Mathematical Analysis
Limit of a Function
The limit of a function, computing limits.
Sequence. Boundedness and monotonicity of a sequence. Limit of a sequence.
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.
Plotting graphs of functions defined explicitly in the Cartesian coordinate system.
The indefinite integral
Integration using variable substitution
Integration of rational functions.
Integration of irrational functions
Integration of trigonometric functions.
Antiderivative and indefinite integral
Definite integral and its applications
Evaluation of definite integrals.
Numerical series
Metric space ℝ^n. Multivariable calculus.
Partial derivatives, differential, directional derivative, gradient.
Higher-order derivatives and differentials.
Substitution of variables in differential expressions.
Multiple and iterated limits of functions of several variables.
Differentiation of complex and implicitly defined functions.
Tangent plane and normal to an explicitly defined surface.
Extrema of multivariable functions
Investigation of functions for local extrema.
Investigation of functions for constrained extrema.
