MTH 128 - Technical Mathematics I

Unit 1: Basic Algebraic Operations

Unit 2: Functions and Graphs

Unit 3: The Trigonometric Functions

Unit 4: Systems of Linear Equations ; Determinants

Unit 5: Factoring and Fractions

Unit 6: Quadratic Equations

Unit 7: Trig Functions For Any Angle

Unit 8: Vectors and Oblique Triangles

Unit 9: Graphs of Trig Functions

Unit 10: Exponents and Radicals

Unit 11: Complex Numbers

Unit 12: Exponential and Logarithmic Functions

Unit 1: Basic Algebraic Operations

- Points on a Number Line

- Finding the Reciprocal of a Mixed Number

- Absolute Value

- Number Sets Example 1

- Number Sets Example 2

- Number Sets Example 3

- Number Sets Example 4

- Word Problem Example

- Adding and Subtracting Negative Numbers

- Multiplying Positive and Negative Numbers

- Dividing Positive and Negative Numbers

- Order of Operations Example 1

- Order of Operations Example 2

- Order of Operations Example 3

- Order of Operations Example 4

- Commutative Law of Addition

- Commutative Law of Multiplication

- Associative Law of Addition

- Associative Law of Multiplication

- The Distributive Property

- Rounding Decimals

- Introduction to Roots

- Simplifying Expressions with Exponents Example 1

- Simplifying Expressions with Exponents Example 2

- Simplifying Expressions with Exponents Example 3

- Converting a Number in From Scientific Notation into a Decimal Number

- Converting Decimal Number into a Number in Scientific Notation

- Multiplying in Scientific Notation

- Scientific Notation Word Problem

- Simplifying Square Roots

- Finding Cube Roots

- Simplifying Cube Roots

- Simplifying Radical Expressions Example 1

- Simplifying Radical Expressions Example 2

- Simplifying Radical Expressions Example 3

- Radicals of Higher Roots

- Simplifying a Polynomial (collecting like terms)

- Adding Polynomials

- Subtracting Polynomials

- Multiplying Monomials

- Multiplying Monomials by Polynomials

- Multiplying Binomials

- Multiplying Polynomials

- Dividing a Monomial by a Monomial

- Dividing a Polynomial by a Monomial 1

- Dividing a Polynomial by a Monomial 2

- Dividing a Polynomial by a Binomial

- Dividing Polynomials with Remainders

- Solving a Linear Equation Example 1

- Solving a Linear Equation Example 2

- Solving a Linear Equation Example 3

- Solving a Linear Equation Example 4

- Solving a Linear Equation Example 5

- Rearrange a Formula to Isolate a Specific Variable

Unit 2: Functions and Graphs

- Introduction to Functions 1

- Introduction to Functions 2

- Introduction to Functions 3

- Introduction to Functions 4

- Evaluate a Formula or Function Using Substitution

- Domain and Range of a Function 1

- Domain and Range of a Function 2

- Domain and Range of a Function 3

- The Coordinate Plane

- Plotting (x,y) Coordinates

- Finding the Length of a Line Segment or Finding the Distance Between Two Points (Distance Formula)

- Graphing a Basic Function

- Graphing a Quadratic Function

- Graphing Exponential Functions

- Graphing Square Root Functions

Unit 3: The Trigonometric Functions

- Language and Notation in Geometry

- Angle Basics

- Measuring Angles in Degrees

- Radians and Degrees

- Using SOH CAH TOA and Pythagoreans Theorem to Solve Right Angle Triangles Part 1

- Using SOH CAH TOA and Pythagoreans Theorem to Solve Right Angle Triangles Part 2

Unit 4: Systems of Linear Equations; Determinants

- Checking if a Point is (or is not) a Solution in a Linear System

- Finding Slope from a Graph

- Finding Slope When Given Two Points (or Ordered Pairs) Example 1

- Finding Slope When Given Two Points (or Ordered Pairs) Example 2

- Graphing a Linear Function by the X and Y Intercept Method

- Graphing a Linear Function (Line) by the Slope Y-Intercept Method Example 1

- Graphing a Linear Function (Line) by the Slope Y-Intercept Method Example 2

- Solving Linear Systems by Graphing

- Solving Linear Systems by Substitution Method Example 1

- Solving Linear Systems by Substitution Method Example 2

- Solving Linear Systems by Elimination (Addition) Method Example 1

- Solving Linear Systems by Elimination (Addition) Method Example 2

- Solving Systems with 3 Unknowns 1

- Solving Systems with 3 Unknowns 2

- Solutions to Three Variable System

Unit 5: Factoring and Fractions

- Binomial Squared (Special Products in Algebra)

