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

JNTUK R20 B.Tech Mechanical 2-1 Mathematics–III Material/ Notes PDF Download: For JNTUK R20 B.Tech Mechanical 2-1 Mathematics–III Material, students can find everything they need to understand topics like gradient, curl, divergence, and more. This material helps students estimate things like work done in fields and how things circulate and flow. They can also learn how to use Laplace transform to solve problems with changing quantities, and figure out the patterns of repeating signals with Fourier series. It also covers integral expressions for different waveforms and ways to solve complex equations. It’s a helpful resource for B.Tech Mechanical students to study and understand Mathematics–III.

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

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

Vector calculus

Vector Differentiation: Gradient — Directional derivative — Divergence — Curl — Scalar Potential.

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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 Mechanical 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 Mechanical M3 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 Mechanical M3 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 Mechanical M3 Material

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 dimensional Wave, Heat and two-dimensional Laplace equation.

JNTUK R20 B.Tech Mathematics–III Material – Outcomes

• Understand how things change in different areas. It helps to see the rate of change of a function at any point in space.
• Grasp rotation and spreading effects in a field. Curl shows how a field swirls around, while divergence indicates how much the field spreads out.
• Calculate the effort against a field, swirling patterns, and how the field flows through a surface. It’s like understanding how much energy is needed to move through different parts of a field.
• Use it to solve problems involving changing quantities. It’s a tool to convert complex problems into simpler ones, making it easier to find solutions.
• Break down repeating signals into simpler components and transform between different types of signals using integral formulas. They help in understanding patterns and changes in signals over time.
• Solve equations describing changes in multiple dimensions, like predicting temperature changes over time. They are used to understand how things change concerning multiple variables, such as space and time.

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