All Materials regarding to B.tech R-20 in Mechanical Engineering 1st Year 1st Semester with unit wise for Every Subjects are available.
| Mechanical 1-2 Mathematics 2 | ||
|---|---|---|
| S.No | Chapters / Units | Download Link |
| 1 | Unit 1 | Download |
| 2 | Unit 2 | Download |
| 3 | Unit 3 | Download |
| 4 | Unit 4 | Download |
| 5 | Unit 5 | Download |
Mechanical 1-2 M2 Important Topics and Important Questions
UNIT – I: Solving systems of linear equations, Eigen values and Eigen vectors: (10hrs)
Rank of a matrix by echelon form and normal form – Solving system of homogeneous and
non- homogeneous linear equations – Gauss Eliminationmethod – Eigen values and Eigen
vectors and properties (article-2.14 in text book-1).
Unit – II: Cayley–Hamilton theorem and Quadratic forms: (10hrs)
Cayley-Hamilton theorem (without proof) – Applications – Finding the inverse and power of
a matrix by Cayley-Hamilton theorem – Reduction to Diagonal form – Quadratic forms and
nature of the quadratic forms – Reduction of quadratic form to canonical forms by
orthogonal transformation.
Singular values of a matrix, singular value decomposition (text book-3).
UNIT – III: Iterative methods: (8 hrs)
Introduction– Bisection method–Secant method – Method of false position– Iteration method
– Newton- Raphson method (One variable and simultaneous Equations) – Jacobi and Gauss-
Seidel methods for solving system of equations numerically.
UNIT – IV: Interpolation: (10 hrs)
Introduction– Errors in polynomial interpolation – Finite differences– Forward differences–
Backward differences –Central differences – Relations between operators – Newton’s
forward and backward formulae for interpolation – Interpolation with unequal intervals –
Lagrange’s interpolation formula– Newton’s divide difference formula.
UNIT – V: Numerical differentiation and integration, Solution of ordinary differential
equations with initial conditions: (10 hrs)
Numerical differentiation using interpolating polynomial – Trapezoidal rule– Simpson’s
1/3rd and 3/8th rule– Solution of initial value problems by Taylor’s series– Picard’s method of
successive approximations– Euler’s method – Runge-Kutta method (second and fourth
order).
Text Books:
1. B. S. Grewal, Higher Engineering Mathematics, 44th Edition, Khanna Publishers.
2. B. V. Ramana,Higher Engineering Mathematics, 2007 Edition, Tata Mc. Graw Hill Education.
3. David Poole, Linear Algebra- A modern introduction, 4th Edition, Cengage.
Reference Books:
1. Steven C. Chapra, Applied Numerical Methods with MATLAB for
Engineering andScience,Tata Mc. Graw Hill Education.
2. M. K. Jain, S.R.K. Iyengar and R.K. Jain, Numerical Methods for Scientific
and EngineeringComputation, New Age International Publications.
3. Lawrence Turyn, Advanced Engineering Mathematics, CRC Press.
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