JNTUK R20 B.Tech Mechanical 1-2 Mathematics – II Material/ Notes PDF Download

JNTUK R20 B.Tech Mechanical 1-2 Mathematics – II Material/ Notes PDF Download: This material covers the topics of Matrices, solving linear algebraic equations, and various numerical methods for solving nonlinear algebraic equations. It also discusses different numerical techniques for numerical integration. The goal is to provide students with a solid understanding of these concepts at an intermediate to advanced level. By studying this material, students will gain the confidence and skills needed to tackle real-world problems and their applications.

JNTUK R20 B.Tech 1-2 M2 Material – Units

Unit 1 Syllabus PDF Download | JNTUK R20 B.Tech 1-2 M2 Materials

Solving systems of linear equations, Eigen values and Eigen vectors: Rank of a matrix by echelon form and normal form – Solving system of homogeneous and nonhomogeneous linear equations – Gauss Elimination method – Eigen values and Eigen vectors and properties.

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Unit 2 Syllabus PDF Download | JNTUK R20 B.Tech 1-2 M2 Material

Cayley–Hamilton theorem and Quadratic forms: 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.

Unit 3 Syllabus PDF Download | JNTUK R20 B.Tech 1-2 M2 Material

Iterative methods: 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 4 Syllabus PDF Download | JNTUK R20 B.Tech 1-2 M2 Material

Interpolation: 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 5 Syllabus PDF Download | JNTUK R20 B.Tech 1-2 M2 Material

Numerical differentiation and integration, Solution of ordinary differential equations with initial conditions: 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.

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JNTUK R20 B.Tech 1-2 M2 Notes – Outcomes

• This section focuses on developing matrix algebra techniques essential for engineers in practical applications.
• Students will learn to solve systems of linear algebraic equations using Gauss elimination, Gauss Jordan, and Gauss-Seidel methods.
• Various algorithms will be introduced to approximate roots of polynomial and transcendental equations.
• Students will apply Newton’s forward and backward interpolation as well as Lagrange’s formulae for both equal and unequal intervals.
• Numerical integral techniques will be applied to solve different engineering problems.
• Different algorithms will be utilized to approximate solutions of ordinary differential equations with initial conditions, complementing analytical computations.