Infinite sums, getting towards the idea of integration

Worked on problems related to the early ideas of calculus today.

The ideas today were closer to integration, finding an area using a summation of infinitely small rectangles using limits.

That meant finding the area of one rectangle and adding up all of them. So a base multiplied by a width.

The actual shape was a triangle and rectangle, but the technique becomes more useful for shapes which are not easy to calculate.

There were quite a few steps, so a single mistake could throw everything off.

Algebra at CSUMB with trig identities- sine, cosine, tangent, cosecant, secant, cotangent

We mostly did problems with trig identities.

SOHCAHTOA
CHOSHACAO

Reduced a few radicals to a simpler form.

Talked about how the 30 60 90 triangle and 45 45 90 triangles have ratios that you should probably know in this context.

Algebra at CSUMB with logarithms

We mostly looked at problems with logarithms.

Used both the properties for the log of a product and the log of a quotient.

Saw how the base, exponent, and result are placed in the equations.

Graphed a few related functions. You can graph functions using an x and y grid and using points. It helps to know the shape in advance, but that’s not completely necessary.

RLS Friday sheet Precalculus tutoring – fourth order polynomial with complex numbers

We started by talking about the Lorentz Force Law which makes many problems with forces and magnetism make more sense in my opinion.

Then looked at a Friday sheet.

Did a problem with complex numbers starting with a fourth order polynomial  that had two zeros given. It involved either long division or synthetic division, we used long division.

Another problem had logarithms. e^x and lnx are functions that counteract each other.

The half angle formula was used for another problem.

Starting to look at limits in precalculus

We looked at limits in the context of the last few weeks of precalculus.

All of the functions we saw had a (single) removable discontinuity or hole. The limits were found for that point and two other points. For the limit to exist, it needs to go to the same place from the right and from the left.

It didn’t exactly make sense to find a limit for points that did not have holes, but that was part of some of the problems.

Tutoring Conceptual Physics at RLS

We looked at conceptual problems related to magnetism. The book used by the school doesn’t use equations much. Which seems like a strange approach to me.

I think it would be useful to see something like the Lorentz Force Law which involves the movement of a point charge in a magnetic field and has a cross product.

F=qvxB, where F, v, and B are vectors. The right hand rule can be used with the cross product.

Can look more at this later on, will bring another book.

Tutoring math at CSUMB, systems of equations and quadratic equations

We started by looking at systems of two equations with two variables and using substitution to solve.

Then did a few problems with three equations and three variables.

Also used u-substitution to solve a few quadratic equations. If they can be factored, that can be easier. Sometimes quadratic equations cannot be easily factored, in which case it can be useful to use the Quadratic Formula.

Tutoring Precal for RLS, Double angle formulas and graphing trig functions

We started by looking at homework which used the double angle formula.

The basic approach was to do two things, could start in either order.

1. Draw the angle with a right triangle on the xy axes.
2. Use a double angle formula which is convenient

You can figure out the ratios for the trig functions using
SOHCAHTOA
CHOSHACAO

Then looked at a previous test with graphing trig functions. Should spend more time on that. But one thing you can do most of the time is plot points by plugging in x values and getting y values. You use again,

SOHCAHTOA
CHOSHACAO

It does help quite a bit to know the basic shape of the functions.

Tutoring RLS Precalculus, trig functions and Friday sheet

We looked at some problems with trig functions, especially sum and difference formulas.

For many of them, the angle does not need to be known if the sides of the triangle are known.

Used the half angle formula a bit. Reviewed the quadrants and which trig functions are positive and negative in different positions.

Then got into the Friday sheet which dealt with logarithms a bit.

Newtons and Distance in an equation

Newtons and meters are sometimes related to each other and you can see the relationships within equations.

One such equation is that work is equal to the dot product of force and distance. Force has units of Newtons, distance has units of meters.

There are other equations with both units as well.