Note: This syllabus is common for EEE, ECE, CSE, EIE, BME, IT, ETE, ECM, ICE.
MA102BS/MA202BS: MATHEMATICS  II
(Advanced Calculus)
B.Tech. I Year II Sem. L T/P/D C
4 1/0/0 4
Prerequisites: Foundation course (No prerequisites).
Course Objectives:
To learn
 concepts & properties of Laplace Transforms
 solving differential equations using Laplace transform techniques
 evaluation of integrals using Beta and Gamma Functions
 evaluation of multiple integrals and applying them to compute the volume and areas of regions
 the physical quantities involved in engineering field related to the vector valued functions.
 the basic properties of vector valued functions and their applications to line, surface and volume integrals.
Course Outcomes: After learning the contents of this course the student must be able to
 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, 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
UNIT – I
Laplace Transforms: Laplace transforms of standard functions, Shifting theorems, derivatives and integrals, properties Unit step function, Dirac’s delta function, Periodic function, Inverse Laplace transforms, Convolution theorem (without proof).
Applications: Solving ordinary differential equations (initial value problems) using Laplace transforms.
UNIT  II
Beta and Gamma Functions: Beta and Gamma functions, properties, relation between Beta and Gamma functions, evaluation of integrals using Beta and Gamma functions.
Applications: Evaluation of integrals.
UNIT – III
Multiple Integrals: Double and triple integrals, Change of variables, Change of order of integration. Applications: Finding areas, volumes & Center of gravity (evaluation using Beta and Gamma functions).
UNIT – IV
Vector Differentiation: Scalar and vector point functions, Gradient, Divergence, Curl and their physical and geometrical interpretation, Laplacian operator, Vector identities.
UNIT – V
Vector Integration: Line Integral, Work done, Potential function, area, surface and volume integrals, Vector integral theorems: Greens, Stokes and Gauss divergence theorems (without proof) and related problems.
Text Books:
 Advanced Engineering Mathematics by R K Jain & S R K Iyengar, Narosa Publishers
 Engineering Mathematics by Srimanthapal and Subodh C. Bhunia, Oxford Publishers
References:
 Advanced Engineering Mathematics by Peter V. O. Neil, Cengage Learning Publishers.
 Advanced Engineering Mathematics by Lawrence Turyn, CRC Press
Note: This syllabus is common for Civil, ME, AE, ME (M), MME, AU, Mining, Petroleum, CEE, ME (Nanotech).
MATHEMATICS II
(Advanced Calculus)
B.Tech. I Year I Sem. L T/P/D C
Course Code: MA102BS/MA202BS 4 1/0/0 4
Prerequisites: Foundation course (No prerequisites).
Course Objectives:
To learn
 concepts & properties of Laplace Transforms
 solving differential equations using Laplace transform techniques
 evaluation of integrals using Beta and Gamma Functions
 evaluation of multiple integrals and applying them to compute the volume and areas of regions
 the physical quantities involved in engineering field related to the vector valued functions.
 the basic properties of vector valued functions and their applications to line, surface and volume integrals.
Course Outcomes: After learning the contents of this course the student must be able to
 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, 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
UNIT – I
Laplace Transforms: Laplace transforms of standard functions, Shifting theorems, derivatives and integrals, properties Unit step function, Dirac’s delta function, Periodic function, Inverse Laplace transforms, Convolution theorem (without proof).
Applications: Solving ordinary differential equations (initial value problems) using Laplace transforms.
UNIT  II
Beta and Gamma Functions: Beta and Gamma functions, properties, relation between Beta and Gamma functions, evaluation of integrals using Beta and Gamma functions.
Applications: Evaluation of integrals.
UNIT – III
Multiple Integrals: Double and triple integrals, Change of variables, Change of order of integration. Applications: Finding areas, volumes & Center of gravity (evaluation using Beta and Gamma functions).
UNIT – IV
Vector Differentiation: Scalar and vector point functions, Gradient, Divergence, Curl and their physical and geometrical interpretation, Laplacian operator, Vector identities.
UNIT – V
Vector Integration: Line Integral, Work done, Potential function, area, surface and volume integrals, Vector integral theorems: Greens, Stokes and Gauss divergence theorems (without proof) and related problems.
Text Books:
 Advanced Engineering Mathematics by R K Jain & S R K Iyengar, Narosa Publishers
 Engineering Mathematics by Srimanthapal and Subodh C. Bhunia, Oxford Publishers
References:
 Advanced Engineering Mathematics by Peter V. O. Neil, Cengage Learning Publishers.
 Advanced Engineering Mathematics by Lawrence Turyn, CRC Press

CreatedDec 15, 2016

UpdatedDec 16, 2016

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