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

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JNTUK R20 B.Tech ECE 1-2 Mathematics – II Material/ Notes PDF Download: Welcome to our guide on JNTUK R20 B.Tech ECE 1-2 Mathematics – II Material. Here, we aim to help students grasp key mathematical concepts crucial to their studies. We cover topics like matrices, which are essential for solving linear algebraic equations, and explore various numerical methods for tackling nonlinear equations. Our material also introduces different numerical techniques for numerical integration, providing practical skills for solving real-world engineering problems.

By offering a range of concepts and tools at an intermediate to advanced level, we aim to boost students’ confidence and ability to handle diverse challenges effectively. Download our JNTUK R20 B.Tech ECE 1-2 M2 Material for comprehensive study notes in PDF format.

JNTUK R20 B.Tech ECE 1-2 Mathematics – II Material – Units

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

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 (article-2.14 in text book-1).

Unit 2 Syllabus PDF Download | JNTUK R20 B.Tech ECE 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 (textbook-3).

Unit 3 Syllabus PDF Download | JNTUK R20 B.Tech ECE 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 ECE 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 ECE 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 (second and fourth order).

JNTUK R20 B.Tech Mathematics – II Material – Outcomes

• Matrix Algebra for Engineers: Gain essential skills in practical matrix algebra tailored for engineering applications.
• Linear Equation Solving: Master methods such as Gauss elimination, Gauss Jordan, and Gauss-Seidel for solving linear algebraic equations.
• Root Approximation: Discover algorithms designed to estimate approximate roots of both polynomial and transcendental equations.
• Interpolation Techniques: Learn to apply Newton’s forward and backward interpolation, as well as Lagrange’s formulae, for intervals of equal and unequal spacing.
• Numerical Integration in Engineering: Utilize numerical integral techniques to solve engineering problems efficiently and accurately.

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