Author: senseadmin

Methods of Integration

Integration is not as easy as differentiation. This is first due to its nature. Finding a derivative of…

Cartesian Coordinates

Using Cartesian Coordinates we mark a point on a graph by how far along and how far up it is: They are also called Rectangular…

Integral Calculus

Gottfried Wilhelm Leibnitz (1646-1716) and Sir Isaac Newton (1643-1727) independently discovered calculus in the mid-17th century. Leibnitz, a German philosopher,…

Lagrange Multipliers

In the previous section we optimized (i.e. found the absolute extrema) a function on a region that contained its…

Finding Maxima and Minima using Derivatives

Where is a function at a high or low point? Calculus can help! A maximum is a high…

Examples on Chain Rule (Differentiation Rules)

Examples on Chain Rule Example 10.8 Find F′(x) if F (x) = √[x2 +1] Solution Take u = g(x) = x2 + 1 and f (u) =√u ∴ F (x) = ( fog)(x) = f (g(x)) Example…

Euler’s Homogeneous Function Theorem

Let  be a homogeneous function of order  so that (1) Then define  and . Then (2) (3) (4) Let , then (5) This can be…

Homogeneous Functions

To be Homogeneous a function must pass this test: f(zx,zy) = znf(x,y) In other words Homogeneous is when we can take…

Higher-Order Partial Derivatives

Fred has mastered differentiating when a function has only one variable. Somehow, he missed the lessons on partial…

Geometry of partial derivatives