## Latest Posts on Mathtuition88.blogspot.com

Recently, I have been blogging at http://mathtuition88.blogspot.com. Here are the latest posts that you may want to check out!

This is a JavaScript app that I wrote to perform the XOR function on two hexadecimal strings. This is to help solve one of the cryptography assignements on Coursera.

I am providing tuition for SMU Calculus module: Math 001. A previous student of mine passed the module, despite not having any H2 Maths background. The module is highly challenging, and includes multivariable calculus.

• Dragon Curve and Jurassic Park
This is to introduce two videos on the mysterious and fascinating fractal: The Dragon Curve. Not many people have heard about it!

Featured Book:  The Fractal Geometry of Nature ### Review

“A rarity: a picture book of sophisticated contemporary research ideas in mathematics.”–Douglas Hofstadter, author of Godel, Escher, Bach

## Second-derivative Test For Extrema Of Functions Of Two Variables

Excerpt:

Proof of the second-derivative test. Our goal is to derive the second-derivative test, which determines the nature of a critical point of a function of two variables, that is, whether a critical point is a local minimum, a local maximum, or a saddle point, or none of these. In general for a function of n variables, it is determined by the algebraic sign of a certain quadratic form, which in turn is determined by eigenvalues of the Hessian matrix [Apo, Section 9.11]. This approach however relies on results on eigenvalues, and it may take several lectures to fully develop. Here we focus on the simpler setting when n = 2 and derive a test using the algebraic sign of the second derivative of the function.

The full proof can be found in the featured book below: T. Apostol, Calculus, vol. II, Second edition, Wiley, 1967

Featured book:  Calculus, Vol. 2: Multi-Variable Calculus and Linear Algebra with Applications to Differential Equations and Probability (Volume 2) ## Undergrad Math Tuition: Maxima and Minima (Multivariable Calculus)

At the undergraduate level, sometimes functions are of two variables (x,y). How do we find the maximum or minimum points of such a function?

Read the following PDF to find out!

Recommended Book:  Multivariable Calculus, 7th Edition This is a highly practical book on Multivariable Calculus. It is also suitable for Engineers / Physics Majors. I learnt Multivariable Calculus from this book. 🙂