Matrices and Calculus detailed syllabus for Mechanical Engineering (ME), 1st Year 1st Sem R22 regulation has been taken from the JNTUH official website and presented for the B.Tech students affiliated to JNTUH course structure. For Course Code, Subject Names, Theory Lectures, Tutorial, Practical/Drawing, Credits, and other information do visit full semester subjects post given below. We make sure the result links and syllabus uploaded here is latest and up to date, also the syllabus PDF files can also be downloaded from the universities official website.
For Mechanical Engineering (ME) 1st Year 1st Sem R22 Regulation Scheme, do visit ME 1st Year 1st Sem R22 Scheme. The detailed syllabus for matrices and calculus is as follows.
Matrices and Calculus Subject Syllabus for ME 1st Year 1st Sem R22 Regulation
Pre-requisites:
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Course Objectives:
To learn
- Types of matrices and their properties.
- Concept of a rank of the matrix and applying this concept to know the consistency and solving the system of linear equations.
- Concept of eigenvalues and eigenvectors and to reduce the quadratic form to canonical form
- Geometrical approach to the mean value theorems and their application to the mathematical problems
- Evaluation of surface areas and volumes of revolutions of curves.
- Evaluation of improper integrals using Beta and Gamma functions.
- Partial differentiation, concept of total derivative
- Finding maxima and minima of function of two and three variables.
- Evaluation of multiple integrals and their applications
Course outcomes:
After learning the contents of this paper the student must be able to
- Write the matrix representation of a set of linear equations and to analyse the solution of the system of equations
- Find the Eigenvalues and Eigen vectors
- Reduce the quadratic form to canonical form using orthogonal transformations.
- Solve the applications on the mean value theorems.
- Evaluate the improper integrals using Beta and Gamma functions
- Find the extreme values of functions of two variables with/ without constraints.
- Evaluate the multiple integrals and apply the concept to find areas, volumes
UNIT-I
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UNIT-II
Eigen values and Eigen vectors 10 L
Linear Transformation and Orthogonal Transformation: Eigenvalues, Eigenvectors and their properties, Diagonalization of a matrix, Cayley-Hamilton Theorem (without proof), finding inverse and power of a matrix by Cayley-Hamilton Theorem, Quadratic forms and Nature of the Quadratic Forms, Reduction of Quadratic form to canonical forms by Orthogonal Transformation.
UNIT-III
Calculus 10 L
Mean value theorems: Rolle’s theorem, Lagrange’s Mean value theorem with their Geometrical Interpretation and applications, Cauchy’s Mean value Theorem, Taylor’s Series. Applications of definite integrals to evaluate surface areas and volumes of revolutions of curves (Only in Cartesian coordinates), Definition of Improper Integral: Beta and Gamma functions and their applications.
UNIT-IV
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UNIT-V
Multivariable Calculus (Integration) 8 L
Evaluation of Double Integrals (Cartesian and polar coordinates), change of order of integration (only Cartesian form), Evaluation of Triple Integrals: Change of variables (Cartesian to polar) for double and (Cartesian to Spherical and Cylindrical polar coordinates) for triple integrals. Applications: Areas (by double integrals) and volumes (by double integrals and triple integrals).
TEXT BOOKS:
- B.S. Grewal, Higher Engineering Mathematics, Khanna Publishers, 36th Edition, 2010.
- R.K. Jain and S.R.K. Iyengar, Advanced Engineering Mathematics, Narosa Publications, 5th Edition, 2016.
REFERENCE BOOKS:
For the complete Syllabus, results, class timetable, and many other features kindly download the iStudy App
It is a lightweight, easy to use, no images, and no pdf platform to make students’s lives easier..
For detailed syllabus of all the other subjects of B.Tech 1st Year Mechanical Engineering (ME), visit Mechanical Engineering (ME) 1st Year Syllabus Subjects.
For results of Mechanical Engineering (ME) 1st Year 1st Sem R22 Regulation, visit ME 1st Year 1st Sem R22 Regulation results direct link.