SEM II (2024-2025)

Subject Code: EME 1102

Applied Mathematics

Teaching Scheme:

TH:3Hrs./week

TUT:1Hr./week

Credits

4

Prerequisite

Differentiation and Integration, Differential Equation, Integral calculus, Basic Concepts of Statistics & Probability, Vector Algebra

L-T-P-C

3-1-0-4

Course Objectives:

1.      To develop mathematical and computational skills.

2.      To enhance analytical and logical thinking power of students and deploy these skills effectively in their disciplines.

3.      To equip the students with concepts and techniques in Integral Transforms.

4.      To enable the students with concepts and techniques in Linear differential equations

Course Outcomes

On completion of the course, learner will be able to

CO1: Solve higher order linear differential equation using appropriate techniques and its applications to model and analyse mass spring systems.

CO2: Apply Laplace transform techniques to solve Linear Differential Equations.

CO3: Express and apply continuous and discrete periodic functions into the Fourier series.

CO4: Apply Statistical methods like correlation, regression in describing the statistical data Numerically and solve problems in Probability theory using Distribution techniques.

CO5: Perform Vector differentiation and analyse the vector fields.

CO-PO Mapping:

Course Contents

UNIT-I Higher order Linear Differential Equations                 07 Hours

LDE of nth order with constant coefficients, Complementary Function ,Particular Integral, General Solution of LDE by General Method, General Solution of LDE by Short-Cut Methods, General Solution of LDE by Variation Parameter Method, Applications of LDE-Modelling of Mass-spring systems, Free &Forced damped and undamped systems.

UNIT-II  Laplace Transform                                                        07 Hours

Laplace Transform, Laplace Transform of standard functions, Properties of Laplace Transform, Inverse LT and its Properties, Linear differential equation with constant coefficients using Laplace Transform, Applications of LDE

UNIT-III Fourier Series                                                                 08 Hours

Dirichlet’s conditions, Fourier series (0, 2π),  (0, 2l), Fourier series (-π, π),  (-l, l), Half range Fourier Sine series, Half range Fourier Cosine series, Applications of Fourier series – Harmonic Analysis, Modelling of Vibrating String

UNIT-IV Statistics & Probability                                                   07 Hours                                                                         

Mean, Mode, Median, Standard Deviation and Variance, Karl Pearson’s Coefficient of Correlation, Lines of regression, Random variables, Probability Bay’s Theorem, Discrete Probability distribution, Continuous probability distribution, Binomial Distribution, Poisson Distribution, Normal Distribution, Applications

UNIT-V Vector Differential Calculus                                              07 Hours

Vector differentiation, Vector differential operator, Gradient, Divergence and Curl, Directional derivative, Solenoidal, Irrotational and Conservative fields, Scalar potential, Vector Identities, Applications Vector differentiation

Books & Other Resources

Text Books

1. Higher Engineering Mathematics by B. V. Ramana (Tata McGraw Hill)

2. Higher Engineering Mathematics by B. S. Grewal (Khanna Publication, Delhi)

Reference Books

  1. Advanced Engineering Mathematics by Erwin Kreyszig (Wiley Eastern Ltd.)

  2. Advanced Engineering Mathematics by M. D. Greenberg (Pearson Education)

  3. Advanced Engineering Mathematics by Peter V. O’Neil (Thomson Learning)

  4. Thomas’ Calculus by George B. Thomas, (Addison-Wesley, Pearson)

  5. Applied Mathematics (Vol. I &Vol.II) by P.N.Wartikar and J.N. Wartikar Vidyarthi Griha   

      Prakashan, Pune.

  6. Linear Algebra –An Modern Introduction, David Poole (Trent University)