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I have used Courant and a little of Spivak for Calculus 1, and loved it! Extremely complete and challenging. Great books.

So, this is exactly what I will need to know:

*Ordinary differential equations*

Families of equations, initial value problems, separable equations, integrating factor, second order differential equation, boundary value problem, nonhomogeneous differential equation. Applications.

Real functions of several variables.

Graphs, isopleths, limits and continuity.

Partial derivatives.

Interpretation, higher order derivatives, tangent planes.

Differentials.

Linear approximation, increment theorem, chain rule, implicit differential (implicit function theorem).

Directional derivative and gradient vector, maximum and minimum values, Lagrange multipliers.

Families of equations, initial value problems, separable equations, integrating factor, second order differential equation, boundary value problem, nonhomogeneous differential equation. Applications.

Real functions of several variables.

Graphs, isopleths, limits and continuity.

Partial derivatives.

Interpretation, higher order derivatives, tangent planes.

Differentials.

Linear approximation, increment theorem, chain rule, implicit differential (implicit function theorem).

Directional derivative and gradient vector, maximum and minimum values, Lagrange multipliers.

What would you guys recommend?