A First Course in Elementary Differential Equations

A First Course in Elementary Differential Equations

A First Course in Elementary Differential Equations

This
note covers the following topics: Qualitative Analysis, Existence and
Uniqueness of Solutions to First Order Linear IVP, Solving First Order Linear
Homogeneous DE, Solving First Order Linear Non Homogeneous DE: The Method of
Integrating Factor, Modeling with First Order Linear Differential Equations,
Additional Applications: Mixing Problems and Cooling Problems, Separable
Differential Equations, Exact Differential Equations, Substitution Techniques:
Bernoulli and Ricatti Equations, Applications of First Order Nonlinear
Equations, One-Dimensional Dynamics, Second Order Linear Differential Equations,
The General Solution of Homogeneous Equations, Existence of Many Fundamental
Sets, Second Order Linear Homogeneous Equations with Constant, Coefficients,
Characteristic Equations with Repeated Roots, The Method of Undetermined
Coefficients, Applications of Nonhomogeneous Second Order Linear Differential
Equations.

This
note covers the following topics: Qualitative Analysis, Existence and
Uniqueness of Solutions to First Order Linear IVP, Solving First Order Linear
Homogeneous DE, Solving First Order Linear Non Homogeneous DE: The Method of
Integrating Factor, Modeling with First Order Linear Differential Equations,
Additional Applications: Mixing Problems and Cooling Problems, Separable
Differential Equations, Exact Differential Equations, Substitution Techniques:
Bernoulli and Ricatti Equations, Applications of First Order Nonlinear
Equations, One-Dimensional Dynamics, Second Order Linear Differential Equations,
The General Solution of Homogeneous Equations, Existence of Many Fundamental
Sets, Second Order Linear Homogeneous Equations with Constant, Coefficients,
Characteristic Equations with Repeated Roots, The Method of Undetermined
Coefficients, Applications of Nonhomogeneous Second Order Linear Differential
Equations.

This note
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 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: Classification of Differential Equations, First
Order Differential Equations, Second Order Linear Equations, Higher Order Linear
Equations, The Laplace Transform, Systems of Two Linear Differential Equations,
Fourier Series, Partial Differential Equations.

This book covers the following topics: 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 explains the following topics: Existence
and Uniqueness, Systems, Stability, Sturm-Liouville Theory, First Order,
Quasi-Linear, Classification, Hyperbolic Problems, Elliptic Problems, Parabolic
Problems.

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 note covers the following topics
related to Partial Differential Equations: The Heat Equation, Separation
of Variables, Oscillating Temperatures, Spatial Temperature Distributions, The
Heat Flow into the Box, Specified Heat Flow, Electrostatics, Cylindrical
Coordinates.

These lecture notes are intended as a straightforward introduction to
partial differential equations which can serve as a textbook for undergraduate
and beginning graduate students. Topics covered includes: Equations of first
order, Classification, Hyperbolic equations, Fourier transform, Parabolic
equations and Elliptic equations of second order.

This note covers the following topics: Entropy and equilibrium, Entropy
and irreversibility, Continuum thermodynamics, Elliptic and parabolic equations,
Conservation laws and kinetic equations, Hamilton–Jacobi and related equations,
Entropy and uncertainty, Probability and differential equations.