Differential equations | Recurrence relations
In mathematics and particularly in dynamic systems, an initial condition, in some contexts called a seed value, is a value of an evolving variable at some point in time designated as the initial time (typically denoted t = 0). For a system of order k (the number of time lags in discrete time, or the order of the largest derivative in continuous time) and dimension n (that is, with n different evolving variables, which together can be denoted by an n-dimensional coordinate vector), generally nk initial conditions are needed in order to trace the system's variables forward through time. In both differential equations in continuous time and difference equations in discrete time, initial conditions affect the value of the dynamic variables (state variables) at any future time. In continuous time, the problem of finding a closed form solution for the state variables as a function of time and of the initial conditions is called the initial value problem. A corresponding problem exists for discrete time situations. While a closed form solution is not always possible to obtain, future values of a discrete time system can be found by iterating forward one time period per iteration, though rounding error may make this impractical over long horizons. (Wikipedia).
Find Two Solutions to a First Order Initial Value Problem
This video explains how to find two solutions to a first order differential equation initial value problem that does not have a unique solution. Library: http://mathispower4u.com Search: http://mathispower4u.wordpress.com
From playlist Introduction to Differential Equations
Find Values Excluded to Guarantee Existence and Uniqueness of Solution to a IVP - y'=f(t,y)
This video explains how to the values of a differential equation must be excluded to guarantee a unique solution exists. dy/dt=f(t,y) http://mathispower4u.com
From playlist Linear First Order Differential Equations: Interval of Validity (Existence and Uniqueness)
Introduction to Initial Value Problems (Differential Equations 4)
https://www.patreon.com/ProfessorLeonard Exploring Initial Value problems in Differential Equations and what they represent. An extension of General Solutions to Particular Solutions.
From playlist Differential Equations
Intro to Initial Value Problems
This video introduces initial value problems. The general solution is given. Video Library: http://mathispower4u.com
From playlist Introduction to Differential Equations
Initial Condition Particular Solution for Antiderivative Calculus 1 AB
If given an Initial Condition (which is a given point a graph passes through) we are able to find a Particular Solution. In other words, instead of just finding a general antiderivative we will be able to find the antiderivative given a derivative and a point the original function passes
From playlist Calculus
Heat Equation Initial Condition
Heat Equation with Initial Condition In this video, I find a solution of the heat equation with an initial condition and rigorously prove that the solution works, namely it satisfies both the equation and the initial condition. The study of this is very delicate, and uses a lot of interes
From playlist Partial Differential Equations
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Initial Value Problems
From playlist Differential Equations
Differential Equation - 2nd Order (8 of 54) The Initial Value Problem
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain the initial value problem on the 2nd order differential equation y”+p(x)y'+q(x)y=f(x). Next video can be seen at: https://youtu.be/9TvmLBytAsU
From playlist DIFFERENTIAL EQUATIONS 11 - 2nd ORDER, A COMPLETE OVERVIEW
Mod-01 Lec-31 Initial Value Problem
Elementary Numerical Analysis by Prof. Rekha P. Kulkarni,Department of Mathematics,IIT Bombay.For more details on NPTEL visit http://nptel.ac.in
From playlist NPTEL: Elementary Numerical Analysis | CosmoLearning Mathematics
Mod-04 Lec-15 Well-posedness and Examples of IVP
Ordinary Differential Equations and Applications by A. K. Nandakumaran,P. S. Datti & Raju K. George,Department of Mathematics,IISc Bangalore.For more details on NPTEL visit http://nptel.ac.in.
From playlist IISc Bangalore: Ordinary Differential Equations and Applications | CosmoLearning.org Mathematics
Numerical Integration of Chaotic Dynamics: Uncertainty Propagation & Vectorized Integration
This video introduces the idea of chaos, or sensitive dependence on initial conditions, and the importance of integrating a bundle of trajectories to propagate uncertainty. We also explore how to vectorize numerical integration in Python and Matlab to make the algorithm orders of magnitud
From playlist Engineering Math: Differential Equations and Dynamical Systems
Linear Systems of Differential Equations with Forcing: Convolution and the Dirac Delta Function
This video derives the fully general solution to a matrix system of linear differential equation with forcing in terms of a convolution integral. We start off simple, by breaking the problem down into simple sub-problems. One of these sub-problems is deriving the response of the system t
From playlist Engineering Math: Differential Equations and Dynamical Systems
Thinking in Systems - Level 6 - Boundary and Initial Conditions
Thinking Slides: https://docs.google.com/presentation/d/1CdqEqXxOs0oY_kAi11pDgBxCd8Db6w4oY8nLeWgcU0Q/template/preview The Wonder of Science: https://thewonderofscience.com/mlccc46 In this video Paul Andersen shows conceptual thinking in a mini-lesson on boundary and initial conditions wit
From playlist Conceptual Thinking Mini-Lessons
Solving PDEs with the Laplace Transform: The Heat Equation
This video shows how to solve Partial Differential Equations (PDEs) with Laplace Transforms. Specifically we solve the heat equation on a semi-infinite domain. @eigensteve on Twitter eigensteve.com databookuw.com %%% CHAPTERS %%% 0:00 Overview and Problem Setup 7:03 How Classic Meth
From playlist Engineering Math: Vector Calculus and Partial Differential Equations
Equilibrium Solutions and Stability of Differential Equations (Differential Equations 36)
https://www.patreon.com/ProfessorLeonard Exploring Equilibrium Solutions and how critical points relate to increasing and decreasing populations.
From playlist Differential Equations
What We've Learned from NKS Chapter 6: Starting from Randomness
In this episode of "What We've Learned from NKS", Stephen Wolfram is counting down to the 20th anniversary of A New Kind of Science with [another] chapter retrospective. If you'd like to contribute to the discussion in future episodes, you can participate through this YouTube channel or th
From playlist Science and Research Livestreams
Forward Sensitivity Approach to dynamic data assimilation - S. Lakshmivarahan
PROGRAM: Data Assimilation Research Program Venue: Centre for Applicable Mathematics-TIFR and Indian Institute of Science Dates: 04 - 23 July, 2011 DESCRIPTION: Data assimilation (DA) is a powerful and versatile method for combining observational data of a system with its dynamical mod
From playlist Data Assimilation Research Program
ME565 Lecture 25: Laplace transform solutions to PDEs
ME565 Lecture 25 Engineering Mathematics at the University of Washington Laplace transform solutions to PDEs Notes: http://faculty.washington.edu/sbrunton/me565/pdf/L25.pdf Course Website: http://faculty.washington.edu/sbrunton/me565/ http://faculty.washington.edu/sbrunton/
From playlist Engineering Mathematics (UW ME564 and ME565)
Introduction to Loops in Java | Loops in Java Tutorial | Edureka
Watch Sample Class Recording: http://www.edureka.co/java-j2ee-soa-training?utm_source=youtube&utm_medium=referral&utm_campaign=loops A situation, when there is a need to execute a block of code, number of times, it is referred to as loop. Watch this video to know more about loops, loopin
From playlist Java Online Training Videos
Applying the first derivative test to a polynomial to determine the increasing and decreasing
👉 Learn how to find the extreme values of a function using the first derivative test. The extreme values of a function are the points/intervals where the graph is decreasing, increasing, or has an inflection point. A method that can be used to obtain the extreme values of a function is the
From playlist First Derivative Test for Functions