Lectures related to Spherical Coordinates: Determinant of Jacobi

Covers the basics of linear mapping and coordinate systems.

Linear Algebra: Matrices and Linear Applications

Covers matrices, linear applications, vector spaces, and bijective functions.

Covers the inverse function theorem, Jacobian matrix, injective functions, bijective functions, and spherical coordinates.

Linear Algebra: Multilinear Groin and Determinants

Explores multilinear groin and determinants, including the Sarrus rule and proof by induction.

Cramer's Rule and Volume

Covers Cramer's Rule, matrix inverse, determinants, and volume in linear algebra.

Linear Independence and Bases

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

Coordinate Systems: Polar, Cylindrical, Spherical

Covers position, velocity, and acceleration in polar, cylindrical, and spherical coordinate systems.

General Physics: Mechanics

Covers mechanics concepts in different coordinate systems, explaining position, velocity, and acceleration vectors.

Characteristic Polynomials and Similar Matrices

Explores characteristic polynomials, similarity of matrices, and eigenvalues in linear transformations.

Coordinate Systems: Polar, Cylindrical, and Spherical

Explains polar, cylindrical, and spherical coordinates in physics, emphasizing their advantages in simplifying motion analysis.

Linear Algebra in 3D: Determinants and Inverses

Explores determinants in 3D space and their role in linear algebra.

Linear Algebra Basics

Covers fundamental concepts in linear algebra, including linear equations, matrix operations, determinants, and vector spaces.

Circular motion: Friction and Newton's Laws

Explores circular motion, friction, and Newton's laws in various coordinate systems.

Coordinate Change: Polar and Spherical Coordinates

Covers coordinate changes, focusing on polar and spherical coordinates and their transformations, determinants, and invertibility.

Physics 1: Harmonic Oscillator and Spherical Coordinates

Explores harmonic oscillators, pendulum movement, and spherical coordinates in physics.

Coordinate Change: Chapter 4

Explores coordinate changes between polar and Cartesian coordinates, and introduces the spherical coordinate system.

Polar Coordinates: Position and Velocity

Explores polar coordinates, position, velocity, and acceleration vectors in Cartesian and polar systems, including cylindrical and spherical coordinates.

Linear Algebra Basics: Vector Spaces, Transformations, Eigenvalues

Covers fundamental linear algebra concepts like vector spaces and eigenvalues.

Generalization of Change of Basis Matrices

Covers linear algebra basics, including matrices, change of basis, and invertible matrices.

Linear Algebra in R³: Vector Spaces

Explores vector spaces in three dimensions, covering linear combinations, subspaces, and properties of families of vectors in R³.