Students those who are studying JNTUK R20 EEE Branch, Can Download Unit wise R20 1-2 Mathematics – III (Vector Calculus, Transforms and PDE-M3) Material/Notes PDFs below.

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.

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)

UNIT-1

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.

UNIT-2

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 (without proof). Applications: Solving ordinary differential equations (initial value problems) using Laplace transforms.

UNIT-3

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.

UNIT-4

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.

UNIT-5:

Second order PDE and Applications:

Second order PDE: Solutions of linear partial differential equations with constant coefficients –Nonhomogeneous term of the type ax by m n e ,sin( ax  by), cos(ax  by), x y . Applications of PDE: Method of separation of Variables– Solution of One dimensional Wave, Heat and two-dimensional Laplace equation

TEXT BOOKS:

1. B. S. Grewal, Higher Engineering Mathematics, 44th Edition, Khanna Publishers, 2018.
2. B. V. Ramana,Higher Engineering Mathematics, 2007 Edition, Tata McGraw Hill Education.

REFERENCE BOOKS:

1. Erwin Kreyszig, Advanced Engineering Mathematics, 10th Edition, Wiley-India. 2015.
2. Dean. G. Duffy, Advanced Engineering Mathematics with MATLAB, 3rd Edition, CRC Press, 2010.
3. Peter O’ Neil, Advanced Engineering Mathematics, 7 th edition, Cengage, 2011..
4. Srimantha Pal, S C Bhunia, Engineering Mathematics, Oxford University Press, 2015.