AM 101. METHODS OF APPLIED MATHEMATICS FOURIER TRANSFORMS: UNIT I: Fourier Transforms : Dirichlet conditions Fourier integral formula ( Complex) – –The Fourier transform Fourier sine and cosine transforms-Relationship of Fourier and – Laplace transforms useful results for direct applications-Linearity property of –Some Fourier transforms of scale property property—Modulation –Change –Shifting theorem or Falting-The convolution or Falting theorem for Fourier –Convolution transforms for Fourier transforms theorem of –Parseval’s identity Rayleigh’s theorem Relation between the Fourier transforms of the derivatives of a Plancherel’s – function Fourier transforms-Applications of Fourier transforms to –Multiple Boundary value problems. ( Chapter 4) UNIT-II Finite Fourier Transforms: Fourier Series finite Fourier sine transform-The –The finite Fourier cosine transforms between the finite Fourier transforms of the –Relation derivations of a function finite Fourier transforms of finite –Multiple –Applications Fourier transforms to boundary value problems-Special case of boundary value problem ( Chapter 5) Scope and standard as in by S. “ Integral Transforms” by Raisinghania, published Chand & Co., New Delhi, 1995 Editon. ALGEBRA: UNIT: III Structure Theory of Groups : Conjugacy and G-Sets, Normal series, Solvable groups, Simplicity of , Sylow theorems. ( Sections 4 of Chapter 5, Sections 1 and 2 of Chapter 6, Section 3 of Chapter 7 and Sections 4 of Chapter 8)
AM 101. METHODS OF APPLIED MATHEMATICS FOURIER TRANSFORMS: UNIT I: Fourier Transforms : Dirichlet conditions – Fourier integral formula –The ( Complex) Fourier transform – Fourier sine and cosine transforms-Relationship of Fourier and Laplace transforms –Some useful results for direct applications-Linearity property of Fourier transforms –Change of scale property –Shifting property—Modulation theorem –Convolution or Falting-The convolution or Falting theorem for Fourier transforms –Parseval’s identity for Fourier transforms Rayleigh’s theorem of Plancherel’s theorem – Relation between the Fourier transforms of the derivatives of a function –Multiple Fourier transforms-Applications of Fourier transforms to Boundary value problems. ( Chapter 4) UNIT-II Finite Fourier Transforms: Fourier Series –The finite Fourier sine transform-The finite Fourier cosine transforms –Relation between the finite Fourier transforms of the derivations of a function –Multiple finite Fourier transforms –Applications of finite Fourier transforms to boundary value problems-Special case of boundary value problem ( Chapter 5) Scope and standard as in “ Integral Transforms” by Raisinghania, published by S. Chand & Co., New Delhi, 1995 Editon. ALGEBRA: UNIT: III Structure Theory of Groups : Conjugacy and G-Sets, Normal series, Solvable groups, Simplicity of , Sylow theorems. ( Sections 4 of Chapter 5, Sections 1 and 2 of Chapter 6, Section 3 of Chapter 7 and Sections 4 of Chapter 8)