In Time and Frequency Domain, Inverse Fourier Transforms.

3 Hrs

1.3

Linearity and Convolution Properties, Convolution Theorem.

3 Hrs

2.

Function of Complex Variable-I 11 Hrs

20%

2.1

Complex Valued Functions of A Complex Variables, Continuity and Differentiability of Complex Valued Function,

1 Hr

2.2

Analytic Function, Cauchy-Riemann Equations (Cartesian and Polar Forms), Necessary and Sufficient Condition For The Function To Be Analytic

1 Hrs

2.3

Harmonic Function and Harmonic Conjugate

3 Hrs

2.4

Mappings By Elementary Functions, Conformal Mapping, Some Standard Conformal Transformations

3 Hrs

2.5

Bilinear (Mobius) Transformations

1 Hr

2.6

Applications of Complex Valued Function In Ece.

2 Hrs

3.

Function of Complex Variable-II 10 Hrs

18%

3.1

Complex Integration,

1 Hr

3.2

Statement and Examples of Cauchy-Goursat Theorem and Cauchy Integral Formula.

3 Hrs

3.3

Singularities,

1 Hr

3.4

Taylor’s and Laurent’s Series,

2 Hrs

3.5

Residue Theorem, Evaluation of Integrals Using Residues

2 Hrs

3.6

Inverse Laplace Transform By Using Residues.

1 Hr

© CHARUSAT 2012 Page 40 of 154

SECTION-II

4.

Z-Transforms 12 Hrs

20%

4.1

Introduction, Representation of Sequence,

1 Hr

4.2

Unit Sample Sequence, Basic Operations On Sequence,

2 Hrs

4.3

Properties of Z-Transforms, Z-Transforms of Basic Sequences,

2 Hrs

4.4

Change of Scale, Shifting Properties, Inverse Z-Transforms By Binomial Expansion,

2 Hrs

4.5

Partial Fraction and Residue Method, Solution of Difference Equation,

2 Hrs

4.6

Multiplication By K, Division By K, Initial Value, Final Value,

2 Hrs

4.7

Partial Sum Theorem, Convolution Theorem.

1 Hr

5.

Numerical Methods 10 Hrs

15%

5.1

Finite Difference, Forward and Backward Differences

1 Hr

5.2

Interpolation and Extrapolation

2 Hrs

5.3

Newton’s Interpolation Formulae:

2 Hrs

5.4

Lagrange’s Interpolation Formula,

1 Hr

5.5

Numerical Integration: Gaussian Integration, Newton – Cotes Quadrature Formula, Composite Rules (Trapezoidal Rule, Simpson’s Rules).

4 Hrs

6.

Numerical Solution of Equations 08 Hrs

12%

6.1

Newton-Raphson Method, False Position (Regula Falsi) Method, Bisection Method.

4 Hrs

6.2

Solution of Ode By Euler’s, Taylor’s Series, Picard’s, Runge Kutta (2nd and 4th Order) Methods.

4 Hrs

D. Instructional Method and Pedagogy:

At the start of course, the course delivery pattern, prerequisite of the subject will be discussed.

Lectures will be conducted with the aid of multi-media projector, black board, ohp etc.

Attendance is compulsory in lectures/laboratory which carries a 5% component of the overall evaluation.

Minimum two internal exams will be conducted and average of two will be considered as a part of 15% overall evaluation.

Assignments based on course content will be given to the students at the end of each unit/topic and will be evaluated at regular interval. it carries a weightage of 5%.

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Two quizzes (surprise test) will be conducted which carries 5% component of the overall evaluation.

H. Student Learning Outcomes:

At the end of course students will able to identify, analyze, formulate and solve mathematical problems related to electronics and communication.

I. Recommended Study Material:

Reference Books:

1. Erwin Kreyszig: Advanced Engineering Mathematics, 8th Ed., Jhon 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

. 4. Prajapati J. C.: Advanced Engineering Mathematics, 1st Ed., Pearson Education