Site Map of Interactive Mathematics

Algebra

• Numbers
  • 1. Integers
  • 2. Number Properties
  • 3. Order of Operations
  • 4. Powers, Roots and Radicals
  • 5. Approximate Numbers
  • 6. Scientific Notation
  • 7. Ratio and Proportion
    • Math of Beauty
    • Pi
• Basic Algebra
  • 1. Addition and Subtraction of Algebraic Expressions
  • 2. Multiplication of Algebraic Expressions
  • 3. Division of Algebraic Expressions
  • 4. Solving Equations
  • 5. Formulas and Literal Equations
  • 6. Applied Verbal Problems
• Money Math
  • 1. Interesting Interest
  • 2. Credit Cards
  • 3. Math of House Buying
  • 4. Gold Rush?
  • 5. Money Charts and Fibonacci
  • 6. Superannuation
• Factoring and Fractions
  • 1. Special Products
  • 2. Factoring: Common Factor and Difference of Squares
  • 3. Factoring Trinomials
  • 4. The Sum and Difference of Cubes
  • 5. Equivalent Fractions
  • 6. Multiplication and Division of Fractions
  • 7. Addition and Subtraction of Fractions
  • 8. Equations Involving Fractions
• Exponents and Radicals
  • 1. Integral Exponents
  • 2. Fractional Exponents
  • 3. Simplest Radical Form
  • 4. Addition and Subtraction of Radicals
  • 5. Multiplication and Division of Radicals
  • 6. Equations With Radicals
• Exponential and Logarithmic Functions
  • 1. Exponential and Log Functions
  • 2. Graphs of Exp and Log Functions
  • 3. Log Laws
  • 4. Logarithms Base 10
  • 5. Natural Logarithms
    • Calculating the Value of e
  • 6. Logarithm Equations
  • 7. Log-Log and Semi-log Graphs
• Series and the Binomial Theorem
  • 1. Arithmetic Progressions
  • 2. Geometric Progressions
  • 3. Infinite Geometric Series
  • 4. The Binomial Theorem
• Systems of Equations
  • 1. Simultaneous Linear Equations
  • 2. Graphs of Linear Functions
  • 3. Graphical Solution of a System
  • 4. Algebraic Solutions of Linear Systems
  • 5. Graphical Solution of non-Linear Systems
  • 6. Algebraic Solution of Systems of Equations
• Quadratic Equations
  • 1. Quadratic Equations: Solution by Factoring
  • 2. Completing the Square
  • 3. The Quadratic Formula
  • 4. Graph of Quadratic Fn
  • 5. Equations in Quadratic Form
• Determinants and Matrices
  • 1. Determinants
  • 2. Larger Determinants
  • 3. Matrices
  • 4. Multiplication of Matrices
  • 5. Finding the Inverse of a Matrix
  • 6. Matrices and Linear Equations
• Inequalities
  • 1. Properties of Inequalities
  • 2. Solving Linear Inequalities
  • 3. Solving Nonlinear Inequalities
  • 4. Inequalities Involving Absolute Values
• Polynomial Equations
  • 1. Polynomial Functions and Equations
  • 2. Factors and Roots of a Polynomial Equation
  • 3. Factors and Roots of a Polynomial Equation

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Trigonometry

• Trigonometric Functions of Any Angle
  • Use of Trigonometry
  • 1. Angles
  • 2. Sine, Cosine, Tangent and the Reciprocal Ratios
  • 3. Values of the Trigonometric Functions
  • 4. The Right Triangle and Applications
  • 5. Signs of the Trigonometric Functions
  • 6. Trigonometric Functions of Any Angle
  • 7. Radians
  • 8. Applications of Radian Measure
  • 9. Radians and the Trigonometric Ratios
• Graphs of Trigonometric Functions
  • Use of Trigonometry
  • 1. Graphs of y = a sin x and y = a cos x
  • 2. Graphs of y = a sin bx and y = a cos bx
    • What are the frequencies of music notes?
  • 3. Graphs of y=asin(bx+c) and y=acos(bx+c)
  • 4. Graphs of tan, cot, sec and csc
  • 5. Applications of Trigonometric Graphs
  • 6. Composite Trigonometric Curves
  • 7. Lissajous Figures
• Analytic Trigonometry
  • 1. Trigonometric Identities
  • 2. Sums and Differences of Angles
  • 3. Double Angle Formulas
  • 4. Half Angle Formulas
  • 5. Trigonometric Equations
  • 6. Expressing in Form R sin(θ + α)
  • 7. The Inverse Trigonometric Functions

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Graphs

• Functions and Graphs
  • 1. Introduction to Functions
  • 2a. Domain and Range of a Function
  • 2b. Functions from Verbal Statements
  • 3. Rectangular Coordinates
  • 4. The Graph of a Function
  • 5. Graphs Using a Computer Algebra System
  • 6. Graphs of Functions from Tables of Data
• Plane Analytical Geometry
  • 1. Basic Definitions
  • 2. The Straight Line
  • 3. The Circle
    • Perpendicular Distance from a Point to a Line
  • 4. The Parabola
  • 5. The Ellipse
  • 6. The Hyperbola
  • 7. Polar Coordinates
  • 8. Curves in Polar Coordinates
    • Equiangular Spiral
• Kinematics
  • 1. Velocity and Acceleration Graphs
  • 2. Acceleration Graphs
  • 3. Kinematics Exercises
• Introduction to Vectors
  • 1. Vector Concepts and Notation
  • 2. Vector Addition in 1-D
  • 3. Vectors in 2 Dimensions
  • 4. Adding Vectors in 2-D
  • 5. Dot Product of 2-D Vectors
  • 6. Three-dimensional Space
  • 7. Vectors in 3-dimensional Space
  • 8. Cross Product of 2 Vectors
  • 9. Variable Vectors
  • 10. Vector Calculus
  • Vector Art

