Lectures related to Vector-valued function

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

Motion Analysis: Cartesian and Polar Coordinates

Covers the analysis of motion using Cartesian and polar coordinates, focusing on kinematics and acceleration components.

Coordinate Systems and Rotations

Covers cylindrical and spherical coordinates, vector positions, velocities, accelerations, and rotations.

Functions: Multivariable Functions and Exact Differentials

Explores functions as a function of time and space, differentiation of multivariable functions, exact differentials, and gradients.

Advanced Physics I

Delves into advanced physics concepts like uniform motion, vectors, and three-dimensional movement, with practical exercises on kinematics and coordinate systems.

Principles of Quantum Physics

Covers the principles of quantum physics, focusing on tensor product spaces and entangled vectors.

Vector Differentiation and Convex Functions

Covers the concepts of vector differentiation and convex functions.

Development of Taylor Polynomials

Covers the development of Taylor polynomials of order p around a point x.

Acceleration and Rotation

Explores acceleration derivation, vector rotation, and coordinate systems in rotational motion.

Design Discussions, Documentation

Explores design discussions and documentation in software development, emphasizing scientific programming and code documentation tools like Doxygen and Sphinx.

Hermitian Forms: Definition and Properties

Explores the definition and properties of Hermitian forms in complex vector spaces.

Physics: Motion in the Plane

Covers the concepts of density, surface, length, reference frames, and vector position.

Differentiability: Functions and Matrices

Explores partial differentiability, the chain rule, and invertibility of vector fields.

Signals & Systems I: Vector Approximation and Signal Comparison

Explores vector approximation, signal detection, correlation, Fourier series, and signal comparison in signals and systems.

Differentiable Functions in R²

Covers the representation of differentiable functions in R² and the concept of changes of coordinates through bijections.

Derivative of a Product of Functions

Explores the derivative of a product of functions and discusses algebraic products and scalar products of functions.

Cauchy Equations and Integral Decomposition

Covers the application of Cauchy equations and integral decomposition, addressing questions related to holomorphic functions and Jacobian matrices.

Vector Functions: Parameterization of Curves

Explains vector functions and the parameterization of curves with examples.

Differentiability: Functions and Matrices

Explores differentiability for functions and matrices, covering partial differentiability, the Jacobean matrix, and the chain rule.

Implications of the Mean Value Theorem

Explores the implications of the mean value theorem and how to predict function values using derivatives.