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How to solve initial value problems
 
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Free ebook http://tinyurl.com/EngMathYT A basic example showing how to solve an initial value problem involving a separable differential equation.
Views: 200936 Dr Chris Tisdell
Initial Value Problem (KristaKingMath)
 
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► My Integrals course: https://www.kristakingmath.com/integrals-course Initial Value Problem calculus example. ● ● ● GET EXTRA HELP ● ● ● If you could use some extra help with your math class, then check out Krista’s website // http://www.kristakingmath.com ● ● ● CONNECT WITH KRISTA ● ● ● Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;) Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!” So I started tutoring to keep other people out of the same aggravating, time-sucking cycle. Since then, I’ve recorded tons of videos and written out cheat-sheet style notes and formula sheets to help every math student—from basic middle school classes to advanced college calculus—figure out what’s going on, understand the important concepts, and pass their classes, once and for all. Interested in getting help? Learn more here: http://www.kristakingmath.com FACEBOOK // https://www.facebook.com/KristaKingMath TWITTER // https://twitter.com/KristaKingMath INSTAGRAM // https://www.instagram.com/kristakingmath/ PINTEREST // https://www.pinterest.com/KristaKingMath/ GOOGLE+ // https://plus.google.com/+Integralcalc/ QUORA // https://www.quora.com/profile/Krista-King
Views: 183350 Krista King
Finding particular linear solution to differential equation | Khan Academy
 
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Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/differential-equations/first-order-differential-equations/differential-equations-intro/e/introduction-to-differential-equations-and-initial-value-problems?utm_source=YT&utm_medium=Desc&utm_campaign=DifferentialEquations Watch the next lesson: https://www.khanacademy.org/math/differential-equations/first-order-differential-equations/differential-equations-intro/v/creating-a-slope-field?utm_source=YT&utm_medium=Desc&utm_campaign=DifferentialEquations Missed the previous lesson? https://www.khanacademy.org/math/differential-equations/first-order-differential-equations/differential-equations-intro/v/differential-equation-introduction?utm_source=YT&utm_medium=Desc&utm_campaign=DifferentialEquations Differential Equations on Khan Academy: Differential equations, separable equations, exact equations, integrating factors, homogeneous equations. About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content. For free. For everyone. Forever. #YouCanLearnAnything Subscribe to KhanAcademy’s Differential Equations channel:: https://www.youtube.com/channel/UCxSQHGkaDv8UKXE0TUbsOIg?sub_confirmation=1 Subscribe to KhanAcademy: https://www.youtube.com/subscription_center?add_user=khanacademy
Views: 625474 Khan Academy
Solving Separable First Order Differential Equations - Ex 1
 
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Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! THERE IS A MISTAKE IN THIS VIDEO; CHECK OUT THE COMMENTS! SORRY! Separable Diff Eq Example #2, with no mistake! http://www.youtube.com/watch?v=XExEixAPK6s For more FREE math videos, visit http://PatrickJMT.com !! Solving Separable First Order Differential Equations - Ex 1. One complete example is shown of solving a separable differential equation.
Views: 823061 patrickJMT
Ex 3:  Solve a Linear First-Order Differential Equation (Initial Value Problem)
 
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This video explains how to find the particular solution to a linear first order differential equation. The solution is verified graphically. Video Library: http://mathispower4u.com Searcy by Topic: http://mathispower4u.wordpress.com
Views: 30570 Mathispower4u
Exact Differential Equations
 
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Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! Exact Differential Equations - In this video I show what it means for a differential equation to be exact and then one solve one problem. For more free math videos, visit http://PatrickJMT.com
Views: 646947 patrickJMT
Cauchy-Euler Initial Value Problem
 
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This video provides an example of how to solve an initial value problem involving a second order homogeneous Cauchy-Euler differential equation. Site: http://mathispower4u.com
Views: 27027 Mathispower4u
Euler's Method - Another Example #1
 
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Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! Euler's Method - Another Example #1. In this video, I show another example of using Euler's method to solve a differential equation. (Ok, we do not find an exact solution when doing this method; rather we are approximating the solution!)
Views: 242337 patrickJMT
ODE | Initial value problems for second order equations
 
