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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §5.3 Summation versus Integration, #34 · Calculus · Integrals

The Schwarz inequality is

The Schwarz inequality is $(\sum_{1}^{n} a_{i} b_{i})^{2} \leq (\sum_{1}^{n} a_{i}^{2}) (\sum_{1}^{n} b_{i}^{2})$ . Compute both sides if $a_{1} = 2$ , $a_{2} = 3$ , $b_{1} = 1$ , $b_{2} = 4$ . Then compute both sides for any $a_{1}, a_{2}, b_{1}, b_{2}$ . The proof in Section 11.1 uses vectors.

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §5.3 Summation versus Integration, #34

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