1. Canonical protein dynamics c: Qualitative graphical solution to differential equation

    04:12

    from David Liao / Added

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    We sketch a slope field corresponding to the differential equation derived in the previous video. We use this slope field to draw a qualitative curve describing how the number of copies of protein…

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    • Canonical protein dynamics b: Differential equation and flowchart

      09:50

      from David Liao / Added

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      We derive a differential equation approximating the time-rate of change of the number of copies of protein in the cell modeled by the animation in the previous video. This differential equation reads,…

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      • Stochasticity d: Memory-free Markov processes and their representations

        04:46

        from David Liao / Added

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        Markov models are often used when developing mathematical models of systems which partially or more fully display aspects associated with stochasticity (depending on how fully a system displays aspects…

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        • Stochasticity c: Fundamentally indeterministic processes

          05:03

          from David Liao / Added

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          In the previous two videos, deterministic systems displayed dynamics with aspects associated with stochasticity. In contrast, some systems not only mimic some aspects associated with stochasticity,…

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          • Stochasticity b: Practically unpredictable deterministic dynamics

            04:29

            from David Liao / Added

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            In a deterministic system with complicated interactions, small differences in initial conditions can quickly avalanche into qualitative differences in dynamics. Since initial conditions can only be…

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            • Numbers d: Infinity is not a number

              01:42

              from David Liao / Added

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              Infinity is not a number. There is no tick mark on the number line labeled "infinity."

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              • Numbers c: Visual representations of numbers

                02:28

                from David Liao / Added

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                Numbers can be represented using a number line, a wedge, and place-value representation. The application of memorized rules for performing arithmetic on numerals formatted in place-value representation…

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                • Numbers b: Bose-Einstein statistics

                  04:40

                  from David Liao / Added

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                  The analysis of a system of particles display Bose-Einstein statistics is an example of a situation in which it is important to be aware whether we are thinking of numbers in terms of distinct manipulatives…

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                  • Curve fitting c: Checklist for undergraduate curve fitting

                    03:45

                    from David Liao / Added

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                    Using the concepts developed in the preceding two videos, we present a checklist of steps necessary for performing fitting of mathematical curves to data with error bars. These steps include checking…

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                    • Curve fitting b: Minimizing chi-squared

                      13:38

                      from David Liao / Added

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                      We slightly modify the definition of chi-squared developed in the previous video for the situation in which a "correct" curve has not been theoretically determined beforehand. We choose a "best guess"…

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