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Examples and explanations for a course in ordinary differential equations. ODE playlist: http://www.youtube.com/playlist?list=PLwIFHT1FWIUJYuP5y6YEM4WWrY4kEmIuS We define and solve an initial value problem for a second order linear differential equation, using solutions found earlier. We also discuss the idea of being able to solve *any* initial value problem.
Views: 45473 commutant
Power Series Solutions of Differential Equations
 
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Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! Example 2: http://www.youtube.com/watch?v=dGoQ4j-SvXM Power Series Solutions of Differential Equations - In this video, I show how to use power series to find a solution of a differential equation. This is a SIMPLE example and the final solution is very NICE compared to what would normally happen with a more complicated differential equation, so please be aware of that!
Views: 374460 patrickJMT
Mod-01 Lec-41 Solving Ordinary Differential Equations - Initial Value Problems
 
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Advanced Numerical Analysis by Prof. Sachin C. Patwardhan,Department of Chemical Engineering,IIT Bombay.For more details on NPTEL visit http://nptel.ac.in
Views: 2200 nptelhrd
The Logistic Equation and the Analytic Solution
 
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Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! The Logistic Equation and the Analytic Solution. In this video, I find the analytic solution to the logistic differential equation.
Views: 115124 patrickJMT
General solutions and initial value problems (differential equations)
 
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Check out http://www.engineer4free.com for more free engineering tutorials and math lessons! Differential Equations Tutorial: General solutions and initial value problems.
Views: 5539 Engineer4Free
The "Classical" Method for Solving Differential Equations
 
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http://adampanagos.org In this course we've shown how the full solution to a differential equation with initial conditions and an arbitrary signal f(t) can be found by summing the zero-input response and zero-state response. A more "classical" approach to this problem involves breaking the solution into the natural response and forced response, where the form of the forced response is "guessed" or looked up in a table based on the form of the input signal. This is a common way of solving the equation as usually presented in a differential equations course. This video makes some general comments and compares these two approaches. If you enjoyed my videos please "Like", "Subscribe", and visit http://adampanagos.org to setup your member account to get access to downloadable slides, Matlab code, an exam archive with solutions, and exclusive members-only videos. Thanks for watching! -~-~~-~~~-~~-~- Checkout my newest video: "Signal Operations: Time Scaling, Downsampling, and Upsampling" https://www.youtube.com/watch?v=RWM-zmyDKp8 -~-~~-~~~-~~-~-
Views: 2544 Adam Panagos
Solving Differential equations using Mathematica
 
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How to solve differential equations in Mathematica. Solving First Order and Second Order Differential equations Solving Differential Equations with boundary conditions, i.e. finding the arbitrary constants. Enjoy, and leave your comments
Views: 85294 Hifas Faiz
Power Series Solutions of Differential Equations, Ex 2
 
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Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! Power Series Solutions of Differential Equations - In this video, I show how to use power series to find a solution of a differential equation. This is a SIMPLE example and the final solution is very NICE compared to what would normally happen with a more complicated differential equation, so please be aware of that!
Views: 210066 patrickJMT
Verifying Solutions to Differential Equations
 
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This video verifies solutions to differential equations when given the a function solution. Search Library at http://mathispower4u.wordpress.com
Views: 53863 Mathispower4u
ODE Solution.avi
 
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This clips shows how to solve a simple differential equation in MathCad. I show how to solve an initial value problem using the Odesolve command in MathCad and then solve it again using a finite difference approximation. Along the way, I show how the solution to the equation is just a specific path through a vector field. The path taken by the solution is defined by the initial value.
Views: 21606 purdueMET
Separable differential equations introduction | First order differential equations | Khan Academy
 
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Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/differential-equations/first-order-differential-equations/separable-equations/e/separable-differential-equations?utm_source=YT&utm_medium=Desc&utm_campaign=DifferentialEquations Watch the next lesson: https://www.khanacademy.org/math/differential-equations/first-order-differential-equations/separable-equations/v/particular-solution-to-differential-equation-example?utm_source=YT&utm_medium=Desc&utm_campaign=DifferentialEquations Missed the previous lesson? https://www.khanacademy.org/math/differential-equations/first-order-differential-equations/differential-equations-intro/v/differential-equation-from-slope-field?utm_source=YT&utm_medium=Desc&utm_campaign=DifferentialEquations Differential Equations on Khan Academy: Differential equations, separable equations, exact equations, integrating factors, homogeneous equations. About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content. For free. For everyone. Forever. #YouCanLearnAnything Subscribe to KhanAcademy’s Differential Equations channel:: https://www.youtube.com/channel/UCxSQHGkaDv8UKXE0TUbsOIg?sub_confirmation=1 Subscribe to KhanAcademy: https://www.youtube.com/subscription_center?add_user=khanacademy
Views: 494314 Khan Academy
Particular solution to differential equation example | Khan Academy
 
