Bachelor Courses Review (Computer Science)
*Linear Algebra
Linear algebra is the branch of mathematics concerning linear equations. [wiki]
Core Knowledege
- Matrix
Matrix
Concept
In mathematics, a matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object.[wiki]
Application in Real Life
In computer graphics, matrices are used to describe geometric transformations of objects. Through matrix operations, operations such as translation, rotation, and scaling of objects can be realized, thereby generating various complex graphic effects.
In mathematics, matrices are often used to solve systems of linear equations. Matrix operations allow you to efficiently solve systems of linear equations with multiple unknowns.
Basic Operations
- Addition
- Multiplication
- Transposition
- Invertible Matrix
https://www.shuxuele.com/algebra/matrix-inverse-minors-cofactors-adjugate.html
Determinant
In mathematics, the determinant is a scalar value that is a function of the entries of a square matrix. The determinant of a matrix A is commonly denoted det(A), det A, or |A|. Its value characterizes some properties of the matrix and the linear map represented, on a given basis, by the matrix. In particular, the determinant is nonzero if and only if the matrix is invertible and the corresponding linear map is an isomorphism. The determinant of a product of matrices is the product of their determinants.
Cofactor Formula
Cramer’s Formula
*Further Mathematics
Further Mathematics is the title given to a number of advanced secondary mathematics courses. The term “Higher and Further Mathematics”, and the term “Advanced Level Mathematics”, may also refer to any of several advanced mathematics courses at many institutions.
Derivative
Integral
*College Physics
In a high school or college physics course, students typically learn about fundamental concepts such as motion, forces, energy, and electricity. They also study topics like thermodynamics, waves, optics, and modern physics, including quantum mechanics and relativity. The courses often include laboratory work to provide hands-on experience and reinforce theoretical concepts. Additionally, students may learn about the history of physics and its impact on society and technology.
Particle Kinematics
A branch of classical mechanics that describes the motion of different particles in space without considering the forces that cause such motion.
Displacement
In geometry and mechanics, a displacement is a vector whose length is the shortest distance from the initial to the final position of a point P undergoing motion. It quantifies both the distance and direction of the net or total motion along a straight line from the initial position to the final position of the point trajectory. A displacement may be identified with the translation that maps the initial position to the final position. Displacement is the shift in location when an object in motion changes from one position to another.
Speed
In everyday use and in kinematics, the speed (commonly referred to as v) of an object is the magnitude of the change of its position over time or the magnitude of the change of its position per unit of time; it is thus a scalar quantity. The average speed of an object in an interval of time is the distance travelled by the object divided by the duration of the interval; the instantaneous speed is the limit of the average speed as the duration of the time interval approaches zero. Speed is the magnitude of velocity (a vector), which indicates additionally the direction of motion.
Acceleration
In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Acceleration is one of several components of kinematics, the study of motion. Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object’s acceleration is given by the orientation of the net force acting on that object.
Newton’s laws of motion
- First Law
Every object perseveres in its state of rest, or of uniform motion in a right line, except insofar as it is compelled to change that state by forces impressed thereon. - Second Law
The change of motion of an object is proportional to the force impressed; and is made in the direction of the straight line in which the force is impressed. - Third Law
To every action, there is always opposed an equal reaction; or, the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.
Work & Energy
In physics, work is the energy transferred to or from an object via the application of force along a displacement. In its simplest form, for a constant force aligned with the direction of motion, the work equals the product of the force strength and the distance traveled. A force is said to do positive work if when applied it has a component in the direction of the displacement of the point of application. A force does negative work if it has a component opposite to the direction of the displacement at the point of application of the force.
In physics, energy is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat and light. Energy is a conserved quantity—the law of conservation of energy states that energy can be converted in form, but not created or destroyed. The unit of measurement for energy in the International System of Units (SI) is the joule (J).
Work is used to quantify the change of Energy.