In first-term calculus, one uses derivatives to approximate complicated functions by straight lines, the tangent lines. This is an example of linear approximation. Linear algebra is the study of linear maps and is pervasive throughout mathematics, both pure and applied. By introducing a small amount of linear algebra into the study of multivariable differential calculus, we will gain a be tter understanding of the derivative of a function of several variables. Neither the term “linear algebra” nor the word “calculus” may sound very geometric, but the course will frequently take on a very geometric flavor.
Both Math 9 and Math 11 are well suited for first-year students with a BC calculus background. In contrast to Math 11, however, Math 9 does not cover integral multivariable calculus. Students who take Math 9 and wish to complete the calculus sequence will go on to Math 13. Math 9 takes a more leisurely path through differentiable multi-variable calculus, while bringing in linear algebra to gain a deeper understanding.
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