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**DrLiangMath****Member**- Registered: 2022-03-24
- Posts: 169

Dear members in this nice community,

My name is Derek Liang, and I am from Canada. I hold a bachelor degree in math education, a PhD in math from China and a PhD in applied math from Canada. I have more than twenty years of experience teaching and tutoring math at both secondary school and university levels.

I am creating some math tutoring videos on **calculus, equation solving, algebra, and geometry & trigonometry**. These short videos focus on developing problem-solving skills. You are welcome to watch and subscribe to the free math tutoring channel: ** Math Tutoring by Dr. Liang**

**Calculus**

**Happy New Year 2023 !! | How to Compare the Two Large Exponents 2022^2023 and 2023^2022?**

**95% Fail !! | Ingenious Method for Computing a Difficult Limit Involving Cosine**

**Powerful Integration Technique - Feynman's Trick: Ideas and Examples | Gaussian Integral**

What Are the Coordinates of the Spiral Center?

What Is the Sum of the Alternating Series 1/1-1/2+1/3-1/4+•••?

What Is the Sum of the Infinite Series 1/1 + 1/2^2 + 1/3^3 + •••?

Ingenious Method | All Functions Satisfying f(x/y)=f(x)/f(y) | Math Olympiad

Cool Tricks for Evaluating Definite Integrals Involving e^x, sin(x) and cos(x)

What is the Derivative of x^x? | Implicit Differentiation | Chain Rule | Natural Logarithm

How to Evaluate Definite Integrals: Some Advanced Techniques

Fundamental Theorem of Calculus: A Step-by-Step Approach

How to Evaluate Definite Integrals: Trigonometric Substitutions

How to Evaluate Definite or Indefinite Integrals: Substitution

How to Evaluate Definite or Indefinite Integrals: Integration by Parts

A Simple Solution to a Difficult Integral

How to Integrate? A Step-by-step Guide

How to evaluate this integral quickly?

**Equation Solving**

**Solving the Beautiful Diophantine Equation a^2+b^2+c^2=1000 | Math Olympiad**

**Determine the root classification of any polynomial equation without actually solving it?**

**Math Olympiad: How to Solve this Exponential Equation?**

**Cool Tricks!! | Solution to the Sextic Equation x^6+2x^5-18x^2-81=0 | Math Olympiad**

**Beautiful Solution to the Difficult Quartic Equation x^4-16x-12=0**

**Cool Tricks for Solving the Difficult Exponential Equation x^(x^2-2x+1)=2x+1**

**Beautiful Solution to a Difficult Exponential Equation with Two Variables x and y**

**Cool Tricks!! | Beautiful Solution to the Quintic Equation 6x^5-11x^4-11x+6=0**

**Cool Trick for Solving the Diophantine Equation (x+y)^2=x^3+y^3 | Integer Solution**

**Math Olympiad | Beautiful Solution to a Mixed System of Linear and Quintic Equations**

How to Solve the Exponential Equation 3^x+9^x+27^x=14?

Integer solutions to the Radical Equation √m + √n = √325

Ingenious Method | Solutions to Exponential Equation 4^x+64x-192=0

All Solutions to the Diophantine Equation a^2+b^2=2009 | Euclidean Division

How to Solve the Quartic Equation x^4+x^2=90?

How to Solve the Difficult Quartic Polynomial Equation x^4+4x-1=0?

Full Picture of Solutions to the Exponential Equation x^x=a

Simple Way to Solve the Septic Polynomial Equation 16x^7+7x^3+1=0

How to Solve the Difficult Quintic Equation x^5+x^4+1=0?/]

How to Solve the Special Exponential Equation x^(x^x^x^5) =5? | Mathematical Induction

How to Find the Exact Solutions to the Cubic Equation x^3-3x+1=0?

Ingenious Method for Solving a Difficult Quintic Equation via Substitution

Step-by-step Approach for Solving a System of Quadratic Equations

Novel Approach for Finding the Sum of Cubes of Solutions to Cubic Equation x^3-x^2+1=0

Ingenious Method for Solving Radical Equations

How to Solve the Exponential Diophantine Equation 2^a+4^b+8^c=328? | Integer Solution

Cool trick for Solving Algebraic Equations by Reducing the Degree

How to Solve Quadratic Equations with Two Variables? | Sum of Squares

Cool Trick for Solving Cubic Equation | difference of squares | difference of cubes

How to Find Integer Solutions to the Exponential Equation? | Diophantine Equation

How to Solve the Mixed Exponential and Trigonometric Equation?

