As you want here I am giving bellow VTU (Visvesvaraya Technological University ) B.Tech Aeronautical Engineering 3rd sem program syllabus on your demand :
B. E. AERONATICAL ENGINEERING
Choice Based Credit System (CBCS) and Outcome Based Education (OBE)
SEMESTER - III
TRANSFORM CALCULUS, FOURIER SERIES AND NUMERICAL TECHNIQUES
(Common to all Programmes)
Course Code 18MAT31 CIE Marks 40
Teaching Hours/Week (L: T:P) (2:2:0) SEE Marks 60
Credits 03 Exam Hours 03
Course Learning Objectives:
- To have an insight into Fourier series, Fourier transforms, Laplace transforms, Difference equations
and Z-transforms.
- To develop the proficiency in variational calculus and solving ODEs arising in engineering
applications, using numerical methods.
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, Dirichlets condition. Fourier series of periodic functions period 2π and
arbitrary period. Half range Fourier series. Practical harmonic analysis.
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.
Module-4
Numerical Solutions of Ordinary Differential Equations(ODEs):
Numerical solution of ODEs of first order and first degree- Taylors series method, Modified Eulers method.
Runge -Kutta method of fourth order, Milnes and Adam-Bash forth predictor and corrector method (No
derivations of formulae)-Problems.
Module-5
Numerical Solution of Second Order ODEs: Runge-Kutta method and Milnes predictor and corrector
method. (No derivations of formulae).
Calculus of Variations: Variation of function and functional, variational problems, Eulers equation,
Geodesics, hanging chain, problems.
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 in
system 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
etermine the externals of functionals using calculus of variations and solve problems
arising in dynamics of rigid bodies and vibrational analysis