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Complex Numbers

• Complex Numbers With Applications
  • 1. Complex Number Definitions
  • 2. Basic Operations with Complex Numbers
  • 3. Graphical Representation of Complex Numbers
  • 4. Polar Form of Complex Numbers
  • 5. Exponential Form of Complex Number
  • 6. Products and Quotients of Complex Numbers
  • 7. DeMoivre's Theorem
  • 8. Application of Complex Numbers - Definitions
  • 9. Application of Complex Numbers - Impedance
  • 10. Application of Complex Numbers - Alternating Currents
  • 11. Application of Complex Numbers - Exercises
  • 12. Parallel AC Circuits
    • Fractals
    • Complex Numbers Vocabulary

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Counting and Probability

• Counting and Probability - Introduction
  • 1. Factorial Notation
  • 2. Basic Principles of Counting
  • 3. Permutations (Ordered Arrangements)
  • 4. Combinations (Unordered Selections)
  • 5. Introduction to Probability Theory
  • 6. Probability of an Event
    • Singapore TOTO
    • Poker
  • 7. Conditional Probability
  • 8. Independent and Dependent Events
  • 9. Mutually Exclusive Events
  • 10. Bayes' Theorem
  • 11. Probability Distributions - Concepts
  • 12. The Binomial Probability Distribution
  • 13. The Poisson Probability Distribution
  • 14. Normal Probability Distributions

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Differentiation

• Differentiation
  • 1. Limits
  • 2. Slope of Tangent
  • 3. The Derivative
  • 4. Instantaneous Rate of Change
  • 5. Derivatives of Polynomials
  • 6. Derivatives of Products and Quotients
  • 7. Powers of a Function
  • 8. Differentiation of Implicit Functions
  • 9. Higher Derivatives
• Differentiation of Transcendental Functions
  • 1. Derivatives of Sine, Cosine and Tangent
  • 2. Derivatives of Other Trig Functions
  • 3. Derivatives of Inverse Trig Functions
  • 4. Applications
  • 5. Derivative of the Logarithmic Function
  • 6. Derivative of the Exponential Functio
  • 7. Applications: Derivatives of Logarithmic and Exponential Functions
• Applications of Differentiation
  • 1. Tangents and Normals
  • 2. Newton's Method
  • 3. Curvilinear Motion
  • 4. Related Rates
  • 5. Curve Sketching
  • 6. More on Curve Sketching
  • 7. Applied Maximum and Minimum Problems

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Integration

• Integration
  • 1. The Differential
  • 2. Integration
  • 3. Areas Under Curves
  • 4. The Definite Integral
  • 5. Trapeziodal Rule
  • 6. Simpson's Rule
    • Integration Mini-Lectures
    • Millionaire Calculus Game
• Applications of Integration
  • 1. Applications of the Indefinite Integral
  • 2. Area Under a Curve
  • 3. Area between 2 Curves
  • 4. Volume of Solid of Revolution
  • 5. Centroid of an Area
  • 6. Moments of Interia
  • 7. Work
  • 8. Electric Charges
  • 9. Average Value of a Function
    • Head Injury Criterion
  • 10. Force Due to Liquid Pressure
• Methods of Integration
  • 1. The General Power Formula
  • 2. The Basic Logarithm Form
  • 3. The Exponential Form
  • 4. Basic Trigonometric Forms
  • 5. Other Trigonometric Forms
  • 6. Inverse Trigonometric Forms
  • 7. Integration by Parts
  • 8. Integration by Trig Substitution
  • 9. Table of Integrals
  • 10. Integration by Reduction Formulae
  • 11. Integration By Partial Fractions

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Higher Calculus

• Differential Equations
  • 1 Solutions of Diff Equations
  • AIDS
  • 2. Separation of Variables
  • 3. Integrable Combinations
  • 4 Linear DEs, Order 1
  • 5. Application of ODEs: Series RL Circuit
  • 6. Application of ODEs: Series RC Circuit
  • 7. Second Order Homogeneous Linear DEs With Constant Coefficients
  • 8. Damping and the Natural Response
  • 9. The Forced Response
  • 10. Solving Second Order DEs Using Scientific Notebook
• Infinite Series Expansion
  • 1. Taylor Series
  • 2. Maclaurin Series
  • 3. How Does a Calculator Work?
• Fourier Series
  • Helpful Revision for Fourier Series
  • 1. Overview of Fourier Series
  • 2. Full Range Fourier Series
  • 3. Even and Odd Functions
  • 4. Half Range Fourier Series
  • 5. Harmonic Analysis
  • 6. Line Spectrum
  • 7. Fast Fourier Transform
• The Laplace Transform
  • 1a. The Unit Step Function (Heaviside Function)
  • 1b. The Unit Step Function - Products
  • 2. Definition of the Laplace Transform
  • Table of Laplace Transformations
  • 3. Some Properties of Laplace Transforms
  • 4. Laplace Transforms of the Unit Step Function
  • 5. Laplace Transform of a Periodic Function
  • 6. Laplace Transforms of Integrals
  • 7. The Inverse Laplace Transform
  • 8. Using Inverse Laplace Transforms to Solve Differential Equations
  • 9. Solving Integro-Differential and Simultaneous Differential Equations
  • 10. Applications of Laplace

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