JNTUK R19 B.Tech CSE 1-2 Mathematics – II Material/ Notes PDF Download

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JNTUK R19 B.Tech CSE 1-2 Mathematics – II Material/ Notes PDF Download: Welcome to our guide on JNTUK R20 B.Tech CSE 1-2 Mathematics – II Material. Our goal is to help students understand important mathematical concepts crucial for their studies. We cover topics like matrices, which are vital for solving linear algebraic equations, and explore various numerical methods for handling nonlinear equations. Additionally, our material introduces different numerical techniques for numerical integration, offering practical skills for solving real-world engineering problems.

With concepts and tools presented at an intermediate to advanced level, we aim to enhance students’ confidence and ability to tackle diverse challenges effectively. Access our JNTUK R20 B.Tech CSE 1-2 M2 Material for comprehensive study notes in PDF format.

JNTUK R19 B.Tech CSE 1-2 Mathematics – II Material – Units

Unit 1 Syllabus PDF Download | JNTUK R19 B.Tech CSE Mathematics – II 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 R19 B.Tech CSE Mathematics – II 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 R19 B.Tech CSE Mathematics – II 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 R19 B.Tech CSE Mathematics – II 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 R19 B.Tech CSE Mathematics – II 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 R19 B.Tech M2 Material – Outcomes

• Practical Matrix Algebra for Engineers: Develop essential skills in matrix algebra specifically tailored for engineering applications. Understand how matrices are used to represent and solve real-world engineering problems effectively.
• Solving Linear Equations: Master various methods such as Gauss elimination, Gauss Jordan, and Gauss-Seidel for solving linear algebraic equations commonly encountered in engineering problems. These techniques are crucial for accurately determining unknown values in complex systems.
• Approximating Roots: Explore algorithms designed to estimate approximate roots of both polynomial and transcendental equations. These methods provide engineers with efficient tools for finding solutions to equations where exact solutions may be difficult to obtain.
• Interpolation Techniques: Learn practical interpolation techniques like Newton’s forward and backward interpolation, as well as Lagrange’s formulae. These methods enable engineers to estimate values between known data points, crucial for tasks such as curve fitting and data analysis.
• Numerical Integration for Engineering: Utilize numerical integral techniques to solve engineering problems efficiently and accurately. Understanding how to apply numerical integration methods ensures engineers can analyze and model systems with continuous variables, optimizing designs and performance.

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