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

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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

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.

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.

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.

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.

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.

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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.