Recently, I have been blogging at http://mathtuition88.blogspot.com. Here are the latest posts that you may want to check out!
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!
The Fractal Geometry of Nature
“A rarity: a picture book of sophisticated contemporary research ideas in mathematics.”–Douglas Hofstadter, author of Godel, Escher, Bach
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
Calculus, Vol. 2: Multi-Variable Calculus and Linear Algebra with Applications to Differential Equations and Probability (Volume 2)
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!
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. 🙂