<p>I'm just finishing Calculus 1 in my freshman year as a mech engineering major at a semester-based university. The course included topics such as limits, derivatives, implicit differentiation, related rates, exponential/log/inverse trig functions, optimization, Newton's method, Riemann sums, antiderivatives, indefinite and definite integrals, Fundamental Theorem of Calculus, u-substitution, area between curves. It went well and I appear to have an A going into my final exam.</p>
<p>I have a month off before starting Calculus 2 in the spring semester. The catalog says it will be covering applications of the integral, techniques of integration, infinite series including convergence tests and Taylor series, parametric equations, polar coordinates, introduction to differential equations. </p>
<p>If I can bring myself to do it, I thought I might try to get in some general review over my time off before starting the new semester. Are any of the topics in the first paragraph above particularly important to later math -- or relevant to engineering -- and thus worthy of special attention?</p>