Can you please help me lay out some roadmap how to progress with learning? My biggest obstacle is that there is so many things I dont even know where to start.I dont want to learn thing that I cant learn if I dont know some other thing.
I would like to have some rough step by step roadmap so I can tackle with one specific thing at a time.From the previous posts I so far come up with this plan :
Arithmetic > Algebra > Trigonometry > Calculus
Differential equations are another specific category or is it kind of a sub-category of the ones of the above?
You omitted Geometry which usually comes before Trigonometry but otherwise, you have the general idea.
In algebra you deal with all kinds of equations involving one or more variables. There are usually two semesters of algebra called, oddly enough, Algebra I and Algebra II.
Differential equations are different in that the variable and it's derivative (the rate at which the variable is changing, usually as a function of time) appear in the equation. This class is the culmination of a 4 semester program of Calc I, Calc II, Calc III (often called linear algebra) and Differential Equations.
Differential Calculus (Calc I) deals with Change and Motion
Integral Calculus (Calc II) deals with Area and Volume
Linear Algebra deals with matrices and vectors
Differential Equations deals with more complex equations and how the variables change (usually with time)
So when do you use a second order ordinary differential equation? Every time you drive your car! The classic Mass-Spring-Damper equation turns out to be the equation for the suspension system. The mass is the weight of the car on a specific wheel, the spring rate (inches of deflection per unit of weight) comes from the torsion bar or spring and the shock absorber is the damper. Every single day!
Oh, BTW, the exact same equation is used to describe the natural response of a parallel R-L-C circuit. It's amazing how certain equations keep cropping up with different constants but identical form.
There are math courses beyond Differential Equations in the EE curriculum. Remember, those 4 courses are taught in the first two years of a 4 or 5 year program, the lower division. You certainly don't expect to slide through the later years do you? No! They hide the math when the course is called Signal Processing and you spend full time deep in Fourier Analysis (100% math) or Control Systems where you get to play with Laplace Transforms or even electrodynamics where you can enjoy Maxwell's Equations to their fullest. Yes sir, those were the days!
You will also notice that the 4 courses fill up both semesters of both years of the lower division. Everybody assumes you have perfect command of pre-Calc before you get to college. And very few do! As I said earlier, pre-Calc at our community college is a two semester course and takes an entire year all by itself unless you beat yourself to death taking part of it over the short summer semester. And, as discussed above, Calculus is easy, it's the pre-Calc that will kill you. An absolute perfect command of pre-Calc is truly a pre-requisite.
Pre-Calc is algebra, geometry and trigonometry all rolled into a mashed together class covering everything. It is critical to later success.