Overview
 Units 6
 Duration 10:03:49
 Branch B.E/B.Tech
 Language English
Course Description
This course is designed to equip the students with the necessary mathematical skills and techniques that are essential for an engineering course. The skills derived from the course will help the student from a necessary base to develop analytic and design concepts.
Recommended For
B.Tech 1st Year 2nd Sem JNTUK
University
JNTUK
Learning Outcomes
 Determine rank, Eigen values, and Eigen vectors of a given matrix and solve simultaneous linear equations.
 Solve simultaneous linear equations numerically using various matrix methods.
 Determine double integral over a region and triple integral over a volume.
 Calculate the gradient of a scalar function, divergence, and curl of a vector function. Determine line, surface, and volume integrals. Apply Green, Stokes, and Gauss divergence theorems to calculate line, surface, and volume integrals.
Curriculum


UNIT 1 Linear Systems of Equations: Introduction, Rank, Echelon form, Normal form Part 1, Normal form Part 2, GaussJordan method of finding inverse of a matrix, Solution of linear systems, Solution of linear systems Part 1, Gauss Elimination, GaussJordan, Jacobi and Gauss Seidel Method, Jacobi and Gauss Seidel Method Part 1, Applications : Finding the current in electrical circuits1:44:36



UNIT 2 Eigen valuesEigen Vectors and Quadratic forms: Eigen Values and Eigen vectors, Properties, Problems on Eigen Values and Eigen vectors, Problems on Eigen Values and Eigen vectors Part 1, CayleyHamilton theorem, Problems on CayleyHamilton theorem, Problem Inverse and Powers of matrix by using CayleyHamilton theorem, Diagonalization, Problem on Diagonalization, Quadratic forms, Reduction of a Quadratic form to Canonical form, Problems on Reduction of a Quadratic form to Canonical form Part 1, Problems on Reduction of a Quadratic form to Canonical form Part 2, Problems on Reduction of a Quadratic form to Canonical form Part 3, Problems on Reduction of a Quadratic form to Canonical form Part 4, Rank , Positive,Negative forms Quadratic form, Semidefinite and indefinite forms of Quadratic form, Index and Signature of a quadratic form, Applications: Free Vibration of a twomass system2:08:14



UNIT 3 Multiple Integrals: Introduction, Double Integrals, Triple Integrals, Triple Integrals Part 1, Change of variables, Change of order of integration, Applications to find Areas, Applications to find Areas Part 1, Moment of Inertia and volumes, Moment of Inertia and volumes Part 11:40:55



UNIT 4 Special Functions: Gamma Function, Gamma Function Part 1, Beta Function, Properties, Relation between Beta and Gamma functions, Relation between Beta and Gamma functions  Part 1, Relation between Beta and Gamma functions  Part 2, Applications to evaluation of improper integrals, The error function & Complimentory error function1:04:12



UNIT 5 Vector Differentiation: Introduction to Vector Differentiation, Gradient, Directional derivative, Problems on Gradient and Directional Derivative  Part 1, Problems on Gradient and Directional Derivative  Part 2, Divergence, Curl, Problems on Gradient,Divergence and Curl, Problems on Gradient,Divergence and Curl Part 1, Incompressible flow, Solenoidal and irrotational vector fields, Second order Operators, Del applied twice to point function, Del applied twice to point function Problems, Del applied twice to point function Problems Part 1, Del applied to products of point functions, Problems on Del applied to products of point functions, Problems on Del applied to products of point functions Part 1, Vector identities1:58:44



UNIT 6 Vector Integration: Line Integral, Problems On Work Done, Problems On Work Done  Part 1, Potential Function, Area,surface and volume of integrals, Flux, Vector integral theorems, Greens Theorem, Green's Theorem Problems, Stokes Theorem, Stokes Theorem Part 1, Stokes Theorem Part 2, Gauss Divergence theorem, Gauss Divergence theorem Part 11:27:08

Instructor
Dr C N B Rao ., M.Sc ,Ph.D (IIT Kharagpur )
Mr. Rao is a professor in an alumnus of IIT, Kharagpur, and currently working as a professor in Mathematics at SRKR College, Bhimavaram. He has close to 30+ years of experience in teaching mathematics to engineering students. Previously worked in many reputed institutions in the capacity of professor. A mentor, guide, and philosopher to a vast number of successful engineers. Mr. Rao is a life member of ISTE and a Life Member of the AP Society of mathematical sciences. Many students have been guided by Mr. Rao for research activities. He specializes in not just mathematics but applications of Mathematics in further engineering subjects.