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Elements of Vector Algebra and Linear Space Theory.

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

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

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

Coordinate transformation. Transition matrix.

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

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

Eigenvalues and Eigenvectors of Matrices. Methods for Finding Them.

Vector and Mixed Product of Vectors.

Double vector product

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).