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Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/differential-equations/first-order-differential-equations/separable-equations/e/separable-differential-equations?utm_source=YT&utm_medium=Desc&utm_campaign=DifferentialEquations Watch the next lesson: https://www.khanacademy.org/math/differential-equations/first-order-differential-equations/separable-equations/v/separable-differential-equations?utm_source=YT&utm_medium=Desc&utm_campaign=DifferentialEquations Missed the previous lesson? https://www.khanacademy.org/math/differential-equations/first-order-differential-equations/separable-equations/v/separable-differential-equations-introduction?utm_source=YT&utm_medium=Desc&utm_campaign=DifferentialEquations Differential Equations on Khan Academy: Differential equations, separable equations, exact equations, integrating factors, homogeneous equations. About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content. For free. For everyone. Forever. #YouCanLearnAnything Subscribe to KhanAcademy’s Differential Equations channel:: https://www.youtube.com/channel/UCxSQHGkaDv8UKXE0TUbsOIg?sub_confirmation=1 Subscribe to KhanAcademy: https://www.youtube.com/subscription_center?add_user=khanacademy
Views: 284263 Khan Academy
ODE | Phase diagrams
 
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Examples and explanations for a course in ordinary differential equations. ODE playlist: http://www.youtube.com/playlist?list=PLwIFHT1FWIUJYuP5y6YEM4WWrY4kEmIuS In this video we explain how to construct a phase diagram (or phase portrait) for an autonomous first order differential equation using the example of the logistic equation. With one dependent variable, our phase diagram is a phase line. We also give examples of stable and unstable equilibrium points.
Views: 99027 commutant
Mod-07 Lec-25 Ordinary Differential Equations (initial value problems) Part 1
 
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Computational Techniques by Dr. Niket Kaisare, Department of Chemical Engineering, IIT Madras. For more details on NPTEL visit http://nptel.iitm.ac.in
Views: 8356 nptelhrd
Ex 1:  Initial Value Problem - Separation of Variables
 
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This video provides an example of how to solve an initial value problem that requires the technique of separation of variables. Video Library: http://mathispower4u.com Search by Topic: http://mathispower4u.wordpress.com
Views: 8034 Mathispower4u
Ex 2: Initial Value Problem Using Separation of Variables (Square Root)
 
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This video provides an example of how to solve an initial value problem using separation of variables. Site: http://mathispower4u.com
Views: 4899 Mathispower4u
Solving Differential Equations with Power Series
 
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How to generate power series solutions to differential equations
Views: 176420 Houston Math Prep
Mixing Problems and Separable Differential Equations
 
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Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! Mixing Problems and Separable Differential Equations. In this video, I discuss how a basic type of mixing problem can be solved by recognizing that the situation is modeled by a separable differential equation.
Views: 303412 patrickJMT
Solve Differential Equations in MATLAB and Simulink
 
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This introduction to MATLAB and Simulink ODE solvers demonstrates how to set up and solve either one or multiple differential equations. The equations can be linear or nonlinear.
Views: 104244 APMonitor.com
Initial-value problems- (piecewise defined function as the forcing function)[5]
 
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learn more: http://math.rareinfos.com/category/courses/solutions-differential-equations/ Complete Solutions of Problems in Differential Equation
Views: 6582 Rareinfos tun
The Logistic Equation and Models for Population - Example 1, part 1
 
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Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! The Logistic Equation and Models for Population - Example 1, part 1. In this video, we have an example where biologists stock a lake with fish and after one year the population has tripled. Knowing the carrying capacity, I find a formula for the the population at time ' t ' using the analytic solution.
Views: 201400 patrickJMT
Boundary value problem, second-order homogeneous differential equation, complex conjugate roots
 
