Mathematics A 1000-1CHJMATA2

Definite integral. Riemann sums. 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, area of surface of revolution, center of mass. Improper integrals. Linear spaces, including some functional spaces like
polynomials or polynomials of bounded degree, differentiable functions. Complex numbers: absolute value, argument, de Moivre's formula, exponential with complex exponent, Euler's formulae. Several-variable functions: continuity and partial derivatives, Jacobian matrix, gradient, vectors tangent to a level surface of a
differentiable function. Taylor's formula (second order). Locally extreme values and saddles. Separable differential equations. Linear differential equations of first and second order. Quasi-polynomials. Solving second order ODE's with constant coefficients and quasi-polynomial right-hand side. Some iterated integrals. More general areas, volumes and mass centers.