How to Solve this Special Exponential Equation? | Exponent Rule

Number of Real Solutions to the Parametric Cubic Equation x^3-3ax+2=0

How to Solve Inequalities Involving Powers | Integer solution | Compare Exponents

How to Solve System of Linear Equations with a Parameter? | Symmetry | Solution

How to Solve the Exponential Equation? | Pythagorean Triple | Pythagorean | Solution

Solving a Radical Equation with Two Variables? | Rationalization | Perfect Square

How to Solve the Exponential Equation x^x=x? | Exponent and base

Ingenious Method for Solving Systems of Diophantine Equations | Divisibility | Prime

Solutions to Double Quadratic Equation | Perfect Square Formula

Full Solution to Diophantine Equation | Sum of Perfect Squares | Integer Solution

How Many Integer Solutions Does the Diophantine Equation Have?

Sum of Squares of the Solution to Nonlinear Equations? | Quadratic Equation | Cubic Equation

How to Solve the Cubic Diophantine Equation? | prime number | integer solution

All Integer Solutions to the Diophantine Equation? | Perfect Squares | Pythagorean

How to Find Integer Solutions to the Exponential Equation? | Diophantine Equation

How to Solve the Log Equation Involving Square Roots?

How to Solve the Diophantine Equation? | Sum of Perfect Squares

Solving an Exponential Equation? | fraction | rational function | Math Olympiad

How to Solve this Exponential Equation?

How to Find the Sum of Solutions to Nonlinear Equations?

How to Solve this Difficult Radical Equation?

Finding Integer Solutions to an Exponential Equation?

Solving a System of Logarithmic Equations?

How to Solve this Special Exponential Equation?

How to Solve this Mixed Exponential Equation?

Solving an Exponential Equation with Radicals?

How to Solve this Algebraic Equation?

How to Solve this Cubic Equation?

How to Solve this Mixed System of Exponential and Linear Equations?

How to Solve this Mixed System of Algebraic Equations?

Solving a Cubic Equation with Two Variables?

How to Solve Quadratic Equations Related to Pythagorean Triples?

Can You Solve the Cubic Polynomial Equation?

How to Solve the Quartic Polynomial Equation?

How to Solve the System of Exponential Equations?

How to Solve the Exponential Equation?

How to Find Integer Solutions to the Exponential Equation?

How to Solve the Double Cubic Algebraic Equation?

How Many Solutions Does the Special Exponential Equation Have?

How to Solve this Algebraic Equation by Reducing the Degree via Substitution?

How to Solve a Quartic Polynomial Equation with Average Substitution?

How to Solve the Double Exponential Equation 3^5^x = 5^3^x?

How to Solve the Nice Exponential Equation?

**Algebra**

**Cool Tricks for Solving Exponential Equations! | Exponent Rules**

**Cool Algebraic Tricks! | How Many Solutions Can You Find? **

**Cool trick! | What is the 5-digit number?**

**Cool Algebraic Tricks! | How to Solve the Quadratic Diophantine Equation?**

**What Is the Minimum of the Quartic Polynomial (x+1)(x+2)(x+3)(x+4)?**

**Cool algebraic tricks! | What is the value of ab given a-b=10 and a^3-b^3=100?**

**Cool Tricks for Finding the Value of x^100+1/x^100**

**Cool Tricks!! | Finding the Value of the Sum of Squares a^2+b^2?**

**What is the value of a if the 6-digit number 20210a is prime? | You should know these tricks!**

**What Is the Maximum of the Quadratic Expression a^2+b^2-ab?**

**What Is the Value of (60-x)^2+(x-40)^2? | Sum of Squares | Algebra**

**Cool Tricks! | Solving the Challenging Diophantine Equation a^2+ab+b^2=343**

Cool Tricks for Comparing the Large Exponents 2022^2022 and 2021^2023

How to Prove the Inequality 1/1^2+1/2^2+1/3^2+•••1/100^2<2?

What Is the Value of the Sum of Squares a^2+b^2?