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► My Differential Equations course: https://www.kristakingmath.com/differential-equations-course Learn how to solve a boundary value problem given a second-order homogeneous differential equation and two initial conditions. In this particular problem, the roots of the equation are complex conjugate roots and the general solution to the differential equation is written with alpha and beta. ● ● ● GET EXTRA HELP ● ● ● If you could use some extra help with your math class, then check out Krista’s website // http://www.kristakingmath.com ● ● ● CONNECT WITH KRISTA ● ● ● Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;) Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!” So I started tutoring to keep other people out of the same aggravating, time-sucking cycle. Since then, I’ve recorded tons of videos and written out cheat-sheet style notes and formula sheets to help every math student—from basic middle school classes to advanced college calculus—figure out what’s going on, understand the important concepts, and pass their classes, once and for all. Interested in getting help? Learn more here: http://www.kristakingmath.com FACEBOOK // https://www.facebook.com/KristaKingMath TWITTER // https://twitter.com/KristaKingMath INSTAGRAM // https://www.instagram.com/kristakingmath/ PINTEREST // https://www.pinterest.com/KristaKingMath/ GOOGLE+ // https://plus.google.com/+Integralcalc/ QUORA // https://www.quora.com/profile/Krista-King
Views: 42348 Krista King
Numerically Solve ODEs with Mathematica 1
 
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Demonstrates how to use the Mathematica function NDSolve to solve two ordinary differential equations numerically. This is an initial value problem for a batch reactor with a single reaction. Part 1 of 2. Made by faculty at the University of Colorado Boulder Department of Chemical and Biological Engineering. Check out our Engineering Computing playlists: https://www.youtube.com/user/LearnChemE/playlists?sort=dd&view=50&shelf_id=4 Check out the Kinetics Review playlist here: http://www.youtube.com/playlist?list=PL4xAk5aclnUiX_3Z-kR-ExMr5z0wMn1Bx Numerically Solve ODEs with Mathematica 2: https://youtu.be/AFD0UhWWU-Q Are you using a textbook? Check out our website for videos organized by textbook chapters: http://www.learncheme.com/screencasts
Views: 3944 LearnChemE
Ex 1: Solve an Autonomous DE IVP - Logistic Growth Using Separation of Variables
 
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This video explains how to solve an initial value problem involving an autonomous differential equation. (logistic growth model) http://mathispower4u.com
Views: 2320 Mathispower4u
Ex 2: Solve an Autonomous DE IVP - Logistic Growth Using Separation of Variables
 
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This video explains how to solve an initial value problem involving an autonomous differential equation. (logistic growth model) http://mathispower4u.com
Views: 2284 Mathispower4u
Heat equation: How to solve
 
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How to solve the heat equation on the whole line with some initial condition. Suppose one has a function u that describes the temperature at a given location (x, y, z). This function will change over time as heat spreads throughout space. The heat equation is used to determine the change in the function u over time. The rate of change of u is proportional to the "curvature" of u. Thus, the sharper the corner, the faster it is rounded off. Over time, the tendency is for peaks to be eroded, and valleys filled in. If u is linear in space (or has a constant gradient) at a given point, then u has reached steady-state and is unchanging at this point. One of the interesting properties of the heat equation is the maximum principle that says that the maximum value of u is either earlier in time than the region of concern or on the edge of the region of concern. This is essentially saying that temperature comes either from some source or from earlier in time because heat permeates but is not created from nothingness. This is a property of parabolic partial differential equations and is not difficult to prove mathematically (see below). Another interesting property is that even if u has a discontinuity at an initial time t = t0, the temperature becomes smooth as soon as t greater than t0. For example, if a bar of metal has temperature 0 and another has temperature 100 and they are stuck together end to end, then very quickly the temperature at the point of connection will become 50 and the graph of the temperature will run smoothly from 0 to 100. The heat equation is used in probability and describes random walks. It is also applied in financial mathematics for this reason. It is also important in Riemannian geometry and thus topology: it was adapted by Richard Hamilton when he defined the Ricci flow that was later used by Grigori Perelman to solve the topological Poincaré conjecture.
Views: 44730 Dr Chris Tisdell
Euler's method example #2: calculating error of the approximation
 
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Check out http://www.engineer4free.com for more free engineering tutorials and math lessons! Differential Equations Tutorial: Euler's method example #2: calculating error of the approximation.
Views: 20830 Engineer4Free
Homogeneous Second Order Linear Differential Equations
 
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Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! Homogeneous Second Order Linear Differential Equations - I show what a Homogeneous Second Order Linear Differential Equations is, talk about solutions, and do two examples. For more free math videos, visit http://PatrickJMT.com
Views: 530054 patrickJMT
Method of Characteristics: How to solve PDE
 
