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<p></p>
<p>We can copy Taylor's series for <em>e<sup>x</sup> </em>to define <em>e<sup>At</sup></em> for a matrix <em>A</em>. If <em>A</em> is diagonalizable, we can use Λ to find the exact value of <em>e<sup>At</sup></em>. This allows us to solve systems of differential equations <em>du / dt = Au</em> the same way we solved equations like <em>dy / dt = ky.</em></p>
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<p><a href="/assets/courseware/v1/fa8832cb6da4c581bdc4fb6223590629/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18_06_Unit_II_3.0_Chinesetrans.pdf" target="[object Object]">Recitation video transcript (PDF)</a></p>
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<h2 class="hd hd-2 unit-title">Problems and Solutions</h2>
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<p>Work the problems on your own and check your answers when you're done.</p>
<p><a href="/assets/courseware/v1/5191b9fd9b8252001d41dd65cc8b177b/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_II_3.0_Exercises.pdf" target="[object Object]">Exercises on differential equations and e<sup>At</sup> (PDF)</a></p>
<p><a href="/assets/courseware/v1/52a3f2b171a41a2c26ef6cc11c50962c/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_II_3.0_Solutions.pdf" target="[object Object]">Solutions to differential equations and e<sup>At</sup> (PDF)</a></p>
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