Mathematical Analysis
Limit of a Function
Sequence. Boundedness and monotonicity of a sequence. Limit of a sequence.
The limit of a function, computing limits.
Differentiability of a Function, Its Differential, and Derivative.
The derivative of a function. Calculating first-order derivatives.
The differential of a function. First-order differentials.
The geometric interpretation of the derivative.
The derivative of an inverse function.
Approximate calculations using differentials
Higher Order Derivatives and Differentials. Taylor's Formula.
Calculation of higher-order derivatives.
Calculation of higher-order differentials.
Function analysis using derivatives.
Graphs of functions and curves can be represented in Cartesian or polar coordinate systems.
The indefinite integral
Antiderivative and indefinite integral
Integration using variable substitution
Integration of rational functions.
Integration of irrational functions
Integration of trigonometric functions.
Definite integral and its applications
Evaluation of definite integrals.
Numerical series
Metric space ℝ^n. Multivariable calculus.
Higher-order derivatives and differentials.
Multiple and iterated limits of functions of several variables.
Tangent plane and normal to an explicitly defined surface.
Partial derivatives, differential, directional derivative, gradient.
Substitution of variables in differential expressions.
Differentiation of complex and implicitly defined functions.
Extrema of multivariable functions
Investigation of functions for local extrema.
Investigation of functions for constrained extrema.
