Math Animated™
Mathematical Introduction for Physics and Engineering
by Samuel Dagan (Copyright © 2007)

Table of interactive and animated Figures

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Tutorial

Pythagoras: A tutorial for Fig.-windows

Introduction

Intuition: Intuition could play a destructive role

Chapter 1 - Differentiation

1. Real Numbers

• Rational numbers
• Countability
• Convergence of a sequence



2. Real Functions

• Cartesian coordinates
• Strictly monotonic functions
• Shapes
• Inversion of coordinates by 3 dimensional rotation
• Inversion of coordinates by Mirror reflection
• Inverse quadratic function
• Inverse cubic function
• Planar Angles
• Trigonometric functions
• Sine
• Cosine
• Tangent & cotangent
• Arc-sine
• Arc-cosine
• Arc-tangent & cotangent
• Exponent
• Lan
• Hyperbolic functions
• Hyperbolic functions and inverse
• Cycloid
• Straight Line
• Slope and angle
• Parabola - canonical form
• Translation
• Relations between coordinates
• Parabola at Polar coordinates
• Ellipse - canonical form
• Ellipse - focal properties
• Hyperbola



3. Derivatives

• Derivative by limit
• Derivative by zoom
• Scale a function and its derivative
• Derivative of x³
• Derivatives of x²
• Derivatives of x³
• Derivatives of x⁴
• Inflection points
• Infinite derivative
• Limit of sinφ/φ at φ→0
• Derivative of exponent
• tanhx & asymptotes
• Hyperbola-asymptotes
• Folium of Descartes
• $\frac{\sin x}{x}$ sin(x)/x
• Approximations of exponent
• Approximations of lan
• Approximations of lnx via atanhx

Chapter 2 - Integration

1. Indefinite Integrals

• ln|x|
• ∫cos²xdx
• Division of polynomials
• Vertical motion under constant gravity
• Simple harmonic motion



2. Definite Integrals

• Area of parabola(1)
• Area of a trapezoid
• Area of parabola(2)
• The trapezoid method
• Integration with discontinuity
• Enclosed area of parabolas(1)
• Enclosed area of parabolas(2)
• Folium of Descartes loop
• Mean value of a continuous function
• Mean value of a discontinuous function
• Overlaping area of two ellipses
• Improper integral - first kind
• Comparison test
• Improper integral - second kind
• Radioactive decay
• Area of a triangle
• Area with polar coordinates
• Wrong length of a curve
• Correct length of a curve
• Volume of revolution around x
• Volume of revolution around y
• Surface of revolution around x
• Surface of a torus

Chapter 3 - Many Variables

1. Differentiation

• Domain of a function
• Level lines (1)
• Level lines (2)
• Level lines (3)
• Point of discontinuity
• Orientation in 3D
• Point in 3D
• Saddle point
• Infinite level line
• Paraboloid of revolution
• Hyperboloids
• Elliptic paraboloid
• Approximated ellipsoid
• Translation of coordinates
• Rotation of coordinates
• Cylindrical coordinates
• Spherical coordinates
• Sufficient conditions for stationary points
• Level lines of a valley
• Constraints
• Closest approach
• Determinant of order 3



2. Integration

• Definition of double integral
• Convexity of a region
• Convex region
• Non-convex region
• Volume under a surface
• Rectangular pyramid
• Volume of a conical shape
• Jacobian as magnifier
• Mapping transformed points
• Orthogonality of polar coordinates
• Region excluding the origin
• Orthogonality of cylindrical coordinates
• Orthogonality of spherical coordinates
• Volume element of spherical coordinates