Multiplying and dividing large numbers. Simplifying fractions and converting percentages. Handling square roots and exponents. These and other skills are the veritable foundation on which all of mathematics rests. To master them is to unlock the door to more advanced areas of study—such as algebra, geometry, and calculus—and to discover new levels of confidence in dealing with the math of everyday life.
Necessary and sufficient conditions for a weak and strong extremum. Legendre transformation, Hamiltonian systems. Constraints and Lagrange multipliers. Space-time problems with examples from elasticity, electromagnetics, and fluid mechanics. Sturm-Liouville problems. Approximate methods.
Calculus 3 is considered by most to be a very difficult course to master in the realm of Calculus. This is because you will learn about many different topics, and each topic builds on the previous. If you don't understand something early on, the chances of "catching up" are drastically reduced as time goes on.