Site Map of Interactive Mathematics

Algebra, Graphs & Trigonometry

• Numbers
  • 1. Integers
  • 1a. Counting Game
  • 2. Number Properties
  • 3. Order of Operations
  • 4. Powers, Roots and Radicals
  • 5. Approximate Numbers
  • 5b. Pi
  • 6. Scientific Notation
  • 7. Ratio and Proportion
  • 7a. Math of Beauty
  • 8. Tesla Multiplication 3D interactive applet
• 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
  • al-Khwarizmi Father of Algebra
• Money Math
  • 1. Interesting Interest
  • 1a. Rule of 72
  • 2. Credit Cards
  • 3. Math of House Buying
  • 4. Gold Rush?
  • 5. Money Charts and Fibonacci
  • 6. Superannuation
• Introduction to Geometry
  • Functions and Graphs
  • 1. Introduction to Functions
  • 2. Functions from Verbal Statements
  • 3. Rectangular Coordinates
  • 4. The Graph of a Function
  • 4a. Domain and Range of a Function
  • 4b. Domain and Range interactive applet
  • 4c. Comparison calculator BMI - BAI
  • 5. Graphing Using a Computer Algebra System
  • 5a. Online graphing calculator (1): Plot your own graph (JSXGraph)
  • 5b. Online graphing calculator (2): Plot your own graph (SVG)
  • 6. Graphs of Functions Defined by Tables of Data
  • 7. Continuous and Discontinuous Functions
  • 8. Split Functions
  • 9. Even and Odd Functions
• Systems of Equations
  • 1. Simultaneous Linear Equations
  • 2. Graphs of Linear Functions
  • 3. Graphical Solution of Linear Systems
  • 4. Algebraic Solutions of Linear Systems
  • 5. Graphical Solution of non-linear Systems
  • 6. Algebraic Solution of non-Linear Systems
• Matrices and Determinants
  • 1. Determinants
  • Systems of 3x3 Equations interactive applet
  • 2. Large Determinants
  • 3. Matrices
  • 4. Multiplication of Matrices
  • 4a. Matrix Multiplication examples
  • 4b. Add & multiply matrices applet
  • 5. Finding the Inverse of a Matrix
  • 5a. Simple Matrix Calculator
  • 5b. Inverse of a Matrix using Gauss-Jordan Elimination
  • 6. Matrices and Linear Equations
  • Matrices and Linear Transformations
  • Eigenvalues and eigenvectors - concept applet
  • 7. Eigenvalues and Eigenvectors
  • 8. Applications of Eigenvalues and Eigenvectors
  • Eigenvalues and eigenvectors calculator
• Factoring and Fractions
  • 1. Special Products
  • 2. 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
• Quadratic Equations
  • 1. Solving Quadratic Equations by Factoring
  • 2. Completing the Square
  • 3. The Quadratic Formula
  • Sum and product of the roots of a quadratic equation
  • 4. The Graph of the Quadratic Function
  • Interactive Quadratic Function Graph
  • 5. Equations in Quadratic Form
• Trigonometric Functions
  • 1. Angles
  • 2. Sine, Cosine, Tangent & Reciprocals
  • 3. Values of Trigonometric Functions
  • 4. The Right Triangle and Applications
  • 4a. Trigonometry Revision Summary
  • 5. Signs of the Trigonometric Functions
  • 6. Trigonometric Functions of Any Angle
  • 7. Radians
  • 8. Applications of Radian Measure
  • 8a. Pulleys
  • 9. Radians and the Trigonometric Ratios
• 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
  • 4a. Adding Vectors using SVG graphs
  • 5. Dot Product of 2-D Vectors
  • 6. Three-dimensional Space
  • 3D Space Interactive Applet
  • 3-D and Contour Grapher
  • 7. Vectors in 3-dimensional Space
  • 8. Cross Product of 2 Vectors
  • 9. Variable Vectors
  • 10. Vector Calculus
  • 10a. 3-D Earth Geometry
  • 10b. Vector Art
  • 10c. Mathematics of Vector Art
• Graphs of the Trigonometric Functions
  • 1. Graphs of `y = a sin x` and `y = a cos x`
  • 2. Graphs of `y = a sin bx` and `y = a cos bx`
  • 2a. Frequency of Music Notes
  • 2b. Frequencies of Notes on a Piano: Learning object
  • 3. Graphs of `y = a sin(bx+c)` and `y = a cos(bx+c)`
  • 4. Graphs of tan, cot, sec and csc
  • 5. Applications of Trigonometric Graphs
  • 6. Composite Trigonometric Graphs
  • 6a. Biorhythm Graphs
  • 7. Lissajous Figures
• Exponents and Radicals
