Mathmatics - M2

 M2 

Mathematics : M 2

Course Objectives:

The course should enable the students to

·     Solve the Methods of differential equations of first and higher order.

·     Learn the basic properties of vector valued functions and their applications to line Surface and volume integrals.

·      Know the concept of Laplace transforms and apply to solve the ordinary differential equations

Course Outcomes:

After learning the contents of this paper the student must be able to

·         Identify whether the given differential equation of first order is exact or not.

·         Solve higher differential equation and apply the concept of differential equation to real world problems and also evaluate the line, surface and volume integrals and converting them from one to another.

·         Analyze the engineering problems using the concept of Laplace transforms.

·         Gain knowledge to tackle engineering problems using the concepts of Inverse Laplace transforms.  

• Important Formulas : Download 
• Basic Formulas : Download 
• Trigonometric Formula:- Download 

M2 Study Material :

• M2-Important Question Bank - Download

UNIT – 1:  First Order O.D.E - Download

Introduction to Ordinary Differential equations- Exact - linear and Bernoulli’s equations - Applications to Newton’s  law of cooling- law of natural growth and decay-Orthogonal trajectories.  

UNIT –2: Ordinary Differential Equations of higher order-Download 

Homogeneous and Non homogeneous linear differential equations of second and higher order with constant coefficients with RHS terms of type  

UNIT –3:  VectorCalculus-Download

Download 2.V

Introduction-Vector differentiations-Vector differential operator- Gradient – Divergence-Curl and their properties - Vector integration - Line integral-Potential function – Area - Surface and volume integrals- Vector integrals theorems: Green’s theorem - Stoke’s and Gauss’s Divergence theorem (without proof) – problems.

M2 Unit 3 to 5 Important Questions and Answers-Download

UNIT– 4 Laplace Transform-Download

Laplace transform of standard functions– First shifting Theorem - Second shifting theorem- Transforms of derivatives and integrals – Unit step function –Dirac’s delta function- Laplace transform of periodic functions.

UNIT–5 Inverse Laplace Transform-Download

Download 2.I.L.T

Convolution theorem- Differentiation and integration of transform – Inverse laplace transform –Application of Laplace transforms to ordinary differential equations of first and second order.

Inverse LT-Important Question and answers-(CLICK)

Text Books:

1.      Higher Engineering Mathematics, B.S.Grewal, Khanna publishers.

2.      Engineering Mathematics Volume-I &II by T.K.V. Iyengar, S.Chand publication.

Reference Books:

1. Ramana B.V., Higher Engineering Mathematics, Tata McGraw Hill New Delhi, 11^thReprint, 2010.
2. D. Poole, Linear Algebra: A Modern Introduction, 2nd Edition, Brooks/Cole, 2005.
3. N.P. Bali and Manish Goyal, A text book of Engineering Mathematics, Laxmi Publications, Reprint, 2008.
4. Engineering Mathematics, volume-I&II, E. Rukmangadachari& E.Keshava Reddy Pearson Publishers.