Lectures related to Multivariable Integral Calculus

Multivariable Integral Calculus

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

Finding Absolute Extrema in Multivariable Functions

Covers the conditions for finding absolute extrema in multivariable functions.

Linear Independence and Bases in Vector Spaces

Explains linear independence, bases, and dimension in vector spaces, including the importance of the order of vectors in a basis.

Linear Independence and Bases

Covers linear independence, bases, and coordinate systems with examples and theorems.

Integral Calculus: Darboux Sums

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

Introduction and Historical Perspective, Vectors and Kinematics

Explores historical perspective, vectors, kinematics, and mathematical modeling of physical systems.

Differentiable Functions and Lagrange Multipliers

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

Mechanics: Introduction and Calculus

Introduces mechanics, differential and vector calculus, and historical perspectives from Aristotle to Newton.

Integral Calculus of Functions in Several Variables

Covers the integration of functions in several variables, Darboux sums, and Fubini's theorem on a closed box.

Linear Algebra: Linear Dependence and Independence

Explores linear dependence and independence of vectors in geometric spaces.

Linear Transformations: Matrices and Applications

Covers linear transformations using matrices, focusing on linearity, image, and kernel.

Coordinate Systems and Applications

Covers the definition and use of coordinate systems and applications in bases and linear equations.

Orthogonality and Projection

Covers orthogonality, scalar products, orthogonal bases, and vector projection in detail.

Linear Combinations: Vectors and Matrices

Explores linear combinations of vectors and matrices in Rn, demonstrating geometric interpretations and matrix operations.

Lagrange Multipliers Theorem

Explores the Lagrange Multipliers Theorem, covering extrema conditions and geometric interpretations.

Vector Spaces: Bases and Dimension

Explores bases, dimensions, and matrix ranks in vector spaces with practical examples and proofs.

Linear Algebra: Matrices and Vector Spaces

Covers matrix kernels, images, linear applications, independence, and bases in vector spaces.

Linear Independence in Vector Spaces

Explores linear independence in vector spaces and conditions for determining linear independence.

Differential Forms Integration

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Regular Surfaces: Painting with Normal Vectors

Explores regular surfaces and painting with normal vectors, integral calculations, symmetries, and surface orientation.