Lectures related to Complex Numbers: Introduction and Operations

Complex Numbers: Operations and Applications

Covers the fundamental operations and applications of complex numbers.

Complex Numbers: Definitions and Operations

Covers the introduction and operations of complex numbers, including powers and roots.

General Physics: Mechanics SV

Covers the basics of General Physics, focusing on Mechanics SV and key mathematical concepts.

Harmonic Oscillator: Complex Numbers and Solutions

Covers complex numbers, derivatives, and solutions of the damped harmonic oscillator with different damping regimes.

Introduction to Mathematics for Engineers

Introduces the purpose of mastering mathematics and calculation tools for engineers, emphasizing the need to think methodically and rigorously.

Calculus: Derivatives and Integrals

Covers the fundamentals of calculus, focusing on derivatives and integrals.

Fourier Transform: Derivatives and Laplace Transform

Explores the Fourier transform properties with derivatives and introduces the Laplace transform for signal transformation and solving differential equations.

Absolute Value and Complex Numbers

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

Complex Numbers: Algebraic Structures and Applications

Covers algebraic structures, real numbers, fields, and the applications of complex numbers in science and engineering.

Mechanics: Oscillator Harmonics

Explores harmonic oscillators' behavior under various damping conditions, covering Newton's laws, complex numbers, and Euler's formula.

Complex Numbers: Properties and Operations

Explores complex numbers, Euler's formula, Moivre's formula, and proof by induction.

Real Numbers and Functions

Introduces Real Analysis I, covering real numbers, functions, limits, derivatives, and integrals.

Differential Calculation: Trigonometric Derivatives

Explores trigonometric derivatives, composition of functions, and inflection points in differential calculation.

Derivatives and Trigonometry Fundamentals

Introduces derivatives, trigonometry, and motion principles through basic and trigonometric functions differentiation.

Complex Numbers: Polar Form, Powers, Roots

Explores complex numbers in polar form, powers, and roots, including trigonometric relationships and rotation matrices.

Complex Numbers: Polar Form

Explores complex numbers in polar form, Euler's formula, and coordinate transformation.

General Physics I: Course Organization

Covers the organization of a physics course for engineering students, including adjustments due to the current situation and support resources.

Derivatives and Approximations: Logarithmic Functions

Explores derivatives and approximations, focusing on logarithmic functions and their properties.

Derivability and Composition

Covers derivability, linear applications, composition of functions, and the gradient vector.

Verification Strategies for Exercises

Covers general verification strategies for solving exercises in science and engineering, emphasizing the importance of verifying solutions.