This is the fifth video in a series of (five) videos introducing differential questions. In it I use the phase line to reveal the similarity between all linear (first order) DEs and use that to come up with a method of solving them.
Курбан Байрам. Красивое поздравление на Курбан Байрам. Курбан Байрам 2020.
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Taylor polynomial calculation shortcuts - example 2
Taylor polynomial - an application to calculating a series
Taylor polynomial calculation shortcuts - theory and an example
An applied optimization problem
Optimization - a geometric example
Strategies for setting up applied optimization problems
Calculating the global maximum for a two-variable function
Logarithmic differentiation
Phase lines as a qualitative tool for analyzing differential equations
Solving linear ODEs using a phase-line inspired method
Some modelling applications that lead to linear (and one non-linear) differential equations
Slope fields as a qualitative tool to understand solutions to differential equations
Verifying solutions to differential equations and using ansatzes
Sketching Graphs - Rational Power Functions
Sketching Graphs - Critical points that are neither minima, maxima, nor inflection points.
Sketching Graphs - Minimum, Maximum, or Inflection point
The general product rule
Derivative notation
Finding the derivative of an inverse function
Implicit differentiation - infinite slopes on relations
Finding the derivative of arcsin(x)
More derivatives using logarithms - the general power rule and (x^x)'
Implicit differentiation
Exponential functions and their derivatives