Antiderivative

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This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

Ok. I'm taking a linear algebra class, just left class today, and my professor is a little (or a lot) kooky. He uses the Markhov matrices to find populations. Quite orthodox, of course. But the populations are Arachnids who are taking over the world in about 1000 years. Anyways, I usually feel the need to formularize my problem-solving approach (SI leader probs?). Here we go. This is my method for finding out how many Arachnids (adults and babies) exist in say, 1000 years. Can be used for other populations.

1. Set up the matrix, A. Make sure the columns add up 1. (There are exceptions; I am in an undergraduate class and I haven't been introduced to them). They will be in decimals or fractions, but convert the fractions to decimals, please.

2. Find the eigenvalues (λ - lambda) of A.

3. Use the eigenvalues to find the eigenvectors.

4. Use the eigenvectors as columns in matrix S.

5. Find the inverse of S (S^-1)

6. Diagonalize the matrix (Λ- capital lambda). Basically, take a matrix of the size that you are using for the problem, fill all spaces with zero's. Then, take your eigenvalues (λ) and insert them in the diagonal going from the first top right space to the last bottom left space. Tadaa! You have Λ !!!

7. Put Λ to whatever power you've been given (in my case, it was 1000 years). Remember that if an eigenvalue is less than 1 but greater than -1, with a high power it goes to zero (-1<λ<1, λ ^1000 = 0)

8. Multiply through the magic formula of S(Λ^n)(S^-1)(initial values vector)

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Published in 1991 by Wellesley-Cambridge Press, the book is a useful resource for educators and self-learners alike. It is well organized, covers single variable and multivariable calculus in depth, and is rich with applications.  In addition to the Textbook, there is also an online Instructor's Manual and a student Study Guide. Prof. Strang has also developed a related series of videos, Highlights of Calculus, on the basic ideas of calculus.The 2010 second edition of the Calculus textbook includes a new chapter on "Highlights of Calculus" that connects to the video series of the same name.  The new chapter has summaries and practice questions for all of the videos.  It also introduces The Exponential Function (e^x) as presented in Prof. Strang's video on this topic.

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