systems of equations
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Another example of using substitution to solve a first order homogeneous differential equations.
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Systems consisting of pendulums and springs can freely oscillate at their natural frequencies (also called normal modes). When we expose a system to a wide spectrum of frequencies, the response will be very large at the normal mode frequencies (resonances) of that system. Examples include musical instruments (standing waves on violin strings and pressure waves in wind instruments), and torsional standing waves on a bridge driven by strong winds.
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Graphing linear equations.
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U06_L3_T1_we3 Graphing Systems of Inequalities.
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U06_L3_T1_we1 Graphing systems of inequalities.
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U06_L3_T1_we2 Graphing systems of inequalities 2.
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U06_L3_T1_we3 Graphing systems of inequalities 3.
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Genetics controls evolution. There are four major genetic systems, which are combinations of sexual/asexual and haploid/diploid. In all genetic systems, adaptive genetic change tends to start out slow, accelerate in the middle, and occur slowly at the end. Asexual haploids can change the fastest, while sexual diploids usually change the slowest. Gene frequencies in large populations only change if the population undergoes selection.
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Raikes talks about how Microsoft's success at innovating business models equals its success in technology innovation. Before Microsoft, there was no market for a company that did operating systems. The business model to license operating systems was novel and helped to propel Microsoft to success.
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Using an integrating factor to make a differential equation exact.
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Now that we've made the equation exact, let's solve it!
