Lectures related to Derivatives: Tangents and Secants

Tangent to Graph of a Function

Explores finding the equation of the tangent line to a function's graph at a point.

General Mathematics I: Derivatives and Tangents

Explores derivatives, tangents, and elementary function rules in general mathematics.

Generalized Integrals: Convergence and Divergence

Explores the convergence and divergence of generalized integrals using comparison methods and variable transformations.

Limits and Operations on Limits

Covers limits, algebraic operations, and infinite limits with examples of functions' behavior near limit points.

Derivatives and Tangents

Introduces derivatives, tangent lines, rules of differentiation, and practical examples.

Elementary Functions and Derivatives

Covers elementary functions, derivatives, limits, continuity, and differentiability.

Differentiability and Derivatives

Revisits the definition of differentiability and the existence of derivatives for functions in open intervals.

Derivatives and Approximations: Logarithmic Functions

Explores derivatives and approximations, focusing on logarithmic functions and their properties.

Derivatives and Continuity in Multivariable Functions

Covers derivatives and continuity in multivariable functions, emphasizing the importance of partial derivatives.

Analyse I: Summary

Covers real numbers, complex numbers, numerical sequences, series, real functions, function limits, derivatives, Taylor series, integrals, and growth rates of functions.

Limits and Continuity

Covers the concept of limits and continuity in real analysis.

Differential Calculation

Explores the history and concepts of differential calculus, including tangent, derivative, limit, and various function derivatives.

Analysis I Exam Solutions

Provides solutions to an Analysis I exam, covering various topics.

Limits at Infinity: Algebra and Continuity

Covers limits at infinity, algebra, and continuity with examples.

Differentiability of Functions of Several Variables

Covers the differentiability of functions of multiple variables and the significance of directional derivatives and gradients.

Derivatives: Definition and Examples

Covers the definition of derivatives and provides examples of differentiable functions.

Directional Derivatives

Explores directional derivatives, their calculation, examples, and cases of lack of continuity.

Differentiability and Tangent Planes

Explores differentiability in functions and geometric interpretation of tangent planes.

Limits and Continuity

Explores limits, continuity, and elementary functions' properties, emphasizing the importance of understanding continuous functions.

Generalized Finite Increments

Explores generalized finite increments, derivatives, reciprocals, and Bernoulli-L'Hospital rule.