sc VTU B.TECH Civil Engineering SEMESTER – III Syllabus For Transform calculus, fourier series and numerical techniques PDF 2022 – Cynohub

# VTU B.TECH Civil Engineering SEMESTER – III Syllabus For Transform calculus, fourier series and numerical techniques PDF 2022

### Get Complete Lecture Notes for Transform calculus, fourier series and numerical techniques on Cynohub APP

You will be able to find information about Transform calculus, fourier series and numerical techniques along with its Course Objectives and Course outcomes and also a list of textbook and reference books in this blog.You will get to learn a lot of new stuff and resolve a lot of questions you may have regarding Transform calculus, fourier series and numerical techniques after reading this blog. Transform calculus, fourier series and numerical techniques has 5 units altogether and you will be able to find notes for every unit on the CynoHub app. Transform calculus, fourier series and numerical techniques can be learnt easily as long as you have a well planned study schedule and practice all the previous question papers, which are also available on the CynoHub app.

All of the Topic and subtopics related to Transform calculus, fourier series and numerical techniques are mentioned below in detail. If you are having a hard time understanding Transform calculus, fourier series and numerical techniques or any other Engineering Subject of any semester or year then please watch the video lectures on the official CynoHub app as it has detailed explanations of each and every topic making your engineering experience easy and fun.

### Transform calculus, fourier series and numerical techniques Unit One

#### 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 problem s, Convolution theorem to find the inverse Laplace transforms (without Proof) and problems. Solution of linear differential equations using Laplace transforms.

### Transform calculus, fourier series and numerical techniques Unit Two

#### Fourier Series

Periodic functions, Dirichlet’s condition. Fourier series of periodic functions period π2and arbitrary period. Half range Fourier series. Practical harmonic analysis.

### Transform calculus, fourier series and numerical techniques Unit Three

#### Module-3

Fourier Transforms: Infinite Fourier transforms, Fourier sine and cosine transforms. Inverse Fourier transforms. Problems. Difference Equations and Z-Transforms: Difference equations, basic definition, z-transform-definition, Standard z-transforms, Damping and shifting rules, initial value and final value theorems (without proof) and problems, Inverse z-transform and applications to solve difference equations.

### Transform calculus, fourier series and numerical techniques Unit Four

#### 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.

### Transform calculus, fourier series and numerical techniques Unit Five

#### 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.

### Transform calculus, fourier series and numerical techniques Course Objectives

To have an insight into Fourier series, Fourier transforms, Laplace transforms, Difference equationsand Z-transforms. •To develop the proficiency in variational calculus and solving ODE’s arising in engineering applications, using numerical methods.

### Transform calculus, fourier series and numerical techniques Course Outcomes

At the end of the course the student will be able to:•CO1: Use Laplace transform and inverse Laplace transform in solving differential/ integral equation arising in network analysis, control systems and other fields of engineering. •CO2: Demonstrate Fourier series to study the behaviour of periodic functions and their applications insystem communications, digital signal processing and field theory. •CO3: Make use of Fourier transform and Z-transform to illustrate discrete/continuous function arising in wave and heat propagation, signals and systems. • CO4: Solve first and second order ordinary differential equations arising in engineering problems using single step and multistep numerical methods. •CO5:Determine the externals of functional using calculus of variations and solve problems arising in dynamics of rigid bodies and vibrational analysis.

### Transform calculus, fourier series and numerical techniques Text Books

Higher Engineering Mathematics-B. S. Grewal
Engineering Mathematics-Srimanta Pal et al

### Transform calculus, fourier series and numerical techniques Reference Books

Advanced Engineering Mathematics-C. Ray Wylie, Louis C. Barrett
Introductory Methods of Numerical Analysis-S. S. Sastry
Higher Engineering Mathematics -B.V. Ramana
A Textbook of Engineering Mathematics-N. P. Bali and Manish Goyal