JNTUK R20 B Tech CSE 2-1 Mathematics–III Material/ Notes PDF Download

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JNTUK R20 B Tech CSE 2-1 Mathematics–III Material/ Notes PDF Download: Discover the JNTUK R20 B Tech CSE 2-1 Mathematics–III Material for a clear understanding of partial differential equations (PDEs). This resource is designed for JNTUK R20 B Tech students, offering insights into fundamental concepts and techniques at a high school level. The goal is to help learners transition smoothly from basic knowledge to more advanced applications, preparing them for real-world scenarios.

Access the JNTUK R20 B Tech CSE 2-1 Mathematics–III Notes to enhance your mathematical understanding. You can easily download the JNTUK R20 B Tech CSE M3 Material in PDF format for convenient learning. Dive into the world of mathematics and equip yourself with the skills needed to solve practical problems.

JNTUK R20 B Tech CSE 2-1 Mathematics–III Material – Units

Unit 1 Syllabus PDF Download | JNTUK R20 B Tech Mathematics–III Material

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 Syllabus PDF Download | JNTUK R20 B Tech Mathematics–III Material

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 Syllabus PDF Download | JNTUK R20 B Tech Mathematics–III Material

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 transform – Properties – inverse transforms – Finite Fourier transforms.

Unit 4 Syllabus PDF Download | JNTUK R20 B Tech Mathematics–III Material

PDE of the 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 Syllabus PDF Download | JNTUK R20 B Tech Mathematics–III Material

Second order PDE and Applications: Second order PDE: Solutions of linear partial differential equations with constant coefficients – RHS term of the type ax by m n e, sin( axby), cos(ax by), x y.

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

JNTUK R20 B Tech Mathematics–III Material – Outcomes

• Gradient: Understand how things change at different points in space.
• Curl and Divergence: Grasp rotation and spreading effects in a field.
• Work, Circulation, and Flux: Calculate effort against a field, swirling patterns, and field flow through a surface.
• Laplace Transform: Use it to solve problems involving changing quantities.
• Fourier Series: Break down repeating signals into simpler components.
• Fourier Transform: Transform between different types of signals using integral formulas.
• Partial Differential Equations (PDEs): Solve equations describing changes in multiple dimensions, like predicting temperature changes over time.

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