Books for deriving old physical formulas

[ancientlord]

Hi dear forum members,
I'm an undergrad. physics student(freshmen),i've learned that Galilei found g.t^2=s formula(a free falling object's position function with respect to time)without using physical foundations,by using him blood impulses for count time not utilizing acceleration etc,i've learnd it from https://www.amazon.com/s/ref=dp_byl...ksandrov&sort=relevancerank&tag=pfamazon01-20 's mathematics its contend methods and meaning.
He just measured two quantities while one of them changing respect to other.But how could he find g,how could he measure that constant?
Not just Galilei's,there are a lot of physical formula consists constants and i want to the same,i want to derivate formulas on topics that i observed or imagined.I know differential and integral calculus(and although i don't know series and analysis too much,i'm currently working on them).Which branch of mathematics can teach me these?I'm a self-learner ,i can learn from books by myself so don't hesitate to advisig books :) .
What kind of books teach me this process,i mean which subject i should learn?Mathematical modelling,analysis or something else?
My English could be crude,sorry for that,but please help me,i'm really eager to learn expressing any/all kind of physical phenomenas by using math.

 

[ancientlord]

Please give me some advises folks,
I'm really good at dif. and integral calculus and I'm trying to improve my knowledge,and all of my efforts just for becoming a scientist(i want to understand nature).
I'm first grade student and i don't want to wait four years for these subjects(i have enough time now for work on these),
how could i formulate anything that i observed(i can measure which parts of it ( and with what ratio,approximately,) proportional each other,but i can't completely work out!)
Which branch of math should i study;numerical methods,analysis...which?
For clearify everytihg,here what i want to do;
like free body fall equation=g.t^2 or gravitation F=GmM/r^2 or elastic modulus's formulas etc
some of the physical formulas invented just applying math(and some of them include constants), i want to know how could they figure this out,i want to understand this process and be able to use it any of my observations.
Please don't mind my English and tell me which subjects i should learn(whether they are difficult/hard to comprehend,i don't care i want to learn)...