Can a Community college transfer engineering prerequisitesa University?

Oh my god guys I am almost done with my semester at a community college woooo!! After this semester in the summer I’m taking Calculus II. So you don’t get confused I will have my associate in science degree after the summer semester. In the fall I wanna take English 102 and Physics 235 to complete some of my prerequisites. My courses at a community college were inexpensive and fairly easy xD. I’m kind of scared of a university but I’m always ready for a challenge :)) Now my question is will colleges and universities accept a transfer that wants to go to their school in the spring of 2016 with hopefully a 3.8 GPA or possibly higher? So basically I will be done with Cal 1,2 General Chemistry and physics engineering and mechanics to satisfy the prerequisites.

With a total of 68 credit hours in Associate in General Studies

Afterwards at a university I can just complete the rest of my Calculus III , Linear Algebra and then I’ll be in my engineering courses altogether. Now my question is will colleges and universities accept a transfer that wants to go to their school in the spring of 2016 with hopefully a 3.8 GPA or possibly higher? Or should I take a Calculus 3 class in the spring of 2016 because colleges and universities mainly look at transfer students for the fall 2016 semester? By the way I will then have 73 credit hours What do you guys think? I’m looking to apply to good schools. These are some of the schools I have my mind on.

(( Georgia technical institute, UC Berkley , Stanford, UI At Urbana Champaign, University of Arkansas at Pinebluff , University of Iowa and University of Michigan ))