# JNTUK R20 2-1 Mathematics – III Material | Full Notes PDF Download

### JNTUK R20 2-1 Mathematics – III Notes and Materials PDF Download

Students studying JNTUK R20CSE, ECE, and Civil Branches, can download R20 unit-wise. 1 Mathematics III (Vector Calculus, Transforms and PDE-M3) Notes and Material PDFs below.

Course Goals:

• To become familiar with the methods used for partial differential equations.
• To provide the students with basic knowledge and techniques plus two levels to guide them to higher proficiency through various real-world applications.

UNIT-1

Vector calculus:

Vector Differentiation: Gradient – Directional derivative – Divergence – Curl – Scalar Potential. Vector Integration Line Integral Work completed – Area Volume and surface integrals Theorems of Vector Integral: Greens, Stokes and Gauss Divergence theorems (without proof).

UNIT-2

Laplace Transformations

Laplace transforms essential functions – Shifting Theorems Transforms of derivatives and integrals Unit step functions – Dirac’s delta function – inverse Laplace transforms The Convolution Theorem (without evidence).

Applications solving ordinary differential equations (initial value problems) with Laplace transforms.

UNIT-3

Fourier Series and Fourier Transformations

Fourier Series Introduction – Introduction to Periodic functions Fourier Series that have periodic functions – Dirichlet’s Conditions Odd and even functions Variation of interval Cosine and sine series in half-range.

Fourier Transformations Fourier integrals, theorem (without proof) (without evidence) Fourier sine integral and cosine. Sine and cosine transform – Properties – inverted transforms – finite Fourier transforms.

UNIT-4

PDE of the first order:

We are formulating partial differential equations by eliminating arbitrary constants and arbitrary functions Solutions for first, second order linear (Lagrange) equations and nonlinear (standard kinds) equations.

UNIT-5:

Second Order PDE, Applications 2nd order PDE: solutions to PDEs that are linear using constant coefficients RHS terms of the form axe by M N E, Sin(Bixby), cos(axe by) (XY).

Application for PDE: Method of Separation of Variables – Solutions of one-dimensional waves, heat and 2-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 using MATLAB 3rd Edition, CRC Press, 2010.
3. Peter O Neil Advanced Engineering Mathematics, 7th edition, Cengage, 2011.
4. Samantha Pal S C Bhunia, Engineering Mathematics, Oxford University Press 2015.

Course Objectives:

At the end of the course, students will be capable of

• Determine the physical meanings of different operators, such as curvature, gradient and divergence (L5)
• Estimate the work performed against a field, circulation, and flux by using the vector calculus (L5)
• Apply the Laplace transform to solve problems with differential equations (L3)
• Find or calculate or compute the Fourier Series of Periodic Signals (L3)
• Know and be able to use integral equations to apply forwards and reverse Fourier transform to a wide range in non-periodic waves (L3)
• Find solutions for partial differential equations which model the physical process (L3)

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