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AU Mathematics III Sem III
No Units Titles Sub Titles Chapters
1 Unit 1 Vector Calculus Differentiation of vectors, curves in space, Velocity and acceleration, Relative velocity and acceleration, Scalar and Vector point functions, Vector operator ", " applied to scalar point functions, Gradient, " applied to vector point functions, Divergence and curl, Physical interpretations of ", F and " F, " applied twice to point functions, " applied to products of point functions, integration of vectors, Line integral, Circulation, Work, Surface integral-flux, Green s theorem in the plane, Stoke s theorem, Volume integral, Divergence theorem, Irrotational and solenoidal fields, Green s theorem, Introduction of orthogonal curvilinear coordinates : Cylindrical, Spherical and polar coordinates VIEW CHAPTERS
2 Unit 2 Introduction of Partial Differential Equations Formation of partial differential equations, Solutions of PDEs, Equations solvable by direct integration, Linear equations of first order, Homogeneous linear equations with constant coefficients, Rules for finding the complimentary function, Rules of finding the particular integral, Working procedure top solve homogeneous linear equations of any order, Nonhomogeneous linear equations VIEW CHAPTERS
3 Unit 3 Applications of Partial Differential Equations Method of separation of variables, Vibrations of a stretched string-wave equations, Onedimensional and two-dimensional heat flow equations, Solution of Laplace s equation, Laplace s equation in polar coordinates VIEW CHAPTERS
4 Unit 4 Integral Transforms Introduction, Definition, Fourier Integral, Sine and Cosine Integrals, Complex Forms of Fourier Integral, Fourier Transform, Fourier and Cosine Transforms, Finite Fourier Sine and Cosine Transforms, Properties of F - Transforms, Convolution Theorem for F - Transforms, Parseval s Identity for Fourier Transforms, Fourier Transforms of the Derivatives of a Function, Applications to Boundary Value Problems, Using Inverse Fourier Transforms only VIEW CHAPTERS
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