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JNTUK R19 2-1 VCFT Material/Notes PDF Download
Students those who are studying JNTUK R19 Mechanical Branch, Can Download Unit wise R19 2-1 Vector Calculus & Fourier Transforms Material/Notes PDFs below.
JNTUK R19 2-1 VCFT Material/Notes PDF Download
Course Objectives : 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).
UNIT-2
Laplace Transforms: Laplace transforms of standard functions — Shifting theorems — Transforms of derivatives and integrals — Unit step function — Dirac’s delta 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 — inverse transforms — 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: (10 hrs) Second order PDE: Solutions of linear partial differential equations with constant coefficients — RHS term of the type eax + by ,sin(ax + by), cos(ax + by), xm y n 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, 43rd Edition, Khanna Publishers.
2. B. V. Ramana, Higher Engineering Mathematics, 2007 Edition, Tata Mc. Graw Hill Education.
Reference Books:
1. Erwin Kreyszig, Advanced Engineering Mathematics, 10th Edition, Wiley-India.
2. Dean. G. Duffy, Advanced Engineering Mathematics with MATLAB, 3rd Edition, CRC Press.
3. Peter O’ Neil, Advanced Engineering Mathematics, Cengage.
4. Srimantha Pal, S C Bhunia, Engineering Mathematics, Oxford University Press.
