JNTUK R19 B.Tech CSE 1-2 Mathematics – III Material/ Notes PDF Download

JNTUK R19 B.Tech CSE 1-2 Mathematics – III Material/ Notes PDF Download: Begin your journey with JNTUK R20 B.Tech CSE 1-2 Mathematics – III Material, designed to introduce you to vital techniques in partial differential equations. Our carefully crafted resources provide learners with fundamental concepts and techniques suitable for an intermediate level, setting the stage for exploring real-world applications. Access our PDF downloads to dive into the material seamlessly and enhance your comprehension. With thorough preparation using our notes and materials, you can excel in your B.Tech CSE studies with confidence.

JNTUK R19 B.Tech CSE 1-2 Mathematics – III Material – Units

Unit 1 Syllabus PDF Download | JNTUK R19 B.Tech CSE 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).

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Unit 2 Syllabus PDF Download | JNTUK R19 B.Tech CSE 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 R19 B.Tech CSE 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 R19 B.Tech CSE 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 R19 B.Tech CSE 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 R19 B.Tech Mathematics – III Material – Outcomes

• Understanding Gradient, Curl, and Divergence: Gain insight into how things change across different points in space with the concept of Gradient. Explore Curl and Divergence to understand rotational and spreading effects within a field, providing valuable knowledge for analyzing fluid flow, electromagnetism, and more.
• Exploring Work, Circulation, and Flux: Delve into the calculation of effort against a field with Work, while Circulation helps in analyzing swirling patterns within the field. Understand Flux to comprehend the flow of a field through a surface, which is crucial for various applications such as fluid dynamics and heat transfer.
• Utilizing Laplace Transform: Learn to efficiently solve problems involving changing quantities using Laplace Transform. This powerful mathematical tool simplifies differential equations, making it easier to analyze dynamic systems in engineering, physics, and other fields.
• Mastering Fourier Series and Fourier Transform: Develop proficiency in Fourier Series and Fourier Transform, essential for decomposing repeating signals into simpler components and transforming between different types of signals. These techniques find widespread application in signal processing, communications, and image analysis.
• Delving into Partial Differential Equations (PDEs): Explore Partial Differential Equations to solve equations describing changes in multiple dimensions, such as predicting temperature changes over time or modeling fluid flow. Understanding PDEs is crucial in various scientific and engineering disciplines for analyzing complex systems and phenomena.

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