Engineering Mathematics III
207002: Engineering Mathematics III (Mechanical + SW / Production + SW /
Industrial /Automobile Engineering)
Teaching Scheme: Credit Scheme: Examination Scheme:
Lectures: 4 Hrs./Week Theory: 04 Ins-Sem: 50 Marks
Tutorials: 1 Hr./Week Tutorial: 01 End-Sem: 50 Marks
Term work: 25 Marks
Unit I: Linear Differential Equations (LDE) and Applications
LDE of nth order with constant coefficients, Method of variation of parameters, Cauchy’s & Legendre’s DE, Simultaneous & Symmetric simultaneous DE. Modeling of mass-spring systems, free and forced damped and undamped systems.
Unit II: Transforms
Laplace Transform (LT): LT of standard functions, properties and theorems, Inverse LT, Application of LT to solve LDE. Fourier Transform (FT): Fourier integral theorem, Fourier transform, Fourier Sine & Cosine transform, Inverse Fourier Transforms.
Unit III: Statistics and Probability
Measure of central tendency, Standard deviation, Coefficient of variation, Moments, Skewness and Kurtosis, Correlation and Regression, Probability, Probability distributions: Binomial, Poisson and Normal distributions, Population and sample, Sampling distributions, t-distribution, Chi-square distribution.
Unit IV: Vector Differential Calculus
Physical interpretation of Vector differentiation, Vector differential operator, Gradient, Divergence and Curl, Directional derivative, Solenoidal, Irrotational and Conservative fields, Scalar potential, Vector identities.
Unit V: Vector Integral Calculus and Applications
Line, Surface and Volume integrals, Work-done, Green’s Lemma, Gauss’s Divergence theorem, Stoke’s theorem. Applications to problems in Fluid Mechanics, Continuity equations, Streamlines, Equations of motion, Bernoulli’s equation.
Unit VI: Applications of Partial Differential Equations (PDE)
Basic concepts, modeling of Vibrating String, Wave equation, one and two dimensional Heat flow equations, method of separation of variables, use of Fourier series. Solution of Heat equation by Fourier Transforms, Two-dimensional wave equation.
- Lectures 0
- Quizzes 0
- Skill level All levels
- Language English
- Students 0
- Assessments Yes
Engg. Maths 3 Overview, Engg. Maths 3 is application based maths, Lengthy and comprise of derived formulas, M2 is different for different branches and is applicated based, Tricks and tips are crucial to remember methods and procedures, Understanding concepts and then rigorous practice is essential, Crucial for PG level exams - GATE, MTech, UPSC, IES, Gov. Jobs, For Diploma students, Difficulty level remain high, Notations and Variables tend to create a confusion