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

JNTUK R20 B Tech Civil 2-1 Mathematics - III Material
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JNTUK R20 B.Tech Civil 2-1 Mathematics – III Material/ Notes PDF Download: Discovering JNTUK R20 B.Tech 2-1 Mathematics – III Material is now easier than ever! Whether you’re a Civil student or seeking comprehensive notes for Mathematics – III, we’ve got you covered. Dive into our meticulously curated Mathematics – III study material, specially designed to introduce you to the intricacies of partial differential equations.

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

No. of Units Name of the Unit
Unit – 1 Vector calculus
Unit – 2 Laplace Transforms
Unit – 3 Fourier series and Fourier Transforms
Unit – 4 PDE of the First Order
Unit – 5 Second-order PDE and Applications

Unit 1 Syllabus PDF Download | JNTUK R20 B.Tech 2-1 Mathematics – III Material

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) and problems on above theorems.

JNTUK R20 B.Tech Mathematics – III Material – PDF Download
To Download JNTUK R20 B.Tech Civil Mathematics – III Material Unit – 1 PDF Download PDF

Unit 2 Syllabus PDF Download | JNTUK R20 B.Tech 2-1 Mathematics – III Material

Laplace transforms Definition and Laplace transform of some certain functions– Shifting theorems – Transforms of derivatives and integrals – Unit step function –Dirac’s delta functionPeriodic function – Inverse Laplace transforms– Convolution theorem (without proof). Applications: Solving ordinary differential equations (initial value problems) using Laplace transforms.

JNTUK R20 B.Tech Mathematics – III Material – PDF Download
To Download JNTUK R20 B.Tech Civil Mathematics – III Material Unit – 2 PDF Download PDF

Unit 3 Syllabus PDF Download | JNTUK R20 B.Tech 2-1 Mathematics – III Material

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 (article-22.5 in text book-1)– inverse transforms – Convolution theorem (without proof) – Finite Fourier transforms.

JNTUK R20 B.Tech Mathematics – III Material – PDF Download
To Download JNTUK R20 B.Tech Civil Mathematics – III Material Unit – 3 PDF Download PDF

Unit 4 Syllabus PDF Download | JNTUK R20 B.Tech 2-1 Mathematics – III Material

PDE of 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.

JNTUK R20 B.Tech Mathematics – III Material – PDF Download
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Unit 5 Syllabus PDF Download | JNTUK R20 B.Tech 2-1 Mathematics – III Material

Second order PDE: Solutions of linear partial differential equations with constant coefficients – Nonhomogeneous term of the type ax by m n e, sin( ax  by), 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 – PDF Download
To Download JNTUK R20 B.Tech Civil Mathematics – III Material Unit – 5 PDF Download PDF

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JNTUK R20 B.Tech 2-1 Mathematics – III Notes – Outcomes

  • Introduce techniques in partial differential equations, providing a solid foundation for further exploration.
  • Equip learners with fundamental concepts and techniques, bridging the gap between plus two level and advanced applications.
  • Understand the physical significance of operators like gradient, curl, and divergence.
  • Calculate work done against a field, circulation, and flux using vector calculus methods.
  • Apply Laplace transform techniques to solve differential equations efficiently.
  • Compute Fourier series for periodic signals.
  • Apply integral expressions for forward and inverse Fourier transform to analyze various non-periodic waveforms.
  • Identify solution methods for partial differential equations modeling physical processes.