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Lecture
Implicit Functions: Tangent Line
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Implicit Functions Theorem: n=2 and n=3
Explains the Implicit Functions Theorem for n=2 and n=3 cases.
Implicit Functions and Taylor Polynomials
Covers implicit functions, Taylor polynomials, and tangent equations.
Derivatives: Definition and Properties
Explores the definition and properties of derivatives, including slopes of tangent lines and differentiability conditions.
Derivable Functions: Partial Derivatives and Jacobian Matrix
Covers derivable functions, partial derivatives, Jacobian matrix, and rule of composition.
Derivatives and Reciprocal Functions
Covers derivatives, reciprocal functions, Rolle's theorem, and extremum local concepts.
Directional Derivatives
Explores directional derivatives in two-variable functions and extremum points.
Differential Calculus: Definition and Derivability
Explores the definition and derivability of functions in differential calculus, emphasizing differentiability at specific points.
Derivatives and Tangent Planes
Covers derivatives, differentiability, and tangent planes for functions of one and two variables.
Differential Equations: Implicit Solutions
Explores implicit solutions for differential equations and their applications in different scenarios.
Advanced Analysis II: Sequences and Integrals
Explores sequences, integrals, symmetrical functions, differential equations, and the Cauchy problem in advanced analysis.