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You'll learn the two languages for describing fluid motion — Eulerian and Lagrangian — and the material derivative that connects them. You'll learn to split the velocity gradient i…

Mathematical reasoning is about using logic and math skills to solve problems and understand the world. It involves breaking down complex situations, identifying patterns, and usin…

Geometry is all about shapes, sizes, positions, and properties of space. Angles are a fundamental part of geometry, defining how lines or surfaces meet. Understanding these basics…

Triangles are three-sided polygons classified by side lengths (equilateral, isosceles, scalene) or angles (acute, right, obtuse). Key theorems like the triangle inequality and angl…

Polygons are closed shapes made of straight lines, and you can classify them by their sides and angles. Proportionality describes how two shapes are related when one is just a scal…

Right-angled triangles are special because one angle is exactly 90 degrees. The Pythagorean Theorem, $a^2 + b^2 = c^2$, helps you find unknown side lengths in these triangles. This…

Trigonometry is about the relationships between the sides and angles of right-angled triangles. You'll learn three main ratios – sine, cosine, and tangent – to find unknown sides o…

Geometry studies shapes, sizes, and relative positions of figures, while topology focuses on properties that remain unchanged under continuous deformation. These fields, though dis…

Statistical thinking helps you make sense of data and draw reliable conclusions in a world full of numbers. You'll learn to ask the right questions, collect and organize data, and…

A sequence is an ordered list of numbers, and each number in the list is called a term. We often look for a pattern or rule to predict the next term in a sequence. Understanding se…

Matrices are rectangular grids of numbers or symbols, useful for organizing data and solving systems of equations. Understanding basic terms like "element," "row," and "column" is…

Circles are fundamental shapes defined by all points an equal distance from a central point. You'll learn essential terms like radius, diameter, chord, and arc, which describe diff…

…An expression is a combination of variables, constants, and mathematical operations (like add

…solving geometry problems, and interpreting data in applied mathematics. Think of a coordinate system as a grid you use to pinpoint exact locations, like streets and avenues on a c…

Linear equations describe a straight line on a graph, showing a consistent relationship between two variables. You'll learn to recognize, manipulate, and plot these equations to vi…

You'll learn the essential parts of a circle and what they're called, like radius and diameter. Understanding these terms is crucial for solving any circle-related problems. We'll…

…variables, numbers, and operations (like +, -, , /). It's a mathematical phrase, not a complete sentence. x + 5 (Here, x is a variable, 5 is a constant, and + is an operation.) 3y…

Lebesgue outer measure is a way to assign a "size" to any subset of real numbers, extending the intuitive idea of length. It's built by covering sets with open intervals and then t…

Linear algebra is about solving systems of linear equations using vectors and matrices. It provides powerful tools to understand, manipulate, and solve problems in engineering, oft…

Number theory is all about the properties and relationships of whole numbers, especially integers. You'll learn about divisibility, prime numbers, and how numbers behave when you d…