I am a adult learner learning Calculus. I would like to know if it is a must to master Differential and Integral Calculus before moving to Multi-variable Calculus.
If I am not wrong, Differential and Integral Calculus are taught in high school and Multi-variable Calculus is taught in college?
One would be remiss not to study differential and integral calculus before studying multivariable calculus. The meat of multivariable is completely untouchable without exposure to both of the single-variable subjects, and multivariable builds heavily on what is learned in single-variable calculus.
The topics covered in a multivariable calculus course include understanding the derivative and the integral in higher dimensions. These two are the bread and butter of multivariable, so one should be comfortable with the single-variable. The definitions in the multivariable setting draw motivation from the single-variable case, not vice versa.
Depending on your definition of mastery, you can start to get your feet wet with multivariable with some basic understanding of the single-variable derivative and integral. For instance, the definition of a derivative is similar in each setting and multivariable integration has nice geometric interpretations.
The only thing that can really be said here is it's possible to make some headway with basic knowledge of single-variable calculus, but you can only expect deeper connections and greater understanding to come once you have understood the single-variable subject in greater detail.