# 18MAT31: Transform Calculus, Fourier Series and Numerical Techniques MSE Syllabus for BE 3rd Sem 2018 Scheme VTU

Transform Calculus, Fourier Series and Numerical Techniques detailed Syllabus for Manufacturing Science & Engineering (MSE), 2018 scheme has been taken from the VTUs official website and presented for the VTU students. For Course Code, Subject Names, Teaching Department, Paper Setting Board, Theory Lectures, Tutorial, Practical/Drawing, Duration in Hours, CIE Marks, Total Marks, Credits and other information do visit full semester subjects post given below. The Syllabus PDF files can also be downloaded from the official website of the university.

For all other VTU MSE 3rd Sem Syllabus for BE 2018 Scheme, do visit VTU MSE 3rd Sem Syllabus for BE 2018 Scheme Subjects. The detailed Syllabus for transform calculus, fourier series and numerical techniques is as follows.

#### Course Learning Objectives:

For the complete Syllabus, results, class timetable, and many other features kindly download the iStudy App
It is a lightweight, easy to use, no images, and no pdfs platform to make students’s lives easier.
.

#### Module-1

Laplace Transform: Definition and Laplace transforms of elementary functions (statements only). Laplace transforms of Periodic functions (statement only) and unit-step function – problems. Inverse Laplace Transform: Definition and problems, Convolution theorem to find the inverse Laplace transforms (without Proof) and problems. Solution of linear differential equations using Laplace transforms.

#### Module-2

Fourier Series: Periodic functions, Dirichlet’s condition. Fourier series of periodic functions period 2n and arbitrary period. Half range Fourier series. Practical harmonic analysis.

#### Module-3

For the complete Syllabus, results, class timetable, and many other features kindly download the iStudy App
It is a lightweight, easy to use, no images, and no pdfs platform to make students’s lives easier.
.

#### Module-4

Numerical Solutions of Ordinary Differential Equations(ODE’s): Numerical solution of ODE’s of first order and first degree- Taylor’s series method, Modified Euler’s method. Runge -Kutta method of fourth order, Milne’s and Adam-Bash forth predictor and corrector method (No derivations of formulae)-Problems.

#### Module-5

Numerical Solution of Second Order ODE’s: Runge-Kutta method and Milne’s predictor and corrector method. (No derivations of formulae). Calculus of Variations: Variation of function and functional, variational problems, Euler’s equation, Geodesics, hanging chain, problems.

#### Course Outcomes:

For the complete Syllabus, results, class timetable, and many other features kindly download the iStudy App
It is a lightweight, easy to use, no images, and no pdfs platform to make students’s lives easier.
.

#### Question Paper Pattern:

• The question paper will have ten full questions carrying equal marks.
• Each full question will be for 20 marks.
• There will be two full questions (with a maximum of four sub- questions) from each module.
• Each full question will have sub- question covering all the topics under a module. The students will have to answer five full questions, selecting one full question from each module.

#### Text Books:

1. Advanced Engineering Mathematics E. Kreyszig John Wiley & Sons 10th Edition, 2016
2. Higher Engineering Mathematics B. S. Grewal Khanna Publishers 44te Edition, 2017
3. Engineering Mathematics Srimanta Pal et al Oxford University Press 3rd Edition, 2016

#### Reference Books:

For the complete Syllabus, results, class timetable, and many other features kindly download the iStudy App
It is a lightweight, easy to use, no images, and no pdfs platform to make students’s lives easier.
.

#### Web links and Video Lectures:

1. http://nptel.ac.in/courses.php?disciplineID=111
2. http://www.class-central.com/subject/math(MOOCs)