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Basic courses-Sem 1 and 2
Mathematics III (Web)
Syllabus
Co-ordinated by :
IIT Guwahati
Available from :
2009-12-31
Lec :
1
Modules / Lectures
Complex Numbers and Complex Algebra
Motivation
Definition & Geometric Interpretation
Algebraic Operations
Bilinear form
Conjugate of a Complex Number
Modulus of a Complex Number
Polar form
Exponential form
Powers of Complex Numbers
Assignment-Complex Numbers and Complex Algebra
Complex Functions
Planar Sets
Complex Functions
Limits
Continuity
Differentiability
Analytic Functions
Assignment-Complex Functions
Elementary Analytic Function
Exponential Function
Trigonometric Functions
Logarithmic Functions
Assignment-Elementary Analytic Function
Complex Integration
Integration of f:[a,b] -- C
Curves
Line Integrals
Antiderivatives
Cauchy-Goursat Theorem
Cauchy's Integral Formula
Other Important Theorem
Assignment-Complex Integration
Power Series
Introduction
Power Series
Taylors Series and Analytic Functions
Power Series of F(z)
Laurent Series
Assignment-Power Series
Zeros ,Singularities,Residues
Zeros
Singularites
Residues
Residue Theorem
Argument Principle
Rouche's Theorem
Assignment-Zeros ,Singularities,Residues
Application of Contour Integration
Definite Integral of Trigonometric Function
Improper Integrals of Real Functions
Improper Integrals of Certain Functions
Improper Integrals of Rational Functions
Indented Contour Integration
Inverse Laplace Transform
Assignment-Application of Contour Integration
Conformal Mappings and Applications
Conformal Mappings
Riemann Mapping Theorem
Mobius Transform
Assignment-Conformal Mappings and Applications
Fourier Series
Basics from Linear Algebra (Basic Definitions)
Fourier series
Pointwise convergence of Fourier series
Uniform convergence of Fourier series
Bessel's Inequality and Parseval's Identity
Complex Form of Fourier Series
Half Range Series
Assignment-Fourier Series
Second Order PDE
Partial Differential Equation - An Introduction
Formulation of second order PDE
Type Of PDEs
Classification of second order PDE
Canonical forms
Canonical Forms for Hyperbolic Type Equations
Canonical form for Parabolic Type Equations
Canonical Form for Elliptic Type Equations
Assignment-Second Order PDE
Wave Equation
Transverse vibration of a string
Solution of one-dimensional wave equation by the reduction to its canonical form
Initial Value Problem (IVP)
Solutions of the Non-Homogeneous Wave Equation
Solution of non-homogeneous wave equation
Separation of variables method
Assignment-Wave Equation
Heat Equation
Derivation of heat equation
Boundary conditions
Initial Boundary Value Problem
Transforming nonhomogeneous boundary conditions to homogeneous ones
Assignment-Heat Equation
Laplace Equation
Derivation of Laplace Equation
Properties of Harmonic functions
Elliptic Equation in Different Coordinate Systems
Separation of Variables
Dirichlet problem for a circle
Interior Dirichlet problem
Exterior Dirichlet problem
Laplace equation in cylindrical coordinates
Laplace equation in spherical coordinates
Assignment-Laplace Equation
Solution by Transform Methods
Fourier Integral Representation
Fourier Transform and Inverse Fourier Transform
Properties of Fourier Transform
Application of Fourier Transform
Fourier Cosine and Sine Transform
Properties of Cosine and Sine Transform
Application of Cosine and Sine Transforms to solve PDEs
Laplace Transform and its Properties
Inverse Laplace Transform and its Properties
Convolution
Applications of Laplace transform
Exercise-fourier Transform
Exercise-Laplace Transform
Assignment-Fourier Transform
Assignment-Laplace Transform
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