The contents of
this book include: A short mathematical review, Introduction to odes,
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: 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.
describes the main ideas to solve certain differential equations, such us
first order scalar equations, second order linear equations, and systems of
linear equations. It uses power series methods to solve variable
coefficients second order linear equations. Also introduces Laplace
transform methods to find solutions to constant coefficients equations with
generalized source functions.
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,
This note explains the following topics: Solving various types of
differential equations, Analytical Methods, Second and n-order Linear
Differential Equations, Systems of Differential Equations, Nonlinear Systems and
Qualitative Methods, Laplace Transform, Power Series Methods, Fourier Series.
Goal of this
note is to develop the most basic ideas from the theory of partial
differential equations, and apply them to the simplest models arising from
physics. Topics covered includes: Power Series, Symmetry and Orthogonality,
Fourier Series, Partial Differential Equations, PDE’s in Higher Dimensions.
explains the following topics: The translation equation, The wave equation,
The diffusion equation, The Laplace equation, The Schrodinger equation,
Diffusion and equilibrium, Fourier series, Fourier transforms, Gradient and
divergence, Spherical harmonics.
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.
This note describes the
following topics: First Order Ordinary Differential Equations, Applications and
Examples of First Order ode’s, Linear Differential Equations, Second Order
Linear Equations, Applications of Second Order Differential Equations, Higher
Order Linear Differential Equations, Power Series Solutions to Linear
Differential Equations, Linear Systems, Existence and Uniqueness Theorems,
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.