Calculus: I suggest just forget about "precalculus" and, instead, just get a good calculus book and dig in. There are two main parts of calculus, and both can

Calculus: I suggest just forget about "precalculus" and, instead, just get a good calculus book and dig in. There are two main parts of calculus, and both can be well illustrated by driving a car. In the first part, we take the data on the odometer and from that construct the data on the speedometer. The speedometer values are called the (first) derivative of the odometer values. In the second part we take the speedometer values and construct the odometer values. The odometer values are the integral of the speedometer values. In notation, let t denote time measured in, say, seconds, and d(t) the distance, odometer value, at time t. Let s(t) be the speed at time t. Then in calculus s(t) = d'(t) = d/dt d(t) And d(t) is the integral of speed s(t) from time t = 0 to its present time. Those are the basics. Applications are all over physics, engineering, and the STEM fields. Linear Algebra: The subject starts with a system of simultaneous linear equation. The property linearity is fundamental, a pillar of math and its applications. The STEM fields are awash in linearity. E.g., a concert hall performs a linear operation on the sound of the orchestra. E.g., in calculus, both differentiation and integration are linear. In the STEM fields, when a system is not linear, often our first step is to make an attack via a linear approximation. E.g., perpendicular projection onto a plane is a linear operator and the main idea in regression analysis curve fitting in statistics. Most of math can be given simple intuitive explanations such as above.