Lectures related to Multivariable calculus

Covers Darboux sums, properties, and the fundamental theorem of calculus.

Covers multivariable integral calculus, including rectangular cuboids, subdivisions, Douboux sums, Fubini's Theorem, and integration over bounded sets.

Differentiability and Tangent Planes in Multivariable Functions

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

Stochastic Calculus: Foundations and Applications

Explores the foundation of stochastic calculus, emphasizing deterministic and memoryless processes.

Partial Derivatives: Definitions and Interpretations

Explores partial derivatives, their interpretations, and geometric applications in multivariable functions.

Differentiability and Tangent Planes in Multivariable Functions

Explains differentiability in multivariable functions and the geometric interpretation of tangent planes.

Notation in Multivariable Calculus

Reviews the notation used in multivariable calculus, emphasizing accurate translation between different forms of integrals.

Calculus of Variations

Covers topics in Calculus of Variations, including regularity results and implicit function theorems.

Multivariable Integral Calculus

Delves into multivariable integral calculus, covering topics like volume calculations and finding extrema under constraints.

Studying Mechanics: Introduction and Mathematical Tools

Covers the introduction to mechanics, historical figures, importance of experiments, and acceleration.

Vectorial Calculus

Explores vectorial calculus, divergence, curl, gradient, implicit functions, and local inversion theorems.

Introduction: Lightboard 0-1

Serves as a helpful review for vector calculus topics before the final exam.

Vectors and Tensors: Derivatives and Transformations

Explores gradient, divergence, and integral theorems in vector calculus.

Functions on R^n: Limits and Partial Differentiation

Delves into functions on R^n, covering limits and partial differentiation.

Calculus of Variations: Some Topics

Covers fundamental topics in calculus of variations, including minimizers and the Euler-Lagrange equation.

Surface Integrals: Change of Variables

Explores surface integrals, change of variables, and properties of regular surfaces.

Geometric Interpretation of Derivatives

Explores the geometric interpretation of derivatives and properties of derivable functions.

Green Function and Laplacian Formula

Covers the concept of Green function and Laplacian formulas in mathematics.

Generalized Integrals: Type 2

Covers the integration of limit expansions and continuous functions by pieces.

Partial Derivatives and Functions

Explores partial derivatives and functions in multivariable calculus, emphasizing their importance and practical applications.