For 16A, you need Calculus and its applications, Volume One, which looks like this: It consists of Chapters 0 through 6 of Goldstein, Lay, Schneider, Asmar, Calculus and its applications, 11th …

In other words calculus done right. There will be many challenging problems. The second purpose of the course to learn how to read and write proofs. When you do the homework you should bear both …

You will be required to log into zoom at the beginning and sign off at the end after submitting your test electronically. There will be a final exam, conditions similar to the test.

Moreover, using the same argument as that in the proof of Theorem 20.2, one can derive a similar q-analogue of Taylor's formula with the Cauchy remainder in the symmetric q-calculus.

To show this, starting at the beginning of the sequence, keep track of the length of the longest increasing and longest decreasing sequence which ends at each member.

Minimal surfaces date back to Euler and Lagrange and the beginning of the calculus of variations. Many of the techniques developed have played key roles in geometry and partial diferential equations.

straight line y = ax + b, where a and b are to be chosen. Usually when we talk about linear approximations in calculus, we are interested in x close to one special v lue x0; but here I am …

This proposal marked the real beginning of general interest in the calculus of variations. (The term `brachistochrone' derives from the Greek brachistos meaning shortest and chronos meaning time.)

Calculus 1A: Differentiation, Calculus 1B: Integration, Calculus 1C: Coordinate Systems and Infinite Series.

This subject largely consists of the introduction of new multi-dimensional concepts, and description of how they can be calculated or computed by the techniques of one dimensional calculus.