Complex Numbers: Introduction and Operations

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Related lectures (38)

Complex Analysis: Functions and Their Properties Log in to Mediaspace to watch this video

Covers the fundamentals of complex analysis, focusing on complex functions, their properties, and applications in solving differential equations.

Complex Numbers: Trigonometric Formulas Log in to Mediaspace to watch this video

Explores complex numbers, trigonometric functions, De Moivre's formulas, and complex plane representation.

Riemann Sums and Definite Integrals Log in to Mediaspace to watch this video

Covers Riemann sums, definite integrals, Taylor series, and exponential of complex numbers.

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

Covers the definitions and properties of complex numbers, including the field of complex numbers, the conjugate, the real and imaginary parts, algebraic form, modulus, and argument.

Complex Numbers and 2x2 Matrices Log in to Mediaspace to watch this video

Covers complex numbers, quadratic equations, solutions in C, and 2x2 matrices.

Magnetic Fields and Complex Numbers Log in to Mediaspace to watch this video

Explores magnetic fields from moving charges and the properties of complex numbers.

Complex Numbers: Convergence, Equations, and Exponential Functions Log in to Mediaspace to watch this video

Covers convergence of power series, complex equations, exponential functions, and function properties.

Sequences: Definitions and Examples Log in to Mediaspace to watch this video

Covers solving equations over complex numbers, sequences, induction, and properties of complex numbers.

Existence of y: Proofs and EDO Resolution Log in to Mediaspace to watch this video

Covers the proof of the existence of y and the resolution of EDOs with practical examples.

Homogeneous Differential Equations Log in to Mediaspace to watch this video

Explores solving first-order homogeneous differential equations through variable changes and delves into the Bernoulli differential equation.

Real Numbers: Axioms and Bounds Log in to Mediaspace to watch this video

Covers the organization of real numbers, axioms, and bounds, including infimum and supremum.

Linear Combinations: Vectors and Matrices Log in to Mediaspace to watch this video

Explores linear combinations of vectors and matrices in Rn, demonstrating geometric interpretations and matrix operations.

Analysis IV: Laplace Equation Solutions Log in to Mediaspace to watch this video

Explores Laplace equation solutions through separation of variables and general solution writing for complex problems.

Cauchy-Lipschitz Theorem: Local Existence and Uniqueness Log in to Mediaspace to watch this video

Explores the Cauchy-Lipschitz theorem for local existence and uniqueness of solutions to differential equations.

Linear Independence: Definition and Examples Log in to Mediaspace to watch this video

Explores the concept of linear independence in vector spaces through definitions and illustrative examples.

Linear Algebra: Systems of Equations and Vector Operations Log in to Mediaspace to watch this video

Explores systems of equations, vector operations, and geometric interpretations in linear algebra.

Partial Differential Equations: Basics and Classification Log in to Mediaspace to watch this video

Introduces the basics and classification of partial differential equations, including notation, definitions, and examples.

Geometric Properties of Ellipses and Their Applications Log in to Mediaspace to watch this video

Explores the geometric properties of ellipses, their parametric equations, and applications in architecture and design.

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