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 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 note
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.
This note covers the following topics: Notion of ODEs, Linear ODE of
1st order, Second order ODE, Existence and uniqueness theorems, Linear equations
and systems, Qualitative analysis of ODEs, Space of solutions of homogeneous
systems, Wronskian and the Liouville formula.
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 describes
the following topics: First Order Differential Equations, N-th Order
Differential Equations, Linear Differential Equations, Laplace Transforms,
Inverse Laplace Transform, Systems Of Linear Differential Equations, Series
Solution Of Linear Differential Equations.
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.
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 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.
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.
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.