  • 1. Simplifying Expressions with Integral Exponents
  • 2. Fractional Exponents
  • 3. Simplest Radical Form
  • 4. Addition and Subtraction of Radicals
  • 5. Multiplication and Division of Radicals (Rationalizing the Denominator)
  • 6. Equations with Radicals
• Complex Numbers
  • 1. Basic Definitions of Complex Numbers
  • 2. Basic Operations in Complex Numbers
  • 3. Graphical Representation of Complex Numbers
  • 4. Polar Form of Complex Numbers
  • Convert polar to rectangular using hand-held calculator
  • Polar to Rectangular Online Calculator
  • 5. Exponential Form of Complex Numbers
  • Euler Formula and Euler Identity interactive graph
  • 6. Products and Quotients of Complex Numbers
  • Graphical explanation of multiplying and dividing complex numbers
  • 7. Powers and Roots of Complex Numbers
  • 8. AC Circuit Definitions
  • 9. Impedance and Phase Angle: Application of Complex Numbers
  • 10. Reactance and Angular Velocity: Application of Complex Numbers
  • 11. AC Circuit Exercises
  • 12. Parallel AC Circuits
  • Vocabulary
  • Fractals
• Exponential & Logarithmic Functions
  • 1. Definitions: Exponential and Logarithmic Functions
  • 2. Graphs of Exponential and Logarithmic Equations
  • 3. Logarithm Laws
  • 4. Logarithms to Base 10
  • 5. Natural Logarithms (base e)
  • Dow Jones Industrial Average
  • Calculating the value of e
  • 6. Exponential and Logarithmic Equations
  • World Population Live
  • 7. Graphs on Logarithmic and Semilogarithmic Axes
  • Interactive Log Table
• Polynomial Equations of Higher Degree
  • 1. Polynomial Functions and Equations
  • 2. Remainder and Factor Theorems
  • 3. How to factor polynomials
  • 4. Roots of a Polynomial Equation
  • 5. Roots of Polynomial Equations using Graphs
• Inequalities
  • 1. Properties of Inequalities
  • 2. Solving Linear Inequalities
  • 3. Solving Non-Linear Inequalties
  • 4. Inequalities Involving Absolute Values
• Series and the Binomial Theorem
  • 1. Arithmetic Progressions
  • 2. Geometric Progressions
  • 3. Infinite Geometric Series
  • 4. The Binomial Theorem
  • Binomial Series Interactive
• Analytic Trigonometry
  • 1. Trigonometric Identities
  • 1a. Trigonometric Ratios - Interactive Graph
  • 2. Sin, cos, tan of Sum of Two Angles
  • 3. Double Angle Formulas
  • 4. Half Angle Formulas
  • 5. Trigonometric Equations
  • 6. Express in the form R sin (θ + α)
  • 7. Inverse Trigonometric Functions
  • Inverse trigonometric function graph animations
• Plane Analytical Geometry
  • 1. Distance Formula
  • 1a. Gradient (Slope) of a Line, and Inclination
  • 1b. Parallel Lines
  • 1c. Perpendicular Lines
  • 2. The Straight Line
  • Perpendicular Distance from a Point to a Line
  • 3. The Circle
  • 4. The Parabola
  • 4a. Interactive parabola graphs
  • 5. The Ellipse
  • 5a. Interactive ellipse graphs
  • 6. The Hyperbola
  • 6a. Interactive hyperbola graphs
  • 6b. Conic Sections Summary
  • 6c. Conic Sections 3D interactive graph
  • 7. Polar Coordinates
  • 8. Curves in Polar Coordinates
  • Equi-angular Spiral
  • Squaring the Circle: rope method with proof
• Kinematics (velocity & acceleration graphs)
  • 1. Velocity (s-t) Graphs
  • 2. Acceleration (v-t) Graphs
  • 3. Kinematics Exercises
• Counting and Probability - Introduction
  • 1. Factorial Notation
  • 2. Basic Principles of Counting
  • 3. Permutations
  • 4. Combinations
  • 5. Introduction to Probability Theory
  • 6. Probability of an Event
  • Singapore TOTO
  • Probability and Poker
  • 7. Conditional Probability
  • 8. Independent and Dependent Events
  • 9. Mutually Exclusive Events
  • 10. Bayes’ Theorem
  • 11. Probability Distributions - Concepts
  • 12. Binomial Probability Distributions
  • 13. Poisson Probability Distribution
  • 14. Normal Probability Distribution
  • The z-Table
  • Normal Distribution Graph Interactive
• Calculus - An Introduction
  • Calculus Concepts First Principles Applet
  • Vietnamese Translation of IntMath Calculus

