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

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JNTUK R20 B.Tech EEE 1-1 Mathematics – II Material/ Notes PDF Download: The JNTUK R20 B.Tech 1-1 Mathematics – II Material offers comprehensive insights into matrices for solving linear algebraic equations. It also covers various numerical methods for tackling nonlinear algebraic equations and introduces different techniques for numerical integration. With a focus on intermediate to advanced-level mathematics, this material aims to empower students with the skills and confidence to address real-world problems effectively.

JNTUK R20 B.Tech 1-1 Mathematics – II Material – Chapters

Unit 1 Syllabus PDF Download | JNTUK R20 B.Tech 1-1 Mathematics – II Material

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 nonhomogeneous linear equations – Gauss Elimination method – Eigen values and Eigen vectors and properties.

Unit 2 Syllabus PDF Download | JNTUK R20 B.Tech 1-1 Mathematics – II Material

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

Unit 3 Syllabus PDF Download | JNTUK R20 B.Tech 1-1 Mathematics – II Material

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 4 Syllabus PDF Download | JNTUK R20 B.Tech 1-1 Mathematics – II Material

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 5 Syllabus PDF Download | JNTUK R20 B.Tech 1-1 Mathematics – II Material

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).

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JNTUK R20 B.Tech 1-1 Mathematics – II Notes – Outcomes

• R20 B.Tech 1-1 Mathematics – II Enhance the application of matrix algebra techniques essential for practical engineering scenarios.
• Utilize various methods like Gauss elimination, Gauss Jordan, and Gauss-Seidel to solve systems of linear algebraic equations.
• Evaluate approximate roots of polynomial and transcendental equations using different algorithms.
• Apply Newton’s forward and backward interpolation as well as Lagrange’s formulae for both equal and unequal intervals.
• Employ numerical integral techniques to address diverse engineering problems.
• Utilize different algorithms to approximate solutions of ordinary differential equations with initial conditions, complementing analytical computations.