"Mathematics". Faculty of Life Sciences. (Ya. Yakubov)

1. Real-valued functions of a single variable: the domain, the range, graphs, shifting graphs, increasing and decreasing, inverse functions, composite functions. Elementary functions: linear and quadratic, polynomials, power, exponential, logarithmic, trigonometric, hyperbolic, absolute value, integer. Informal definition of limit of functions, continuous functions. Number e as a limit, the limit of Sin(x) devided by x. The intermediate value theorem of Cauchy. Weierstrass theorem.
2. Derivative: derivative as a tangent slope, tangent and normal lines to functions. Calculating derivatives of polynomials, Sin(x), Cos(x). Differentiation rules, derivative of inverse functions. Parametrizations of plain curves and their derivatives. Implicit functions and their derivatives. Fermat, Rolle and Lagrange theorems.
3. Investigation of functions: extreme values, increasing and decreasing, concavity, asymptotics, graphs.
4. Minimum and maximum problems: in engineering, physics, biology, chemistry, economics.
5. Taylor and Maclaurin formulas: application in approximation. Bernoulli-l'Hopital's rule.
6. Integrals of functions of a single variable: antiderivative (indefinite integral), integral formulas, substitution, integral of rational functions, integration by parts, trigonometric substitutions, improper integral. Definite integral and area. The fundamental theorem of calculus, evaluating integrals. Applications of integrals: area between curves, the length of curves, volumes of solids of revolution, moments and centers of mass.
7. Ordinary differential equations of the first order: separation of variables, linear equations, existence and uniqueness of a solution of equations with an initial condition, solution of problems using ODE.