How to Find the Smallest Positive Integers for the Inequality 12/11<y/x<11/10?

Cool Trick for Evaluating a Quadratic Expression (a-2000)^2

Cool Tricks for Evaluating Algebraic Expressions | You Should Know

Two Methods for Proving the Polynomial Inequality x^16-x+1>0

How to Find the Value of the Trigonometric Expression

Cool Tricks for Simplifying the Radical Expression (1+3√2-2√3)/(√2+√3+√6)

Ingenious Tricks for Evaluating the Hexic Algebraic Expression x^6+1/x^6

Cool Tricks for Simplifying Cube Roots

Simple Method for Calculating Exponents Involving Radicals

How to Find the Sum of Squares? | Perfect Square

Cool Trick for Evaluating an Algebraic Expression with Three Variables

How to Compare Fractions Involving Exponents? | Which One Is Larger?

An Ingenious Trick for Evaluating a Tricky Algebraic Expression a^8+7/a^4

90% Give Up! | Which Exponent Is Larger, e^? or ?^e?

Cool Trick for Finding the Value of the Algebraic Expression x^2/(x^4-x^2+1)

How to Evaluate an Algebraic Expression with Three Variables?

Cool Trick for Finding the Largest Prime Factor | Prime Factorization

Finding the Sum of Quartic Numbers Giving the Sum and the Sum of Squares?

Simple Method to Compare Two Close Fractions | Which One Is Larger?

Evaluating Algebraic Expression Giving a Quadratic Equation | polynomial

How to Compare Two Large Numbers? | Which Exponent Is Greater?

Square Root of a Large Number | Prime Factorization | Square Number | Perfect Square

Express a Fraction as a Sum of Fractions | Diophantine Equation | Integer Solution

Which Exponent Is Greater? | Compare Two Large Numbers

How to Find the Expression of a Function f(x)?

How to Find the Difference of a Sextic Polynomial and Its Reciprocal?

What is the Value of the Algebraic Expression? | Golden Ratio | Conjugate

What Is the Product of Two Huge Numbers?

How to Evaluate the Difference of High Exponents?

How to Evaluate this Algebraic Expression?

How to Factor this Quartic Polynomial?

What Is the Value of this Infinite Radical?

How to Solve this Quintic Polynomial Related Problem?

How to Compare Two Very Large Exponents?

Can You Calculate the Square Root Quickly Without Calculator?

Can You Calculate the Square Root Quickly Without Calculator (Part 2)?

How to Evaluate This Algebraic Expression Wisely?

Solving an Algebraic Problem Involved Exponentials?

Can You Solve the Number Puzzle (Cryptarithm) in 30 Seconds?

How to Simplify the Square Root Expression?

Factoring a Quartic Polynomial with Two Terms Over the Real Numbers?

What Is the Sum of the Two Reciprocal Exponents?

What is the Value of the Algebraic Expression with Radicals?

Factoring Polynomials: Some Advanced Techniques

Factoring Polynomial Expressions: Step-by-Step Procedures

Three Methods for Finding the Greatest Common Factor (GCF) of Two or More Integers

Three Methods for Finding the Least Common Multiple (LCM) of Two or More Integers

How to Find the Inverse of a Function Which Is Not One-to-One?

How to Find the Maximum or Minimum of a Quadratic Function?

Domain and Range of a Function: an Easy and Practical Approach

**Geometry & Trigonometry**

**COOL!! | How to Find the Area of the Incircle of a Right Triangle? | Pythagorean Triple**

What Are the Coordinates of the Spiral Center?

Simple and Understandable Proof: How to prove a Tangent Line is Perpendicular to the Radius?

A Straightforward but Powerful Approach for Proving Trigonometric Identities

How to Find the Area Between Three Tangent Unit Circles?

90% Give Up! | Cool Tricks for Finding the Area | Circle | Triangle

Finding Area of a Circle? | Square | Pythagorean Theorem | Tangent Line | Radius

What is the Area of the Square? | Circle | Pythagorean Theorem

How to Find the Length of the Hypotenuse of a Right Triangle?

