Overview
 Units 6
 Duration 08:21:30
 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 JNTUH
University
JNTUH
Learning Outcomes
 Use Laplace transform techniques for solving DE’s.
 Evaluate integrals using Beta and Gamma functions.
 Evaluate the multiple integrals and can apply these concepts to find areas, volumes, the moment of inertia, etc of regions on a plane or in space.
 Evaluate the line, surface, and volume integrals and converting them from one to another.
Curriculum


UNIT 1 Laplace Transforms: Introduction, transforms of elementary functions, transforms of elementary functionsPART 01, transforms of elementary functions Problems, transforms of elementary functions Problems Part 1, First Shifting theorem, Problems on First Shifting theorem, Properties of laplace transforms, properties of laplace transforms Part 1, Transform of Derivatives & Integrals, Problems transforms of derivatives, transforms of integrals, Multiplication by t power n& Division by t, multiplication by t power n, division by t .(statements only), Dirac�s delta function, Periodic�function2:10:31



UNIT 1.2 Inverse transforms: IT Introduction, Basic Formulas of Inverse Laplace Transform, Problems on Inverse Laplace Transform, Method of Partial fraction, Method of Partial fraction Part 1, First Shifting theorem (Table), Problem on First Shifting theorem, Second Shifting Theorem, Inverse Laplace Transform of Derivatives,Integrals, Multiplication & Division by S, IT Convolution theorem, Convolution theorem (without proof), applications to differential equations., applications to differential equations  Part 11:25:48



UNIT 2 Beta and Gamma 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 function, Evaluation of integrals using Beta and Gamma functions1:04:12



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 1, volumes & Center of gravity (evaluation using Beta�and Gamma functions)1:40:55



UNIT 4 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, �Laplacian operator, Vector identities1:58:44



UNIT 5 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 1, Problems1:27:08

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.