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Mathematics III

This advanced course focuses on the "logical" application of Fourier series, complex variables, and partial differential equations (PDEs). It provides the "technical clarity" for mathematical modeling and utilizes Z-transforms to analyze "Communication Systems" and discrete data.

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TabFlux . Engineering Mathematics III . TU . BCT-NEW

Engineering Mathematics III

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Course Title: Engineering Mathematics III

Course No: ENSH201

Nature of the Course: THEORY

Semester: 3

Full Marks: 40 + 60

Pass Marks: 16 + 24

Credit Hours: 3

Course Description

Course Objectives

Course Contents

1. Fourier Series and Fourier Transform

12 hrs18 marks

1.1. Review of periodic, odd and even functions

1.2. Fourier series of a function over an interval of length 2l and 2π; Euler's formula, Dirichlet's condition for uniform convergence of Fourier series, Fourier series of discontinuous functions

1.3. Half range Fourier sine and cosine series

1.4. Complex form of Fourier series; frequency and amplitude of a function

1.5. Fourier integral theorem, Fourier sine and cosine integrals, complex form of Fourier integral

1.6. Fourier transform, Fourier sine transform, Fourier cosine transform and their inversion formulas

1.7. Fourier transform of the derivative of a function

1.8. Relation between Fourier and Laplace transform

2. Functions of Complex Variable

12 hrs18 marks

2.1. Intuitive idea of limit, continuity and differentiability of functions of complex variable

2.2. Analytic functions, the Cauchy Reimann equations both in Cartesian and polar form, construction of analytic functions

2.3. Harmonic functions, the orthogonal system

2.4. Application of analytic functions in flow problems

2.5. Transformation (Mapping), conformal mapping, translation, rotation and magnification; inversion, bilinear transformation

2.6. Complex integration, simply and multiply connected regions, Cauchy's integral theorem and formula

2.7. Series of complex terms, power series, circle of convergence and radius of convergence, Taylor's and Laurent's series

2.8. Zeros, singularities, poles; residue at poles, Cauchy's residue theorem and evaluation real and improper integrals

3. Partial Differential Equations

5 hrs6 marks

3.1. Definition and formation of partial differential equations

3.2. Partial differential equations solvable by direct integration

3.3. Linear partial differential equation of the first order, Lagrange's linear equations and their solution

3.4. Nonlinear partial differential equation of first order; equations of the form f(p,q)=0, z=px+qy+f(p,q), f(z,p,q)=0, f1(x,p)=f2(y,q)

3.5. Charpit's method of solving nonlinear partial differential equations of first order

4. Modelling through Partial Differential Equation

10 hrs10 marks

4.1. Second order partial differential equation and classification

4.2. One-dimensional wave equation

4.3. One-dimensional heat equation

4.4. Two-dimensional heat equation, Laplace equation in Cartesian form

4.5. Mass balance equation; equation of continuity in fluid dynamics, Navier-Stoke's equation

4.6. Momentum balance equation; Euler's equation of motion for inviscid fluid flow

5. Z-transform and its Applications

6 hrs8 marks

5.1. Representation of a sequence and basic operations

5.2. Definition and existence of Z-transform, Z-transform of standard sequences

5.3. Properties of Z-transform; linearity, change of scale, shifting properties, initial and final value theorems

5.4. Differentiations of Z-transform

5.5. Inverse Z-transform; partial fraction and residue methods

5.6. Convolution of sequences, convolution of Z-transform

5.7. Difference equations, application of Z-transform to solve difference equations and to find the sum of series

Reference Books

1.Jeffery A. (2002). Advanced Engineering Mathematics (2nd edition). San Diego: Harcourt Academic Press.
2.O'Neill, P.V. (2011). Advanced Engineering Mathematics (7th edition). India: Thompsons, USA/Baba Baghanath Printers.
3.Kreyszig, A. (2020). Advanced engineering Mathematics (10th edition). USA: Wiley Publications.
4.Sastry S.S. (2014). Engineering Mathematics vol I and II (4th edition). India: PHI Learning Pvt. Ltd.
5.Wylie C., Barrett L. (1988). Advanced Engineering Mathematics (5th edition). McGraw Hill.
6.Dutta, D. (2006). A text book of Engineering Mathematics Vol I and II (2nd edition). India: New Age International Publishers.
7.Ogata, K. (2015). Discrete Time Control System (2nd edition). Pearson Publications.
8.Sharma, Sanjay. (2017). Signals and Systems (9th edition). India: S.K.Kataria and Sons.

Notes:

Source:

This course covers Fourier series, Fourier transform, functions of complex variable, partial differential equations, mathematical modelling through PDEs, and Z-transform with applications.

The objective of this course is to equip students with understanding and practical application of Fourier series, Fourier transform, function of complex variable, partial differential equations and obtaining mathematical models and Z-transform.

This syllabus follows the official BCT curriculum of Tribhuwan University. In case of any doubt or revision, the university's published syllabus shall be considered authoritative. https://ioe.tu.edu.np/pages/computer-engineering-curriculum-structure-2635