Lectures in course MATH-101(d): Analysis I

Analysis I: Functions of a Variable Log in to Mediaspace to watch this video

Introduces fundamental concepts of Analysis I, focusing on functions of a variable and numerical sequences.

Basic Notations: Sets and Subsets Log in to Mediaspace to watch this video

Covers basic notations related to sets and subsets, including elements and subsets.

Number Theory: Operations and Equivalence Log in to Mediaspace to watch this video

Covers operations and equivalence relations in number theory, including addition, subtraction, multiplication, division, and properties of neutral and inverse elements.

Solving Mathematical Equations Log in to Mediaspace to watch this video

Covers the resolution of mathematical equations and series convergence.

Real Numbers: Structure and Properties Log in to Mediaspace to watch this video

Covers the structure and properties of real numbers, including the introduction to the axiomatic system and the implications of Archimedean property.

Real Numbers: Order and Completeness Log in to Mediaspace to watch this video

Covers the properties of real numbers, focusing on the total order and completeness, including the Archimedean property and the concepts of supremum and infimum.

Real Numbers: Definitions and Equivalence Classes Log in to Mediaspace to watch this video

Covers the existence of real numbers and equivalence classes of Cauchy sequences.

Inequalities and Absolute Value Log in to Mediaspace to watch this video

Explores inequalities, absolute value, and mathematical identities, emphasizing their importance in mathematical reasoning.

Properties of Real Numbers Log in to Mediaspace to watch this video

Covers countability and bijections between sets, demonstrating the uncountability of real numbers.

Absolute Value and Complex Numbers Log in to Mediaspace to watch this video

Covers the absolute value function, complex numbers, Euler's formula, and trigonometry applications.

Complex Numbers: Operations and Properties Log in to Mediaspace to watch this video

Covers the representation and properties of complex numbers, including real and imaginary parts and geometric applications.

Inverse Element for Multiplication Log in to Mediaspace to watch this video

Covers the inverse element for multiplication and introduces the Euler and Moivre formulas in complex numbers.

Complex Numbers: Polar Form Log in to Mediaspace to watch this video

Covers the polar form of complex numbers and its applications in mathematical calculations.

Functions: Elementary Functions Log in to Mediaspace to watch this video

Covers elementary functions like tan(x), sin(x), and cos(x) along with trigonometric identities and Pythagorean theorem.

Complex Numbers: Polar Form and Multiplication Log in to Mediaspace to watch this video

Covers the polar form of complex numbers and its advantages in multiplication.

Complex Numbers: Operations and Applications Log in to Mediaspace to watch this video

Covers the properties and operations of complex numbers and their applications.

Real Numbers Sequences Log in to Mediaspace to watch this video

Covers real number sequences, including convergence and boundedness concepts.

Real Number Sequences Log in to Mediaspace to watch this video

Introduces real number sequences, notations, properties, and recursive sequences with examples and graphical representations.

Convergence of Sequences Log in to Mediaspace to watch this video

Explains convergence of sequences, including increasing, decreasing, and limits.

Limites and Divergence Log in to Mediaspace to watch this video

Explores limits, divergence, and algebraic operations on sequences approaching infinity.