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“**Nice guy and effective tutor.**”

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My approach to teaching and comprehension is basic principles and clear communication of subject matter. It's always good to hear from students and people when they express how they really enjoyed the experience of learning.

I am an Electrical

In-person lessons

He visited us twice, and he was very effective as my daughter said she learned more in those two visits than in two weeks on class. We will certainly use him again and I would recommend him for anyone.

I am very happy to say that Avery has the knowledge that I need to get basic and necessary help with Algebra 3. I really need to pass this class to stay on track to graduate and he has been quite helpful.

Math:

Algebra 1,
Science:

Chemistry, Electrical Engineering, Physical Science, Homeschool:

Algebra 1,
Test Preparation:

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Integer Exponents In this section we will start looking at exponents and their properties.

Rational Exponents We will define rational exponents in this section and extend the properties from the previous section to rational exponents.

Real Exponents This is a short acknowledgment that the exponent properties from the previous two sections will hold for any real exponent.

Radicals Here we will define radical notation and relate radicals to rational exponents. We will also give the properties of radicals.

Polynomials We will introduce the basics of polynomials in this section including adding, subtracting and multiplying polynomials.

Factoring Polynomials This is the most important section of all the preliminaries. Factoring polynomials will appear in pretty much every chapter in this course. Without the ability to factor polynomials you will be unable to complete this course.

Rational Expressions In this section we will define rational expressions and discuss adding, subtracting, multiplying and dividing them.

Complex Numbers Here is a very quick primer on complex numbers and how to manipulate them.

Solving Equations and Inequalities

Solutions and Solution Sets We introduce some of the basic notation and ideas involved in solving in this section.

Linear Equations In this section we will solve linear equations, including equations with rational expressions.

Applications of Linear Equations We will take a quick look at applications of linear equations in this section.

Equations With More Than One Variable Here we will look at solving equations with more than one variable in them.

Quadratic Equations, Part I In this section we will start looking at solving quadratic equations. We will look at factoring and the square root property in this section.

- Topics included in this set of notes/tutorial are :

Preliminaries - Exponent Properties, Rational Exponents, Negative Exponents, Radicals, Polynomials, Factoring, Rational Expressions, Complex Numbers

Solving Equations and Inequalities - Linear Equations, Quadratic Equations, Completing the Square, Quadratic Formula, Applications of Linear and Quadratic Equations, Reducible to Quadratic Form, Equations with Radicals, Linear Inequalities, Polynomial & Rational Inequalities, Absolute Value Equations & Inequalities.

Graphing and Functions - Graphing Lines, Circles, and Piecewise Functions, Function Definition, Function Notation, Function Composition, Inverse Functions.

Common Graphs - Parabolas, Ellipses, Hyperbolas, Absolute Value, Square Root, Constant Function, Rational Functions, Shifts, Reflections, Symmetry.

Polynomial Functions - Dividing Polynomials, Zeroes/Roots of Polynomials, Finding Zeroes of Polynomials, Graphing Polynomials, Partial Fractions.

Exponential and Logarithm Functions - Exponential Functions, Logarithm Functions, Solving Exponential Functions, Solving Logarithm Functions, Applications.

Systems of Equations - Substitution Method, Elimination Method, Augmented Matrix, Nonlinear Systems.

Differential Equations, another Mathematics course, is a little unusual at first glance. And this may be because most pre-requisite for the courses, such as Calculus I and II along with all the Algebra courses, involve Familiar letters, symbols & numbers, mostly algebraic. Unlike Differential Equations which involves mostly just that " Differential Equations ."

My experience with Differential Equations has grown with the repetition in which we used them during my college years. The better you are at integration the easier they get. The more familiar you are with a subject the easier it is for you to comprehend. As a Student Studying Engineering, we use math sort of like a carpenters uses his tool-box, its second-nature and very necessary. So with a firm foundation of Calculus, Integration, Derivation and basic Algebraic skills there is no reason why you shouldn't excel in this subject. And I for one enjoy making Differential Equations, a sometimes uncomfortable subject, an easy and clear Mathematics course.

Integer Exponents In this section we will start looking at exponents and their properties.

Rational Exponents We will define rational exponents in this section and extend the properties from the previous section to rational exponents.

Real Exponents This is a short acknowledgment that the exponent properties from the previous two sections will hold for any real exponent.

Radicals Here we will define radical notation and relate radicals to rational exponents. We will also give the properties of radicals.

Polynomials We will introduce the basics of polynomials in this section including adding, subtracting and multiplying polynomials.

Factoring Polynomials This is the most important section of all the preliminaries. Factoring polynomials will appear in pretty much every chapter in this course. Without the ability to factor polynomials you will be unable to complete this course.

Rational Expressions In this section we will define rational expressions and discuss adding, subtracting, multiplying and dividing them.

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