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Free ebook http://tinyurl.com/EngMathYT How to solve PDE via the method of characteristics. An example involving a semi linear PDE is presented, plus we discuss why the ideas work. Such a technique is used in solving a wide range of problems.
Views: 79189 Dr Chris Tisdell
Separation of Variables - Heat Equation Part 1
 
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We use Separation of Variables to find a general solution of the 1-d Heat Equation, including boundary conditions.
Differential Equations - A Logistic Model with Harvesting
 
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This homework problem comes from Section 3.2 in Zill's Intro to DE. In this video, we consider a differential equation of a logistic model with harvesting. We use a phase portrait to determine under what initial conditions the population will become extinct. We also solve the initial value problem to determine at what time the extinction would occur.
Views: 4004 SplineGuyMath
Exponential Growth / Population Growth Problem.
 
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Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! In this video, we know that a population is growing exponentially; we also know there were 200 bacteria 3 days ago and 1000 bacteria yesterday. How many bacteria will be present tomorrow?
Views: 321481 patrickJMT
Ex 1: Solve an Autonomous DE IVP - Logistic Growth (Shortcut)
 
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This video explains how to solve an initial value problem involving an autonomous differential equation. (logistic growth model) http://mathispower4u.com
Views: 557 Mathispower4u
Separable Differential Equation, Example 2
 
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Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! Separable Differential Equation, Example 2. In this video, I solve another separable differential equation.
Views: 334665 patrickJMT
Mod-05 Lec-24 Boundary Value Problems, Question of Stability in IVP Solution
 
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Mathematical Methods in Engineering and Science by Dr. Bhaskar Dasgupta,Department of Mechanical Engineering,IIT Kanpur.For more details on NPTEL visit http://nptel.ac.in
Views: 1305 nptelhrd
Introduction to autonomous differential equations
 
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See http://mathinsight.org/autonomous_differential_equation_introduction for context.
Views: 45545 Duane Nykamp
Ka Kb Kw pH pOH pKa pKb H+ OH- Calculations - Acids & Bases, Buffer Solutions , Chemistry Review
 
01:09:54
This general chemistry video tutorial focuses on acids and bases and buffer solutions. It shows you how to calculate the pH and pOH of the solution. It contains plenty of examples and practice problems to help you review for your next test or exam. It also contains calculations involving Ka, Kb, and Kw. General Chemistry Video Playlist: https://www.youtube.com/watch?v=bka20Q9TN6M&list=PL0o_zxa4K1BV-uX6wXQgyqZXvRd0tUUV0&index=3 Access to Premium Videos: https://www.patreon.com/MathScienceTutor Facebook: https://www.facebook.com/MathScienceTutoring/ Here is a list of topics: 1. The 6 common strong acids - HCl, HBr, HI, H2SO4, HNO3, HClO4 2. Weak Acids - HF, HNO2, H2SO3, H2CO3, NH4+, and HC2H3O2 3. Examples of Strong Bases - NaOH, KOH, LiOH, and Ca(OH)2 4. Strongs Acids - Ionize Completely - 100% 5. Ionization Equation of Strong and Weak Acids with Water 6. HCl, H+, Cl-, HF, H2O, H3O+, F- 7. Reversibility of Weak Acid Equation - ICE Table 8. Acid and Base Dissociation Constant Ka & Kb 9. Auto Ionization Constant of Water Kw = [H+][OH-] = 1 x 10^-14 10. How To Identify The Conjugate Acid and Conjugate Base 11. Bronsted Lowry Acid - Proton Donor, Bronsted Lowry Base - Proton Acceptor 12. How To Balance a Neutralization Equation 13. NH3 + H2O = NH4+ + OH- 14. HF + H2O = H3O+ + OH- 15. H2SO4 + KOH = H2O + K2SO4 16. HCl + NaOH = H2O + NaCl 17. H3PO4 + Mg(OH)2 = Mg3(PO4)2 + H2O 18. How To Find The pH of a Solution Given a Monoprotic Strong Acid 19. How To Find The pH Given a Weak Acid(HF) and Ka 20. How To Find pH, pOH, and [OH-] Given [H3O+] 21. How To The pH Given Grams and mL of KOH 22. How To Find pH Given Molarity of a Weak Base (NH3) and Kb 23. How To Find The pH of a Salt Given NH4Cl and NaF 24. How To Find The pH of a Buffer Solution Given Molarity of Ka 25. Buffer Solution - Weak Acid + Conjugate Weak Base 26. Henderson hasselbach Equation 27. pH = pKa + log (Base / Acid) 28. How To Find Ka From Kb 29. How To Find pKa and pKb Given Ka or Kb 30. How To Identify a Buffer Solution 31. List of Acid Base Formulas For Ka, Kb, Kw, pH, and pOH
Using Green's Functions to Solve Nonhomogeneous ODEs
 
