**JNTUK R20 2-1 Mathematics – III Notes and Materials PDF Download**

Students studying JNTUK R20CSE, ECE, and Civil Branches, can download R20 unit-wise. 1 Mathematics III (Vector Calculus, Transforms and PDE-M3) Notes and Material PDFs below.

**Course Goals:**

- To become familiar with the methods used for partial differential equations.
- To provide the students with basic knowledge and techniques plus two levels to guide them to higher proficiency through various real-world applications.

**UNIT-1**

**Vector calculus:**

**Vector Differentiation**: Gradient – Directional derivative – Divergence – Curl – Scalar Potential. Vector Integration Line Integral Work completed – Area Volume and surface integrals Theorems of Vector Integral: Greens, Stokes and Gauss Divergence theorems (without proof).

**Download UNIT-1 Material PDF** | **Reference-2**

**UNIT-2**

**Laplace Transformations**

Laplace transforms essential functions – Shifting Theorems Transforms of derivatives and integrals Unit step functions – Dirac’s delta function – inverse Laplace transforms The Convolution Theorem (without evidence).

**Applications** solving ordinary differential equations (initial value problems) with Laplace transforms.

**Unit-2 Materials PDF Download** | **Reference 2**

**UNIT-3**

**Fourier Series and Fourier Transformations**

Fourier Series Introduction – Introduction to Periodic functions Fourier Series that have periodic functions – Dirichlet’s Conditions Odd and even functions Variation of interval Cosine and sine series in half-range.

**Fourier Transformations** Fourier integrals, theorem (without proof) (without evidence) Fourier sine integral and cosine. Sine and cosine transform – Properties – inverted transforms – finite Fourier transforms.

**Unit-3 Materials PDF Download**| **Reference 2**

**UNIT-4**

**PDE of the first order:**

We are formulating partial differential equations by eliminating arbitrary constants and arbitrary functions Solutions for first, second order linear (Lagrange) equations and nonlinear (standard kinds) equations.

**Unit-4 PDF Material Download** – **Reference 2**

**UNIT-5:**

**Second Order PDE, Applications** 2nd order PDE: solutions to PDEs that are linear using constant coefficients RHS terms of the form axe by M N E, Sin(Bixby), cos(axe by) (XY).

**Application for PDE:** Method of Separation of Variables – Solutions of one-dimensional waves, heat and 2-dimensional Laplace equation.

**Unit-5 Materials PDF Download** | **Reference 2**

**Text Books:**

- B. S. Grewal, Higher Engineering Mathematics, 44th Edition, Khanna Publishers, 2018.
- B. V. Ramana, Higher Engineering Mathematics 2007, Edition Tata McGraw Hill Education.

**REFERENCE Books:**

- Erwin Kreyszig, Advanced Engineering Mathematics, 10th Edition, Wiley-India. 2015.
- Dean. G. Duffy, Advanced Engineering Mathematics using MATLAB 3rd Edition, CRC Press, 2010.
- Peter O Neil Advanced Engineering Mathematics, 7th edition, Cengage, 2011.
- Samantha Pal S C Bhunia, Engineering Mathematics, Oxford University Press 2015.

**Course Objectives:**

At the end of the course, students will be capable of

- Determine the physical meanings of different operators, such as curvature, gradient and divergence (L5)
- Estimate the work performed against a field, circulation, and flux by using the vector calculus (L5)
- Apply the Laplace transform to solve problems with differential equations (L3)
- Find or calculate or compute the Fourier Series of Periodic Signals (L3)
- Know and be able to use integral equations to apply forwards and reverse Fourier transform to a wide range in non-periodic waves (L3)
- Find solutions for partial differential equations which model the physical process (L3)