Level Curves and Graphs of Functions

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Related lectures (29)

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Morse Theory: Critical Points and Non-Degeneracy

Covers Morse theory, focusing on critical points and non-degeneracy.

Limits and Continuity: Analysis 1

Explores limits, continuity, and uniform continuity in functions, including properties at specific points and closed intervals.

Advanced Analysis II: Tangent Plan and Differentiability

Explores tangent planes and differentiability in advanced analysis, emphasizing the properties of tangent planes and the conditions for differentiability.

Implicit Functions Theorem

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

Real Functions: Definitions and Properties

Covers real functions' definitions, properties, periodicity, and reciprocity, including maximum, minimum, and composition of functions.

Integration by Substitution

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

Differentiable Functions and Lagrange Multipliers

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

Trigonometric Functions: Sin and Cos

Covers the definition of sine and cosine functions, their graphs, and notable points.

Piecewise Functions Composition

Covers the composition of piecewise functions and introduces the signum and Heaviside functions.