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 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 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 book explains the following topics: 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.

This note
gives an understanding of numerical methods for the solution of ordinary and
partial differential equations, their derivation, analysis and applicability.

This book covers
the following topics: Laplace's equations, Sobolev spaces, Functions of one
variable, Elliptic PDEs, Heat flow, The heat equation, The Fourier transform,
Parabolic equations, Vector-valued functions and Hyperbolic equations.

This is a textbook for an introductory course on linear partial
differential equations (PDEs) and initial/boundary value problems (I/BVPs). It
also provides a mathematically rigorous introduction to Fourier analysis
which is the main tool used to solve linear PDEs in Cartesian coordinates.

This book covers the following
topics: Sequences, limits, and difference equations, Functions and their properties,
Best affine approximations, Integration, Polynomial approximations and Taylor
series, transcendental functions, The complex plane and Differential equations.

These notes are a concise understanding-based presentation of the
basic linear-operator aspects of solving linear differential equations.
Topics covered includes: Operators and Linear Combinations, Homogeneous
linear equations, Complex Exponentials and Real Homogeneous Linear
Equations, Non-homogeneous linear equations and Systems of Linear
Differential Equations.