Mathematics 1000-1CHMMAT1

Definitions of elementary functions: sine, cosine, tangent, logarithm,
exponential function, root functions. Limits of functions. Continuity:
intermediate value theorem, Weierstrass Maximum Principle. Definition of
the derivative. Tangent to the graph of the function. Differentiation
rules. Sketching graphs of functions: monotonicity, locally extreme
values. Taylor formula, L'Hopital's rule. Taylor series. Primitive
functions. Simple integrals. Basic techniques of integration:
substitution and integration by parts. Definite integral. Basic
applications of integrals: area of plane sets bounded by graphs of two
functions, volume of a solid as an integral of area of plane sections,
length of a curve. Complex numbers: absolute value, argument, de
Moivre's formula. Matrices and determinants. Linearity with regard to
columns or rows, skew symmetry, row reduction, Cramer's formulae,
eigenvalues. Linear spaces. Several-variable functions: continuity and
partial derivatives, Jacobian matrix, gradient, vectors tangent to a
level surface of a differentiable function. Locally extreme values and
saddles.