Differentiation

• Differentiation - Introduction
  • 1. Limits and Differentiation
  • 2. The Slope of a Tangent to a Curve (Numerical)
  • 3. The Derivative from First Principles
  • 4. Derivative as an Instantaneous Rate of Change
  • 5. Derivatives of Polynomials
  • 5a. Derivative interactive graphs - polynomials
  • 6. Derivatives of Products and Quotients
  • 7. Differentiating Powers of a Function
  • 7a. Differentiation interactive applet - products and quotients
  • 8. Differentiation of Implicit Functions
  • 9. Higher Derivatives
  • 10. Partial Derivatives
• Applications of Differentiation
  • 1. Tangents and Normals
  • 2. Newton's Method
  • Newton's Method Interactive Graph
  • 3. Curvilinear Motion
  • 4. Related Rates
  • 5. Curve Sketching Using Differentiation
  • 6. More Curve Sketching Using Differentiation
  • 7. Applied Maximum and Minimum Problems
  • 8. Radius of Curvature
• Differentiation of Transcendental Functions
  • 1. Derivatives of Sin, Cos and Tan Functions
  • 2. Derivatives of Csc, Sec and Cot Functions
  • Differentiation interactive applet - trigonometric functions
  • 3. Derivatives of Inverse Trigonometric Functions
  • 4. Applications: Derivatives of Trigonometric Functions
  • 5. Derivative of the Logarithmic Function
  • 6. Derivative of the Exponential Function
  • 7. Applications: Derivatives of Logarithmic and Exponential Functions
  • Table of Derivatives

Integration

• Integration
  • 1. The Differential
  • 2. Antiderivatives and The Indefinite Integral
  • 3. The Area Under a Curve
  • 4. The Definite Integral
  • 5. Trapezoidal Rule
  • 6. Simpson’s Rule
  • 6a. Riemann Sums
  • 6b. Fundamental Theorem of Calculus Applet
  • 7. Integration Mini-lectures
  • 7a. The Differential
  • 7b. Difference Between Differentiation and Integration
  • 7c. Given dy/dx, find y = f(x)
  • 7d. Integration by Substitution
  • 7e. Difference Between Definite and Indefinite Integrals
  • 7f. Area Under a Curve
• Applications of Integration
  • 1. Applications of the Indefinite Integral
  • 2. Area Under a Curve by Integration
  • 3. Area Between 2 Curves using Integration
  • 4a. Volume of Solid of Revolution by Integration
  • 4b. Shell Method: Volume of Solid of Revolution
  • 5. Centroid of an Area by Integration
  • 6. Moments of Inertia by Integration
  • 7. Work by a Variable Force using Integration
  • 8. Electric Charges by Integration
  • 9. Average Value of a Function by Integration
  • Head Injury Criterion (HIC) pt 1: Severity Index
  • Head Injury Criterion (HIC) pt 2: HIC Index, example
  • 10. Force Due to Liquid Pressure by Integration
  • 11. Arc Length of a Curve using Integration
  • 12. Arc Length of Curve: Parametric, Polar Coordinates
• Methods of Integration
  • 1. Integration: The General Power Formula
  • 2. Integration: The Basic Logarithmic Form
  • 3. Integration: The Exponential Form
  • 4. Integration: The Basic Trigonometric Forms
  • Riemann Sums - Discontinuous Functions
  • 5. Integration: Other Trigonometric Forms
  • 6. Integration: Inverse Trigonometric Forms
  • 7. Integration by Parts
  • 8. Integration by Trigonometric Substitution
  • 9. Integration by Use of Tables
  • Table of Common Integrals
  • 10. Integration by Reduction Formulae
  • 11. Integration by Partial Fractions

