This book explains the following
topics: IFirst-order differential equations, Direction fields, existence and
uniqueness of solutions, Numerical methods, Linear equations, models,
Complex numbers, roots of unity, Second-order linear equations, Modes and
the characteristic polynomial, Good vibrations, damping conditions,
Exponential response formula, spring drive, Complex gain, dashpot drive,
Operators, undetermined coefficients, resonance, Frequency response, LTI
systems, superposition, RLC circuits, Engineering applications, Fourier
series, Operations on fourier series , Periodic solutions; resonance, Step
functions and delta functions, Step response, impulse response, Convolution,
First order systems, Linear systems and matrice, Eigenvalues, eigenvectors,
etc.
Author(s): Prof. Haynes Miller, Prof. Arthur Mattuck,
Massachusetts Institute of Technology
This note explains the following topics:
Functions of Several Variables, Partial Derivatives and Tangent Planes, Max
and Min Problems on Surfaces, Ordinary Differential Equations,
Parametrisation of Curves and Line Integrals and MATLAB Guide.
This book
explains the following topics: First Order Equations, Second Order Linear
Equations, Reduction of Order Methods, Homogenous Constant Coefficients
Equations ,Power Series Solutions, The Laplace Transform Method, Systems of
Linear Differential Equations, Autonomous Systems and Stability, Boundary
Value Problems.
This book explains the following
topics: IFirst-order differential equations, Direction fields, existence and
uniqueness of solutions, Numerical methods, Linear equations, models,
Complex numbers, roots of unity, Second-order linear equations, Modes and
the characteristic polynomial, Good vibrations, damping conditions,
Exponential response formula, spring drive, Complex gain, dashpot drive,
Operators, undetermined coefficients, resonance, Frequency response, LTI
systems, superposition, RLC circuits, Engineering applications, Fourier
series, Operations on fourier series , Periodic solutions; resonance, Step
functions and delta functions, Step response, impulse response, Convolution,
First order systems, Linear systems and matrice, Eigenvalues, eigenvectors,
etc.
Author(s): Prof. Haynes Miller, Prof. Arthur Mattuck,
Massachusetts Institute of Technology
This note covers the following topics: First Order Equations,
Numerical Methods, Applications of First Order Equations, Linear Second
Order Equations, Applcations of Linear Second Order Equations, Series
Solutions of Linear Second Order Equations, Laplace Transforms, Linear
Higher Order Equations.
This note covers the
following topics: The trigonometric functions, The fundamental theorem of
calculus, First-order odes, Second-order odes, constant coefficients, The
Laplace transform, Series solutions, Systems of equations, Nonlinear
differential equations, Partial differential equations.
This note
covers the following topics: Geometrical Interpretation of ODE, Solution of
First Order ODE, Linear Equations, Orthogonal Trajectories, Existence and
Uniqueness Theorems, Picard's Iteration, Numerical Methods, Second Order Linear
ODE, Homogeneous Linear ODE with Constant Coefficients, Non-homogeneous Linear
ODE, Method of Undetermined Coefficients, Non-homogeneous Linear ODE, Method of
Variation of Parameters, Euler-Cauchy Equations, Power Series Solutions:
Ordinary Points, Legendre Equation, Legendre Polynomials, Frobenius Series
Solution, Regular Singular Point, Bessle Equation, Bessel Function, Strum
Comparison Theorem, Orthogonality of Bessel Function, Laplace Transform, Inverse
Laplace Transform, Existence and Properties of Laplace Transform, Unit step
function, Laplace Transform of Derivatives and Integration, Derivative and
Integration of Laplace Transform, Laplace Transform of Periodic Functions,
Convolution, Applications.
This note introduces students to differential equations. Topics covered
includes: Boundary value problems for heat and wave equations, eigenfunctionexpansions, Surm-Liouville theory and Fourier series, D'Alembert's
solution to wave equation, characteristic, Laplace's equation, maximum principle
and Bessel's functions.
This lecture note introduces three main types of partial differential
equations: diffusion, elliptic, and hyperbolic. It includes mathematical
tools, real-world examples and applications.
This note covers the
following topics: First Order Equations and Conservative Systems, Second Order
Linear Equations, Difference Equations, Matrix Differential Equations, Weighted
String, Quantum Harmonic Oscillator, Heat Equation and Laplace Transform.
These
are the sample pages from the textbook. Topics Covered: Partial differential equations, Orthogonal functions, Fourier Series, Fourier
Integrals, Separation of Variables, Boundary Value Problems, Laplace Transform,
Fourier Transforms, Finite Transforms, Green's Functions and Special Functions.
This
elementary text-book on Ordinary Differential Equations, is an attempt to present as much of the subject as is necessary for
the beginner in Differential Equations, or, perhaps, for the student of
Technology who will not make a specialty of pure Mathematics. On account of the
elementary character of the book, only the simpler portions of the subject have
been touched upon at all ; and much care has been taken to make all the
developments as clear as possible every important step being illustrated by easy
examples.
This book covers the following topics: Geometry and a Linear Function,
Fredholm Alternative Theorems, Separable Kernels, The Kernel is Small, Ordinary
Differential Equations, Differential Operators and Their Adjoints, G(x,t) in the
First and Second Alternative and Partial Differential Equations.