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

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JNTUK R20 B.Tech ECE 2-1 Mathematics – III Material/ Notes PDF Download:  Embark on your journey with JNTUK R20 B.Tech ECE 2-1 Mathematics – III Material, meticulously curated to introduce you to essential techniques in partial differential equations. Our comprehensive resources aim to equip learners with fundamental concepts and techniques at the plus-two level, paving the way for advanced exploration of real-world applications. Access our PDF downloads to delve into the material effortlessly and elevate your understanding. Prepare thoroughly with our notes and materials to excel in your B.Tech ECE studies.

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

Unit 1 Syllabus PDF Download | JNTUK R20 B.Tech ECE M3 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 ECE M3 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 ECE M3 Material

Fourier series and Fourier Transforms

Fourier Series: Introduction – Periodic functions – Fourier series of periodic functions – 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 ECE M3 Material

PDE of the first order: Formation of partial differential equations by eliminating arbitrary constants and arbitrary functions – Solutions of first-order linear (Lagrange) and nonlinear (standard types) equations.

Unit 5 Syllabus PDF Download | JNTUK R20 B.Tech ECE M3 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

• Understand the concept of Gradient, which explains how things change across different spatial points.
• Learn about Curl and Divergence, helping to comprehend rotational and spreading effects within a field.
• Explore Work, Circulation, and Flux, enabling the calculation of effort against a field, analyzing swirling patterns, and understanding the flow of a field through a surface.
• Utilize Laplace Transform to solve problems involving changing quantities efficiently.
• Master Fourier Series and Fourier Transform, are essential for breaking down repeating signals into simpler components and transforming between different types of signals using integral formulas.
• Additionally, delve into Partial Differential Equations (PDEs) to solve equations describing changes in multiple dimensions, such as predicting temperature changes over time.

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