I Year - II Semester
MATHEMATICS-III
Unit Wise Question Bank
UNIT I: Linear systems of equations:
Rank-Echelon form-Normal form – Solution of linear systems – Gauss elimination - Gauss Jordon-
Gauss Jacobi and Gauss Seidal methods.Applications: Finding the current in electrical circuits.
Click Here To Download Unit_1 Question Bank
UNIT II: Eigen values - Eigen vectors and Quadratic forms:
Eigen values - Eigen vectors– Properties – Cayley-Hamilton theorem - Inverse and powers of a matrix by
using Cayley-Hamilton theorem- Diagonalization- Quadratic forms- Reduction of quadratic form to
canonical form – Rank - Positive, negative and semi definite - Index – Signature.
Applications: Free vibration of a two-mass system.
using Cayley-Hamilton theorem- Diagonalization- Quadratic forms- Reduction of quadratic form to
canonical form – Rank - Positive, negative and semi definite - Index – Signature.
Applications: Free vibration of a two-mass system.
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UNIT III: Multiple integrals:
Curve tracing: Cartesian, Polar and Parametric forms.
Multiple integrals: Double and triple integrals – Change of variables – Change of order of integration.
Applications: Finding Areas and Volumes.
Multiple integrals: Double and triple integrals – Change of variables – Change of order of integration.
Applications: Finding Areas and Volumes.
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UNIT IV: Special functions:
Beta and Gamma functions- Properties - Relation between Beta and Gamma functions- Evaluation of
improper integrals.
Applications: Evaluation of integrals.
improper integrals.
Applications: Evaluation of integrals.
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UNIT V: Vector Differentiation:
Gradient- Divergence- Curl - Laplacian and second order operators -Vector identities.
Applications: Equation of continuity, potential surfaces
Applications: Equation of continuity, potential surfaces
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UNIT VI: 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.
Applications: Work done, Force.
theorems: Greens, Stokes and Gauss Divergence theorems (without proof) and related problems.
Applications: Work done, Force.
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