Sine or Cosine Writing Sinusoidal Functions Given Graphs

Simply Graphing Sine Cosine and Sinusoidal Functions with Transformations

Evaluating Trigonometric Ratios: Step-by-Step Procedures

**Puzzles & Miscellaneous**

**Money Puzzle: Can You Help the Cashier? | Diophantine Equation**

A Practical Way for Solving Math Problems by An Experienced Math PhD | How to Get Better at Math

What Is Wrong with the Proof 3=0? | Paradox | Cubic Root

*Last edited by DrLiangMath (2023-03-24 00:49:42)*

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**Bob****Administrator**- Registered: 2010-06-20
- Posts: 9,635

hi Dr Liang,

Welcome to the forum.

Thanks for this link. I'm sure many will find these videos most useful.

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Sometimes I deliberately make mistakes, just to test you! …………….Bob

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**DrLiangMath****Member**- Registered: 2022-03-24
- Posts: 169

Hi Bob,

Thank you very much for your encouragement and for giving me the chance to post my YouTube link in this nice community.

Derek

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**DrLiangMath****Member**- Registered: 2022-03-24
- Posts: 169

A new free math tutoring video "How to Find the Inverse of a Function Which Is Not One-to-One?" is now available

https://www.youtube.com/watch?v=2yK9ztPcGWY&t=1s

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**MathIsMagical****Member**- From: Encanto
- Registered: 2022-03-05
- Posts: 10

this is advertising, right?

call me a queen uwu cuz im cute uwu and im better than u guys uwu and i deserve to have a life uwu unlike u guys uwu and im smarter than u cuz i know that 1+1=2 uwu and i am glam uwu i love myself uwu i am galaxy girl uwu i am infinity girl uwu

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**Bob****Administrator**- Registered: 2010-06-20
- Posts: 9,635

The forum rules do state "No Spam. Spam includes messages .... that are .... promotional in nature."

If someone advertises a commercial product I remove the post and usually the member. I have checked out these videos and they are genuinely mathematical teaching aids, offered for free. We have had, for some time, another member regularly posting links to similar material and no one has objected to that. I have, therefore, been happy to allow these links to remain.

Many U tube videos start with a commercial advert. These don't.

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Sometimes I deliberately make mistakes, just to test you! …………….Bob

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**DrLiangMath****Member**- Registered: 2022-03-24
- Posts: 169

Hi Bob, thank you for your support.

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**jabah013.307****Member**- From: Kingdom Of Jabah013.307
- Registered: 2021-07-05
- Posts: 165
- Website

Nice!

Quote Of The Month:

'Whether it's the best of times or the worst of times, it's the only time we've got.' - Art Buchwald.

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**DrLiangMath****Member**- Registered: 2022-03-24
- Posts: 169

Thanks!

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**DrLiangMath****Member**- Registered: 2022-03-24
- Posts: 169

** My post has been successful updated! Now you can watch the video you like by simply clicking the link!**

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**DrLiangMath****Member**- Registered: 2022-03-24
- Posts: 169

Today's new video: **What is the Value of the Algebraic Expression with Radicals? | Math Olympiad**

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**DrLiangMath****Member**- Registered: 2022-03-24
- Posts: 169

How to Solve the Nice Exponential Equation? | Math Olympiad

*Last edited by DrLiangMath (2022-07-29 23:28:14)*

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**DrLiangMath****Member**- Registered: 2022-03-24
- Posts: 169

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**DrLiangMath****Member**- Registered: 2022-03-24
- Posts: 169

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**DrLiangMath****Member**- Registered: 2022-03-24
- Posts: 169

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**DrLiangMath****Member**- Registered: 2022-03-24
- Posts: 169

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**DrLiangMath****Member**- Registered: 2022-03-24
- Posts: 169

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**DrLiangMath****Member**- Registered: 2022-03-24
- Posts: 169

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**DrLiangMath****Member**- Registered: 2022-03-24
- Posts: 169

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**DrLiangMath****Member**- Registered: 2022-03-24
- Posts: 169

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**DrLiangMath****Member**- Registered: 2022-03-24
- Posts: 169

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**DrLiangMath****Member**- Registered: 2022-03-24
- Posts: 169

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**DrLiangMath****Member**- Registered: 2022-03-24
- Posts: 169

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**DrLiangMath****Member**- Registered: 2022-03-24
- Posts: 169

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**DrLiangMath****Member**- Registered: 2022-03-24
- Posts: 169

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