Mathematics: Basics and Applications

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Related lectures (28)

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Polynomial Equations: Determining Coefficients

Covers the process of determining coefficients in polynomial equations.

Complex Roots and Polynomials

Explores complex roots, polynomials, and factorizations, including roots of unity and the fundamental theorem of algebra.

Solving the Quintic: Dominant Balance Analysis

Explores dominant balance analysis in solving the quintic polynomial, revealing insights into root behavior and the importance of symbolic expressions.

Hyperbolic Functions: Tangent and Cotangent

Covers the definitions and examples of hyperbolic tangent and cotangent functions.

Differential Equations: Methods and Solutions

Discusses methods for solving first-order linear differential equations, focusing on separation of variables and the integrating factor method.

Advanced Analysis II: Variation of Constants Method

Covers the variation of constants method for solving first-order linear differential equations, detailing its steps and implications for general and particular solutions.

Differentiable Functions and Lagrange Multipliers

Covers differentiable functions, extreme points, and the Lagrange multiplier method for optimization.

Viète Relations: Polynomial Roots and Coefficients

Explores Viète's identities, relating polynomial roots and coefficients to solve equations.

Polynomials: Definitions and Operations

Covers the definition and operations of polynomials, including addition and multiplication, degree, coefficients, and their role in algebraic systems.

Polynomials, Division, and Ideals

Explores polynomials, their operations, and the concept of ideals in polynomial rings.