Theme: Functions

Concept of function. Concept of continuity. List of basic functions. Inverse functions.

Extending naive Bayes

Concept of limit of a function. Limit at a point. Vertical asymptotes. Limit at infinity. Horizontal asymptotes. List of standard limits.

Theme: Derivatives

Rate of change of a function. Definition of derivative. Calculating derivatives from definition. Derivatives of basic functions. One-side derivative.

Theme: Derivative and differential

Concept of differential. Derivatives of sum, product, and ratio of two functions. The chain rule. Logarithmic derivative.

Theme: Derivative applications.

Linear approximation. Equation for the tangent of a function. Maximum and minimum values. Second derivative. Analysis of a function using derivative. Asymptotic functions.

Theme: Integrals

Antiderivatives. Indefinite integrals. Deriving the list of indefinite integrals for basic functions.

Theme: Integration

Integration techniques. Substitution rule.

Theme: Integrals of rational functions

Integration of rational functions.

Theme: Preliminary test

Breaking words down into characters. Character-based models. Convolutional networks in NLP.

Theme: Definite integral

Area under curve. Fundamental theorem of calculus. Definite integral. Area between curves.

Theme: Average value

Definition of average value. Calculation of average values.

Theme: Further directions

Giving slight overview of the further topics. Function of many variable. Partial derivative. Differential equations.

Theme: Overview

Overview of the studied material. Preparation for the final exam.

Theme: Final exam

Neural language models and word2vec

Indeterminate forms. L’Hospital rule. Optimisation problems. Newton-Raphson method.