Higher Calculus

• Differential Equations
  • Predicting AIDS - a DEs example
  • 1. Solving Differential Equations
  • 2. Separation of Variables
  • 3. Integrable Combinations
  • 4. Linear DEs of Order 1
  • 5. Application: RL Circuits
  • 6. Application: RC Circuits
  • 7. Second Order DEs - Homogeneous
  • 8. Second Order DEs - Damping - RLC
  • 9. Second Order DEs - Forced Response
  • 10. Second Order DEs - Solve Using SNB
  • 11. Euler's Method - a numerical solution for Differential Equations
  • 12. Runge-Kutta (RK4) numerical solution for Differential Equations
• Infinite Series Expansion
  • 1. Taylor Series
  • 2. Maclaurin Series
  • Taylor and Maclaurin Series interactive applet
  • 3. How Does a Calculator Work?
• Fourier Series
  • Helpful Revision
  • 1. Overview of Fourier Series
  • 2. Full Range Fourier Series
  • 3. Fourier Series of Even and Odd Functions
  • Fourier Series Graph Interactive
  • 4. Fourier Series of Half Range Functions
  • 5. Harmonic Analysis
  • 6. Line Spectrum
  • 7. Fast Fourier Transform
• Laplace Transforms
  • 1a. The Unit Step Function - Definition
  • 1a.i. Oliver Heaviside
  • 1b. The Unit Step Function - Products
  • 2. Laplace Transform Definition
  • 2a. Table of Laplace Transformations
  • 3. Properties of Laplace Transform
  • 4. Transform of Unit Step Functions
  • 5. Transform of Periodic Functions
  • 6. Transforms of Integrals
  • 7. Inverse of the Laplace Transform
  • 8. Using Inverse Laplace to Solve DEs
  • 9. Integro-Differential Equations and Systems of DEs
  • 10. Applications of Laplace Transform

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• Using KaTeX (and MathJax) fonts outside of KaTeX (and MathJax)
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  • ASCIIsvg-IM Draggables using Event.js
  • Heights, widths and re-size for SVG applets
  • Implicit plots in ASVG via Interval Arithmetic, D3 and Function Plot
  • Curve Shape for the Movement of a Piston
  • Trigonometry function graphs - Using d3
  • Trigonometry function graphs - Using JSXGraph
  • Trigonometry function graphs - Using JSXGraph (with an array)
  • JSXGraph Axes Ticks and Grids
  • JSXGraph Coding Summary
  • JSXGraph Internal Angles of a Triangle
  • Embed a Desmos graph in your own page
  • SVG Screen Resolution
• MathJax and KaTeX comparison
  • ASCIIMathML input, KaTeX and MathJax output
  • SVG Display Options
  • svgPHPGrapher Syntax Examples
• Math art in code
  • Evolute of a curve
  • Animated Lissajous figures
  • Solid of Revolution maker
  • CSS Animated Hexagon Wave
  • Spinning clock
  • Moiré effect
  • Delaunay Triangulation
  • Flux - a Perlin noise example
  • Animated Moore Curve
  • Bubble sort rainbow
  • CSS Matrix - a mathematical explanation
  • CSS matrix interactive applet
• Historical Math Curves
  • Witch of Agnesi
  • Lemniscate of Bernoulli
  • Quadratrix of Dinostratus
• Putnam Mathematical Competition
  • 1985 Putnam Question A-2: Solution Part 1
  • 1985 Putnam Question A-2: Solution Part 2
  • 1985 Putnam Question A-2: Solution Part 3
  • 1985 Putnam Question A-2: Solution Part 4
  • 1985 Putnam Question A-2: Solution Part 5
  • 1985 Putnam Question A-2: Solution Part 6
  • 1985 Putnam Question A-2: Solution Part 7