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I'm facing a tough decision and I would like to ask you for some guidance and tips regarding my situation.

I want to apply for econ grad school this fall and I'm missing some math essentials. The program I followed did not put so much emphasis on the mathematical background, which is a pity. I figured I need at least Calculus III for any program I would like to apply for. During my undergrad I did Calc I. Nothing else. I would like to use the summer to do Calc III in a 5 week course, since I don't have enough time to get Calc II done, before.

The curriculum of the Calculus course I want to take looks as follows:

Vectors and the Geometry of Space

Cylinders and Quadric Surfaces

Vector Functions

Partial Derivatives

Multiple Integrals

Vector Calculus

Differential Equations

My question is: Do I have a realistic chance to pass Calc III, without having done Calc II? Also, does it build heavily on Calc II or is there a lot of new material?

Thanks for your help!

Captain Math