Page 26 - Microsoft Word - B.Tech. Course Structure (R20) WITH 163 CREDITS

JNTUA College of Engineering (Autonomous), Ananthapuramu
Department of Computer Science & Engineering
DIFFERENTIAL EQUATIONS AND TRANSFORMATIONS
Course Code: Semester – II(R20) L T P C: 3 0 0 3
Course Objectives:

1) To enlighten the learners in the concept of differential equations and multivariable calculus.
2) To furnish the learners with basic concepts and techniques at plus two level to lead them into
advanced level by handling various real-world applications.

Course Outcomes:

UNIT – I: Linear differential equations of higher order (Constant Coefficients)
Definitions, homogenous and non-homogenous, complimentary function, general solution, particular
integral, Wronskian, method of variation of parameters. Simultaneous linear equations, Applications to
L-C-R Circuit problems and Mass spring system.

UNIT – II: Partial Differential Equations
Introduction and formation of Partial Differential Equations by elimination of arbitrary constants and
arbitrary functions, solutions of first order equations using Lagrange’s methodand non-linear PDEs
(Standard Forms)

UNIT – III: Applications of Partial Differential Equations
Classification of PDE, method of separation of variables for second order equations. Applications of
Partial Differential Equations: One dimensional Wave equation, One dimensional Heat equation.

UNIT – IV: Laplace Transforms
Definition-Laplace transform of standard functions-existence of Laplace Transform – Inverse
transform – First shifting Theorem, Transforms of derivatives and integrals – Unit step function –
Second shifting theorem – Dirac’s delta function – Convolution theorem – Laplace transform of
Periodic function. Differentiation and integration of transform – solving Initial value problems to
ordinary differential equations with constant coefficients using Laplace transforms.

Fourier Series: Determination of Fourier coefficients (Euler’s) – Dirichlet conditions for the existence
of Fourier series – functions having discontinuity-Fourier series of Even and odd functions – Fourier
series in an arbitrary interval – Half-range Fourier sine and cosine expansions- typical wave forms -
Parseval’s formula- Complex form of Fourier series.

UNIT – V: Fourier transforms & Z Transforms
Fourier integral theorem (without proof) – Fourier sine and cosine integrals-complex form of Fourier
integral. Fourier transform – Fourier sine and cosine transforms – Properties – Inverse transforms –
convolution theorem.

Z-transform – Inverse z-transform – Properties – Damping rule – Shifting rule – Initial and final
value theorems. Convolution theorem – Solution of difference equations by z-transforms

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