- Difference of Squares (Special Products in Algebra)

- Finding The Greatest Common Factor (GCF)

- More GCF Examples

- Common Factoring Example

- More Common Factoring Examples

- Factoring Easy Trinomials (Trinomial with a Leading One Coefficient)

- Factor by Grouping (Triple Common Factor)

- Factoring Hard Trinomials (Trinomials with a Non-One Coefficient)

- Factoring a Trinomial with a Common Factor First

- Factoring a Perfect Square Trinomial

- Factoring a Difference of Squares

- Factoring a Sum of Cubes

- Factoring a Difference of Cubes

- Simplifying Rational Expressions

- Multiplication and Division of Rational Expressions

- Adding and Subtracting Rational Expressions Example 1

- Adding and Subtracting Rational Expressions Example 2

- Adding and Subtracting Rational Expressions Example 3

- Solving Rational Equations Example 1

- Solving Rational Equations Example 2

Unit 6: Quadradic Equations

- Solving Quadratics by Factoring Example 1

- Completing the Square

- Completing the Square to Solve Quadratics

- Quadratic Formula 1

- Quadratic Formula 2

- Quadratic Formula 3

- Quadratic Formula 4

- Graphing a Quadratic

Unit 7: Trig Functions For Any Angle

Unit 8: Vectors and Oblique Triangles

- Introduction to Scalars and Vectors

- Visualizing Vectors in Two Dimensions

- Vector Addition and Subtraction Examples

- Proof: Law of Sines

- Proof: Law of Cosines

Unit 9: Graphs of Trig Functions

- Graphs of Trigonometric Functions - Sine

- Graphs of Trigonometric Functions - Cosine

- Graphs of Trigonometric Functions - Tangent

- Graphing Trigonometric Functions: Transformations

- Finding the Trigonometric Equation From the Graph 1

- Finding the Trigonometric Equation From the Graph 2

Unit 10: Exponents and Radicals

- Law of Exponents: Multiplication (LEM)

- Law of Exponents: Division (LED)

- Law of Exponents: Powers (LEP)

- Simplifying Rational Expressions Using Exponent Laws - Example

- Law of Exponents: Extension of LEP 1

- Law of Exponents: Extension of LEP 2

- Law of Exponents: Negative Exponents

- Rational Exponents and Exponent Laws

- Simplifying Expressions With Rational Exponents

- Simplifying Radical Expressions Example 1

- Simplifying Radical Expressions Example 2

- Simplifying Radical Expressions Example 3

- How to Rationalize a Denominator

- Addition of Radical Expressions

- Subtraction of Radical Expressions

- Adding and Subtracting Radical Expressions

- Multiplying Rational Expressions Example 1

- Multiplying Rational Expressions Example 2

- How to Rationalize a Denominator

Unit 11: Complex Numbers

- Introduction to i and Complex Numbers

- Real and Imaginary Parts of a Complex Number

- Basic Operations with Complex Numbers

- Complex Conjugates

- Graphical Representation of a Complex Number

- Adding Complex Numbers

- Subtracting Complex Numbers

- Multiplying Complex Numbers

- Dividing Complex Numbers

- Operations of Complex Numbers Addition

- Operations of Complex Numbers Subtraction

- Operations of Complex Numbers Multiplication

- Operations of Complex Numbers Division

- Polar Form of a Complex Number

- Exponential Form of a Complex Number

Unit 12: Exponential and Logarithmic Functions

- Graphing Exponential Functions

- Solving Exponentials with Logarithms

- Logarithm Properties (Sum and Difference Properties)

- Logarithm Properties (Multiple Property and Change of Base)

- Proof of the Sum Property of Logarithms

- Proof of the Difference and Multiple Property of Logarithms

- Simplifying Logarithms

- Change of Base Formula

- Calculating a Logarithm with a Calculator

- Logarithmic Equations

- Solving Logarithmic Equations

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