Download “* Engineering Mathematics -2 Notes*” just in one click made by fully experienced teachers. The notes can be downloaded without any Login or Signup. These notes are made from the best books of Engineering Mathematics and are specially designed in pdf format for easy download and contain Lecture notes in simple and easy languages with examples of each topic and with the full explanation. These notes are mainly for the students of B.Tech 2nd year.

**On completion of this course, students are able to: **

• Use ordinary differential equations to model engineering phenomena such as electrical circuits, forced oscillation of mass-spring and elementary heat transfer.

• Use partial differential equations to model problems in fluid mechanics, electromagnetic theory, and heat transfer.

• Evaluate double and triple integrals to find the area, volume, mass and moment of inertia of plane and solid region.

• Use curl and divergence of a vector function in three dimensions, as well as apply the Green’s Theorem, Divergence Theorem and Stokes’ theorem in various applications like electricity, magnetism and fluid flow.

• Use Laplace transforms to determine general or complete solutions to linear ODE.

**The notes covers following concepts:**

** Unit-1:**

Differential equations-1:

Linear differential equations with constant coefficients: Solutions of second and higher order differential equations – inverse differential operator method, a method of undetermined coefficients and method of variation of parameters.

**Unit-2:**

Differential equations-2: Solutions of simultaneous differential equations of first order.

Linear differential equations with variable coefficients: Solution of Cauchy’s and Legendre’s linear differential equations.

Nonlinear differential equations – Equations solvable for p, equations solvable for y, equations solvable for x, general and singular solutions, Clairauit’s equations and equations reducible to Clairauit’s form.

**Unit-3:**

Partial Differential equations: Formulation of PDE by the elimination of arbitrary constants/functions, a solution of non-homogeneous PDE by direct integration, a solution of homogeneous PDE involving derivative with respect to one independent variable only. Derivation of one-dimensional heat and wave equations and their solutions by the variable separable method.

Double and triple integrals: Evaluation of double integrals. Evaluation by changing the order of integration and changing into polar coordinates. Evaluation of triple integrals.

**Unit-4:**

Integral Calculus: Application of double and triple integrals to find area and volume. Beta and Gamma functions, definitions, Relation between beta and gamma functions and simple problems.

Curvilinear coordinates Orthogonal curvilinear coordinates – Definition, unit vectors and scale factors. Expressions for gradient, divergence, and curl. Cylindrical and spherical coordinate systems.

**Unit-5:**

Laplace Transform:

Definition and Laplace transform of elementary functions. function – problems Inverse Laplace Transform: Inverse Laplace Transform – problems, Convolution theorem and problems, the solution of linear differential equations using Laplace Transforms.

Download Engineering Mathematics -2 Notes

Feel free to comment below regarding notes.

If you want some more notes on any of the topics please mail to us or comment below. We will provide you as soon as possible and if you want yours notes to be published on our site then feel free to email your content to contribute@edutechlearners.com ( The contents will be published by your Name ).