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Elements of Vector Algebra and Linear Space Theory.

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

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

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

Coordinate transformation. Transition matrix.

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

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

Eigenvalues and Eigenvectors of Matrices. Methods for Finding Them.

Double vector product

Vector and Mixed Product of Vectors.

Operations with geometric 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).