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In this video, I describe how to use Green's functions (i.e. responses to single impulse inputs to an ODE) to solve a non-homogeneous (Sturm-Liouville) ODE subject to ANY arbitrary input f(x). All this involves is integrating the Green's function with the input f(x) over the domain. The input, by the way, is the function that makes the ODE non-homogeneous. This approach is made possible because of the orthogonality relation of the Sturm-Liouville Theorem and the fact that the eigenfunctions of a REGULAR Sturm-Liouville problem form a complete set. By the way, at 2:05, I say that we can make the eigenvalue 'any real number we want'. I should clarify that and say that we can make the 'n' in lambda_n 'whatever integer we want'. Lambda is still restricted by the boundary conditions. Nonetheless, the point that a smaller set of functions (eigenfunctions of a REGULAR Sturm-Liouville Problem) can be used to describe a larger set of functions (all nice/smooth functions) still holds. Questions/requests? Let me know in the comments! The oft-requested PDE version of my Green's Function video is coming out soon, so stay tuned! Prereqs: Know the Sturm-Liouville Theorem. Also, this playlist will help: https://www.youtube.com/playlist?list=PLdgVBOaXkb9ATVsK2Q84ghjBgIk5faHNc Sturm-Liouville Video: https://www.youtube.com/watch?v=_F0ck1JncLE Lecture Notes: https://drive.google.com/open?id=0BzC45hep01Q4cW5WU1ZkeHBqTnc Patreon: https://www.patreon.com/user?u=4354534 Twitter: https://twitter.com/FacultyOfKhan/
Views: 19426 Faculty of Khan
Second-order Differential Equations with Constant Driving Functions
 
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In this lecture we summarize a method for solving second-order differential equations with constant driving functions, and show how to use initial conditions to solve for the natural response of the system. We also explain the situations that lead to over damped, critically-damped and underdamped solutions.
Views: 5104 Timothy Schulz
Ksp Chemistry Problems - Calculating Molar Solubility, Common Ion Effect, pH, ICE Tables
 
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This general chemistry video tutorial focuses on Ksp – the solubility product constant. It has plenty of examples and practice problems for you to work on to pass your next chemistry exam / test. Here is a list of topics: 1. How to Calculate Molar Solubility Using Ksp for AgCl and and Ca3(PO4)2 2. How to Convert Molar Solubility from M or mol/L to g/L 3. How to determine the concentration of the ions [Ag+], [Cl-], [Ca2+], [PO4 -3] 4. How To Find Ksp given molar solubility in moles per liter and grams per liter using PbCl2 and CuCl 5. Common Ion Effect – Calculating Molar solubility of CaF2 given Molarity of CaCl2 in a saturated solution 6. Calculating Molar Solubility of Al(OH)3 using Ksp and the pH of the solution 7. pH, pOH, [H+] and [OH-] equations and formulas 8. Le chatelier’s Principle – Chemical Equilibrium & Ksp – Reactant and Production Concentration 9. The effect of adding a common ion on solubility, dissolution, and precipitation 10. The effect of temperature on Ksp – Which way does the reaction shift? 11. The effect of adding CaCl2 to CaF2 on the pH of the solution 12. Solving for Ksp and Molar Solubility Using Ice Tables 13. How To Write The Equation or Equilibrium Expression For Ksp
20. Boundary Value Problem 1
 
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MIT 10.34 Numerical Methods Applied to Chemical Engineering, Fall 2015 View the complete course: http://ocw.mit.edu/10-34F15 Instructor: William Green Students learned numerical methods to solve ordinary differential equation with boundary value problems. License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
Views: 1660 MIT OpenCourseWare
❖ Lots of Limit Examples, Part 1 ❖
 
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Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! Lots of Limit Examples, Part 1. Here I start working through a bunch of random limit problems!
Views: 174583 patrickJMT