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Elements of Vector Algebra and Linear Space Theory.

Polar, cylindrical, and spherical coordinate systems. Transition formulas.

Linear combinations, linear dependence of vectors. Collinear and coplanar vectors.

Projections of a vector. Direction cosines. Cauchy-Schwarz inequality.

Basis of a linear space. Decomposition of a vector by basis.

Coordinate transformation. Transition matrix.

Scalar product of vectors, properties. Length of vectors. Angle between vectors.

Eigenvalues and Eigenvectors of Matrices. Methods for Finding Them.

Double vector product

Operations with geometric vectors.

Vector and Mixed Product of Vectors.

Tables and Formulas

Derivative Table.

Table of Derivatives of Composite Functions.

Table of Higher Order Derivatives.

Table of Integrals

Taylor Series

Comparison of functions O(f) and o(f).