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Elements of Vector Algebra and Linear Space Theory.

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

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

Eigenvalues and Eigenvectors of Matrices. Methods for Finding Them.

Double vector product

Vector and Mixed Product of Vectors.

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

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).