Michael T

Colorado Springs, CO

Math And Physics Expertise



I have extensive teaching experience over 40 years:

Physics lecturer at LSU
Physics teaching assistant at LSU
Tutored athletes at UCONN
Mentored engineers and technicians
at TI, Atmel and IMFT
Private tutoring at Cheyenne Mountain High School

I have a masters degree in physics (LSU) and bachelors degree in computer science (UCCS). I have worked as a semiconductor engineer around the world for 35 years. I have given countless presentations and training sessions.

I bring a unique understating of math and physics. The material I present is formal and rigorous, but my presentation style is informal and fun. Understanding comes quicker if the material is made to be enjoyable.


MS physics LSU

Subjects of Expertise

SAT Math, ACT Math, GMAT Math, Pre-Algebra, Algebra 1, Algebra 2, Geometry, Trigonometry, Calculus, Statistics, Physics, Pre-Calculus

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8 Tutorials by Michael T


This tutorial will not give the solution to a specific problem. Rather it will show how we define the definition of a number raised to the zero power, a fractional power or a negative power.

A Complicated Logarithm Problem

I hope you know that the following theorems are true log_ab^c=c*log_ab log_ax + log_ay = log_a(x*y) log_ax - log_ay = log_a(x/y) We are going to use all of these theorems to simplify a complicated logarithm expression

What is a Logarithm

For every function there is an inverse function. If y can be written as an expression of x, then, inversely, x can be written as an expression of y. For example, say you know that y=2*x. Then… x = \frac{y}{2}} An exponential, like all functions, has an inverse. That inverse is called a logarithm. So…

Product Rule for Logarithms

Let’s show that log_a(c*d)=log_a(c) + log_a(d) PROOF: 1. Let log_a(c)=x …. We can name it anything we like 2. Let log_a(d)=y …. Again we can name it anything we like 3. a^x=c and a^y=d … Equivalent exponential forms of the statements in steps 1 and 2. 4. a^x•a^y=c*d .. Reason: If A=B & C=D, then…

Mathematical Induction

Mathematical induction is a form of proof that takes place in two parts. It is surprisingly useful. Part 1) Prove that the statement is true for the number 1. Part 2) Prove that if it is true for any number n then it is also true for the number n+1. Think about it… we first…

Square Roots of Complex Numbers

Just like for real numbers there will be two square roots for a complex number. Finding these roots involves solving a system of two equations in two unknowns Let’s say we want the square root of 3 + 4i. The square root will be of the form a + bi Then $(a+bi)^2 = a^2 +…

Keeping Track of Minus Signs in Parentheses: Subtraction

When evaluating an expression, the operations inside parentheses must be performed first. So 3 - (4-2) is the same as 3 - 2. Both are equal to 1. The correct treatment of plus and minus signs often causes confusion, especially when there are variables in the expression.

Multiplying Complex Numbers

We wish to multiply two complex numbers, say (a+bi)(c+di) We will use the FOIL method: First Outer Inner Last. ******************************************** PLOT (PL)(OT) (PO) + (PT) + (L0) + (LT) F…………O…………I…………L your plot has been foiled 🙂 ********************************************