Integration of Rational Functions

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Covers the integration of rational functions, decomposition into irreducible factors, and step-by-step integration examples.

Covers matrix rank, determinant, and decomposition in linear algebra.

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Covers the extension of the logarithm to complex numbers and explores the relationship with trigonometric functions.

Covers the integration of rational functions, including the decomposition into partial fractions and the use of complex zeros.

Explores linear applications, vector spaces, kernels, and invertibility in linear algebra.

Covers matrix representations of linear applications in R³ and the invariance of rank.

Explores Gram-Schmidt process, orthogonal projection, QR factorization, and least squares solutions for linear systems.

Explores complex numbers in reciprocal space and the Bragg condition, emphasizing linear algebra's importance for engineers.

Explains the step-by-step process of finding the singular value decomposition of a matrix.