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Differential Equations I MATB44H3F . This is an other great mathematics book cover the following topics of Differential Equations.
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1. Introduction 2. First Order Ordinary Differential Equations 3. Applications and Examples of First Order ode’s 4. Linear Differential Equations 5. Second Order Linear Equations 6. Applications of Second Order Differential Equations 7. Higher Order Linear Differential Equations 8. Power Series Solutions to Linear Differential Equations 9. Linear Systems 10. Existence and Uniqueness Theorems 11. Numerical Approximations
1. Introduction 2. First Order Equations & Conservative Systems 3. Second Order Linear Equations 4. Difference Equations 5. Matrix Differential Equations 6. Weighted String 7. Quantum Harmonic Oscillator 8. Heat Equation 9. Laplace Transform
Introduction First Order Equations Numerical Methods Applications of First Order Equations1em Linear Second Order Equations Applcations of Linear Second Order Equations Series Solutions of Linear Second Order Equations Laplace Transforms Linear Higher Order Equations Linear Systems of Differential Equations Boundary Value Problems and Fourier Expansions Fourier Solutions of Partial Differential Equations Boundary Value Problems for Second Order Linear Equations
Partial differential equations Orthogonal functions Fourier Series Fourier Integrals Separation of Variables Boundary Value Problems Place Transform Fourier Transforms Finite Transforms Green's Functions Special Functions
0. A short mathematical review 1. Introduction to odes 2. First-order odes 3. Second-order odes, constant coefficients 4. The Laplace transform 5. Series solutions 6. Systems of equations 7. Nonlinear differential equations 8. Partial differential equations
Integral Equations Ordinary Differential Equations Partial Differential Equations
Genesis of the ordinary differential euqation in two vairables. The simultaneous system and the equivalent linear partial differential euqation. The fundamental theorems of lie's theory of the group of one parameter connection between euler's integrating factor and lie's infinitesimal transformation. Geometrical applications of the integrating factor. orthogonal trajectories and iso- thermal systems. Differential equations of the first order, but not of the first degree. singular solutions. Riccati's equation, and clairaut's equation. Total differential equations of the first order and degree in three variables which are derivable from a single primitive. Ordinary differential equations of the second order in two variables. The general linear differential equation in two variables. Methods for the integration of the simultaneous system.
1. Heat and diffusion 2. Waves and signals 3. Quantum mechanics 4. Linear partial differential equations 5. Classification of PDEs and problem types 6. Some functional analysis 7. Fourier sine series and cosine series 8. Real Fourier series and complex Fourier series 9. Multidimensional Fourier series 10. Proofs of the Fourier convergence theorems 11. Boundary value problems on a line segment 12. Boundary value problems on a square 13. Boundary value problems on a cube 14. Boundary value problems in polar coordinates 15. Eigenfunction methods on arbitrary domains 16. Separation of variables 17. Impulse-response methods 18. Applications of complex analysis 19. Fourier transforms on unbounded domains 20. Fourier transform solutions to PDEs
Topics of this book display here later
Mathematics, Physics and PDEs G. F. B. Riemann Riemmann, complex variables and 2-D fluids Riemmann and Geometry
Preliminary ideas and motivation Solution of Laplace and Poisson equation Solution to other equations by Green’s function
Preliminaries Partial Differential Operators with Constant Coefficients L2 Sobolev Spaces Basic Theory of Pseudo Differential Operators LP and Lipschitz Estimates
Introduction 1-dimensional waves Heat equation in 1D Separation of variables and Fourier Series Fourier transform Separation of variables Laplace equation Separation of variables Wave equation Variational methods Distributions and weak solutions Nonlinear equations Eigenvalues and eigenfunctions Miscellaneous Appendices
Distributions in 1d Several variables calculus The Laplacean Convolution of distributions The Fourier Transform The wave equation Sobolev spaces Lebesgue Integration Hilbert spaces