JNTUK B.TECH R20 2-1 Syllabus For Vector calculus fourier transforms and pde PDF 2022

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Vector calculus fourier transforms and pde Unit One

Vector calculus

Vector Differentiation: Gradient– Directional derivative – Divergence– Curl– Scalar Potential.

Vector Integration: Line integral – Work done – Area– Surface and volume integrals – Vector integral theorems: Greens, Stokes and Gauss Divergence theorems (without proof) and problems on above theorems.

Vector calculus fourier transforms and pde Unit Two

Laplace Transforms

Laplace transforms – Definition and Laplace transforms of some certain functions– Shifting theorems – Transforms of derivatives and integrals – Unit step function –Dirac’s delta functionPeriodic function – Inverse Laplace transforms– Convolution theorem (with out proof).

Applications: Solving ordinary differential equations (initial value problems) using Laplace transforms.

Vector calculus fourier transforms and pde Unit Three

Fourier series and Fourier Transforms

Fourier Series: Introduction– Periodic functions – Fourier series of periodic function –Dirichlet’s conditions – Even and odd functions –Change of interval– Half-range sine and cosine series.

Fourier Transforms: Fourier integral theorem (without proof) – Fourier sine and cosine integrals – Sine and cosine transforms – Properties (article-22.5 in text book-1)– inverse transforms – Convolution theorem (without proof) – Finite Fourier transforms.

Vector calculus fourier transforms and pde Unit Four

PDE of first order

Formation of partial differential equations by elimination of arbitrary constants and arbitrary functions – Solutions of first order linear (Lagrange) equation and nonlinear (standard types) equations.

Vector calculus fourier transforms and pde Unit Five

Second order PDE and Applications

Second order PDE: Solutions of linear partial differential equations with constant coefficients –Non- homogeneous term of the type eaxby ,sin( ax  by), cos(ax  by), xm yn .

Applications of PDE: Method of separation of Variables– Solution of One dimensional Wave, Heat and two-dimensional Laplace equation.

Vector calculus fourier transforms and pde Course Objectives

To familiarize the techniques in partial differential equations

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.

Vector calculus fourier transforms and pde Course Outcomes

At the end of the course, the student will be able to

interpret the physical meaning of different operators such as gradient, curl and divergence (L5)

estimate the work done against a field, circulation and flux using vector calculus (L5)

apply the Laplace transform for solving differential equations (L3)

find or compute the Fourier series of periodic signals (L3)

know and be able to apply integral expressions for the forwards and inverse Fourier transform to a range of non-periodic waveforms (L3)

identify solution methods for partial differential equations that model physical processes (L3)

Vector calculus fourier transforms and pde Text Books

B. S. Grewal, Higher Engineering Mathematics, 44th Edition, Khanna Publishers.

B. V. Ramana,Higher Engineering Mathematics, 2007 Edition, Tata Mc. Graw Hill Education.

Vector calculus fourier transforms and pde Reference Books

Erwin Kreyszig, Advanced Engineering Mathematics, 10th Edition, Wiley-India.

Dean. G. Duffy, Advanced Engineering Mathematics with MATLAB, 3rd Edition, CRC Press.

Peter O’ Neil, Advanced Engineering Mathematics, Cengage.

Srimantha Pal, S C Bhunia, Engineering Mathematics, Oxford University Press.

Scoring Marks in Vector calculus fourier transforms and pde

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