Taylor polynomials and Leibniz' ruleA series of free Engineering Mathematics video lessons.
Taylor polynomials: functions of two variables This is a basic tutorial on how to calculate a Taylor polynomial for a function of two variables. The ideas are applied to approximate a difficult square root. Such concepts are seen in university mathematics.
Leibniz' rule: Integration via differentiation I discuss and solve an example where, given a simpler integral, a more complicated integral is evaluated through differentiation. The method features an application of Leibniz' rule for differentiating an integral. Such an example is seen in 2nd-year university mathematics.
Evaluating challenging integrals via differentiation: Leibniz rule I discuss and solve a challenging integral. The method involves differentiation and then the solution of the resultant differential equation. The so-called Leibniz rule for differentiating integrals is applied during the process. Such an example is seen in 2nd-year university mathematics.
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