Lectures related to Notation in Multivariable Calculus

Integral on S-up

Covers the properties of the integral on S-up, including linearity and monotony.

Advanced Analysis II: Generalisations and Gradients

Explores generalisations of functions and the concept of gradients in advanced analysis.

Improper Integrals: Convergence and Comparison

Explores improper integrals, convergence criteria, comparison theorems, and solid revolution.

Analytic Continuation: Residue Theorem

Covers the concept of analytic continuation and the application of the Residue Theorem to solve for functions.

Laws of Transformation of Velocities and Accelerations

Covers the laws of transformation of speeds and accelerations, including the rotation of points and dynamic movement principles.

Calculus: Derivatives and Integrals

Covers the fundamentals of calculus, focusing on derivatives and integrals.

Advanced Physics I: Orders of Magnitude

Explores the triumph of determinism in modern mechanics and the methodology of scientific development, with practical exercises on estimating surgical mask usage and analyzing atomic bomb energy.

Equivalent Sliding Reflection to Three Axial Reflections

Explores the composition of three axial reflections into an equivalent sliding reflection in a plane.

Proteins: Central Dogma and Translation

Explains protein synthesis, translation, and the central dogma of molecular biology.

Functions xr, r>0, on 10,1

Covers the properties of functions xr, r>0, on 10,1, including limits and integrals.

Values Representation: Tagging and Boxing

Explores improving translation, source context-based translations, and value representation techniques like tagging and boxing.

Advanced Analysis II: Integrals and Functions

Covers advanced topics in analysis, focusing on integrals, functions, and their properties.

Calculus Fundamentals

Covers the fundamentals of calculus, including limits, derivatives, and integrals.

Integration Techniques: Change of Variable and Integration by Parts

Explores advanced integration techniques such as change of variable and integration by parts to simplify complex integrals and solve challenging integration problems.

Geometric Transformations: Translation and Homothety

Explores geometric transformations like translation and homothety in the plane.

Fundamental Theorem of Calculus: Integrability, Anti-derivatives, Integration by Parts

Covers integrability, anti-derivatives, and integration by parts in calculus.

Rotation Dynamics: Symmetry Axis

Explores rotation dynamics around a symmetry axis, covering angular momentum, center of mass theorem, and solid body movement.

Comparison Series and Integrals

Explores the relationship between series and integrals, highlighting convergence criteria and function examples.

Riemann Sums

Introduces Riemann sums, a method to approximate area under a curve.

Protein Synthesis: Translation

Explains protein synthesis through translation, covering ribosomes, tRNA, amino acids, genetic code accuracy, and translation stages.