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

JNTUK R20 B Tech CSE 1-2 Mathematics – II Material/ Notes PDF Download: Unlock the world of JNTUK R20 B Tech CSE 1-2 Mathematics – II Material, designed to simplify the understanding of matrices and their role in solving linear algebraic equations. Navigate the complexities of nonlinear algebraic equations effortlessly through our straightforward explanations of various numerical methods. Explore the practical applications of different numerical techniques for numerical integration. Our material aims to provide students with a solid grasp of intermediate to advanced mathematical concepts, empowering them to confidently tackle real-world problems.

Download the JNTUK R20 B Tech CSE 1-2 Mathematics – II Material PDF to access comprehensive resources that bridge the gap between theoretical knowledge and practical application. Start your mathematical journey with confidence and practical skills for real-world problem-solving.

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

Unit 1 Syllabus PDF Download | JNTUK R20 B Tech CSE 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 CSE 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 CSE 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 CSE 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 CSE 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).

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JNTUK R20 B Tech Mathematics – II Material – Outcomes

• Matrix Algebra for Engineers (L6): Acquire practical matrix algebra skills crucial for engineering applications.
• Linear Equation Solving (L3): Learn Gauss elimination, Gauss Jordan, and Gauss-Seidel methods for solving linear algebraic equations.
• Root Approximation (L5): Explore algorithms to find approximate roots of polynomial and transcendental equations.
• Interpolation Techniques (L3): Apply Newton’s forward and backward interpolation, and Lagrange’s formulae for equal and unequal intervals.
• Numerical Integration in Engineering (L3): Use numerical integral techniques to address engineering problems.
• ODE Solutions Approximation (L3): Apply algorithms to approximate solutions of ordinary differential equations, connecting theoretical and practical aspects.