This lecture is all about Newton's First (inertia), Second (F=ma) and Third (action=-reaction) Laws. He builds on past discussion of vector forces, moving on to decompose forces in the x and y directions. As the class comes to an end, Professor Lewin ends with a bizarre demo involving two identical strings, one suspending a mass, the other suspending from the mass. Which one breaks when you pull on the lower string, the upper string or t...more
Nullspace Of A Matrix(Continued), Range Of A Matrix, Inverse, Rank Of A Matrix, Conservation Of Dimension, 'Coding' Interpretation Of Rank, Application: Fast Matrix-Vector Multiplication, Change Of Coordinates, (Euclidian) Norm, Inner Product, Orthonormal Set Of Vectors
Orthogonal Projections - Scalar and Vector Projections. In this video, we look at the idea of a scalar and vector projection of one vector onto another.
Parametric Equations of Line Passing Through a Point. In this video, I show how to find the parametric equations of a line that passes through a given point with a given direction vector.
Partial Derivatives of Vector-Valued Functions.
Showing that if a vector field is the gradient of a scalar field, then its line integral is path independent.
Using a position vector valued function to describe a curve or path.
Determining a Position Vector-Valued Function for a Parametrization of Two Parameters.
Preprocessing Commands - #Define as a Glorified Find and Replace, Preprocessing Macros - Preprocessor Commands With Arguments, Example of Macro Usage in the Vector assignment to Calculate the Address of the Nth Element, Assert Macro Implementation, How Asserts are Stripped Out for the Final Product Using #Ifdef and #Define, C Macro Drawbacks When Given More Complex Arguments, #Include as a Search and Replace Operation, < > Vs. " ", Output ...more
This course serves as an introduction to the theory and practice behind many of today's communications systems. 6.450 forms the first of a two-course sequence on digital communication. The second class, 6.451, is offered in the spring. Topics covered include: digital communications at the block diagram level, data compression, Lempel-Ziv algorithm, scalar and vector quantization, sampling and aliasing, the Nyquist criterion, PAM and QAM m...more
Solving the second part to the projectile motion problem (with wind gust) using ordered set vector notation.
Determining the position vector as a function of time.