<p>There are three basic calculus courses. Differential calculus, integral calculus, and multivariable calculus (corresponding to A, B, and C). There are two levels of rigor. The two levels are not sequential. You either take 10A-C or you take 20A-C, but you don't take 20A after 10C. 10A, 10B, and 10C are somewhat easier than 20A, 20B, and 20C. Technical majors (such as engineering) usually require the 20 series because it's more rigorous. Less technical majors (like biology) that still require calculus let you choose between the series. Many people in those majors take the 10 series, but that can be a mistake if you want to learn more or there's a possibility of changing to a major that requires the 20 series. Here are the descriptions from the course catalog (ucsd.edu/catalog):</p>
<p>10A: Differentiation and integration of algebraic functions. Fundamental theorem of calculus. Applications.</p>
<p>10B: Further applications of the definite integral. Calculus of trigonometric, logarithmic, and exponential functions. Complex numbers. </p>
<p>10C: Vector geometry, velocity, and acceleration vectors. </p>
<p>20A: Foundations of differential and integral calculus of one variable. Functions, graphs, continuity, limits, derivative, tangent line. Applications with algebraic, exponential, logarithmic, and trigonometric functions. Introduction to the integral. </p>
<p>20B: Integral calculus of one variable and its applications, with exponential, logarithmic, hyperbolic, and trig-onometric functions. Methods of integration. Infinite series. Polar coordinates in the plane and complex exponentials. </p>
<p>20C: Vector geometry, vector functions and their derivatives. Partial differentiation. Maxima and minima. Double integration,</p>