# JNTUK B.TECH R20 1-2 Syllabus For Mathematics –ii PDF 2022

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You will be able to find information about Mathematics –ii along with its Course Objectives and Course outcomes and also a list of textbook and reference books in this blog.You will get to learn a lot of new stuff and resolve a lot of questions you may have regarding Mathematics –ii after reading this blog. Mathematics –ii has 5 units altogether and you will be able to find notes for every unit on the CynoHub app. Mathematics –ii can be learnt easily as long as you have a well planned study schedule and practice all the previous question papers, which are also available on the CynoHub app.

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### Mathematics –ii Unit One

#### 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 non- homogeneous linear equations – Gauss Elimination method – Eigenvalues and Eigen vectors and properties (article-2.14 in text book-1).

### Mathematics –ii Unit Two

#### 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 (text book-3)

### Mathematics –ii Unit Three

#### 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.

### Mathematics –ii Unit Four

#### 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.

### Mathematics –ii Unit Five

#### 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).

### Mathematics –ii Course Objectives

To instruct the concept of Matrices in solving linear algebraic equations

To elucidate the different numerical methods to solve nonlinear algebraic equations

To disseminate the use of different numerical techniques for carrying out numerical integration.

To equip the students with standard concepts and tools at an intermediate to advanced level mathematics to develop the confidence and ability among the students to handle various real world problems and their applications.

### Mathematics –ii Course Outcomes

At the end of the course, the student will be able to

develop the use of matrix algebra techniques that is needed by engineers for practical applications (L6)

solve system of linear algebraic equations using Gauss elimination, Gauss Jordan, Gauss Seidel (L3)

evaluate the approximate roots of polynomial and transcendental equations by different algorithms (L5)

apply Newton’s forward & backward interpolation and Lagrange’s formulae for equal and unequal intervals (L3)

apply numerical integral techniques to different Engineering problems (L3)

apply different algorithms for approximating the solutions of ordinary differential equations with initial conditions to its analytical computations (L3)

### Mathematics –ii Text Books

B. S. Grewal, Higher Engineering Mathematics, 44th Edition, Khanna Publishers.

B. V. Ramana,Higher Engineering Mathematics, 2007 Edition, Tata Mc. Graw Hill Education.

David Poole, Linear Algebra- A modern introduction, 4th Edition, Cengage.

### Mathematics –ii Reference Books

Steven C. Chapra, Applied Numerical Methods with MATLAB for Engineering and Science,Tata Mc. Graw Hill Education.

M. K. Jain, S. R. K. Iyengar and R. K. Jain, Numerical Methods for Scientific and Engineering Computation, New Age International Publications.

Lawrence Turyn, Advanced Engineering Mathematics, CRC Press.