Implicit Functions Theorem

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Implicit Functions Theorem

Covers the Implicit Functions Theorem, providing a general understanding of implicit functions.

Applications of Theorems

Demonstrates the practical application of theorems in calculus through two clever examples.

Differentiability and Tangent Planes in Multivariable Functions

Covers differentiability in multivariable functions and the existence of tangent planes, emphasizing geometric interpretations and practical applications.

Bernoulli's Hospital Rule

Covers the statement of the Bernoulli's Hospital Rule and its application.

Advanced Analysis II: Derivatives and Functions

Covers the review of derivatives and functions, including the concept of chain rule and graphical representation.

Integration by Substitution

Explores integration by substitution with proofs and examples on anti-derivatives and function equivalence.

Linear Independence: The Wronskian Concept

Explains the Wronskian and its role in determining linear independence of solutions to differential equations.

Calculus: Derivatives and Integrals

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

Differential Equations: Implicit Function Theorem Applications

Discusses the reduction of higher-order differential equations to first-order systems using the implicit function theorem.

Implicit Functions Theorem

Covers the Implicit Functions Theorem and its applications in defining functions implicitly.