Applied Mathematics in Engineering 1

Contents:

• Sets, numerical sets. Short review of high school material. Examples.
• Matrix algebra: matrices, matrix calculations, inverse matrix, matrix equations, determinants, inverse matrix calculation, systems of linear equations.
• Vector algebra: vectors, addition and subtraction of vectors, multiplication of a vector by a scalar, scalar product, vector product, linear dependence.
• Planes and lines in space.
• Sequences and series: neighborhood, convergence, limit, arithmetic and geometric sequence, series, geometric series.
• Functions of one variable: basic concepts, continuity of a function, limit of a function, properties of continuous functions, overview of elementary functions, function design. Examples
• Differential calculus: derivative of a function, geometric meaning of derivative, rules for differentiation, derivatives of elementary functions, differential, higher derivatives, use of derivative: extrema, inflections.