Table of Contents
0.0: Copyright
0.1: References
1.0: Foreword (General)
1.0.0: Computers are icumen in
1.0.1: Kindergarten
1.0.2: Apology
1.0.3: Historical foreword on Oct 4, 1996
1.1: An apology of a mathematics teacher
1.1.0: Preface to College of Engineering
1.1.1: Preface to Libral Education
1.1.2: The pedagogy
1.1.3: History and culture as a totality
1.1.4: Role of computers
1.1.5: Role of interactive multimedia
1.1.6: Role of the NET
1.2: Table of contents
1.2.0: Table of dependences
1.3: Table of threads
1.3.0: Thread for Mechanical Engineering
1.3.1: Thread for Libral Education
1.4: Table of time
2.0: Newton
2.1: Leibniz
2.2: Archimedes
2.3: Euler
2.4: Gauss
2.5: Riemann
2.6: Fourier
2.7: Hardy
2.8: Taylor
2.9: Maclaurin
2.10: L'Hopital
2.11: Heaviside
2.12: Godel
2.13: Cantor
2.14: Russell
2.15: Hilbert
2.16: von Neumann
2.17: Weierstrass
2.18: Copernicus
2.19: Galileo
2.20: Dirichlet
2.21: Bernoulli
2.22: Fermat
2.23: LiShanLan
2.24: Pythagoras
2.25: Barrow
2.26: Pascal
3.3: Integers and Rationals
3.4: Translations
3.5: Number Theory
3.6: Continuum Hypothesis
3.7: Hardy's Apology
3.8: Riemann Hypothesis
3.9: Russell's Paradox
3.10: Hilbert Problems
3.11: Four-Color Problem
3.12: Eratosthenes Measured the Earth
3.13: Fermat's Last Theorem
3.14: ICM, IMU and Fields Medal
3.15: Pythagoras Theorem
4.0: One Variable Functions
4.1: Multi-Variable Functions
4.2: Function Definition
4.3: One-to-one Functions
4.4: Onto Functions
4.5: Counting
5.0: Elementary Functions
5.1: Non Elementary Functions
5.2: Power Function
5.2.1: Polynomial
5.2.2: Linear Function
5.2.3: Rational Function
5.3: Exponential Function
5.4: Logarithm Function
5.5: Trignometric Function
5.5.0: Radian vs Degree
5.6: Composed Function
5.7: Inverse Function
5.8: Inversed Trignometric Function
5.9: Hyperbolic Functions
5.10: Inversed Hyperbolic Functions
5.11: Odd and Even Functions
5.12: Periodic Functions
6.1.1: Iteration
7.0: Differentiation, What Is It
7.0.0: A Simple Situation
7.0.1: Derivative, math definition
7.0.2: Derivative, graphical approach
7.0.3: Derivative, numerial approach
7.1: Differentiation, Algebraically
7.4: Derivative of sine
7.4.1: Derivatives of trigonometric functions
7.4.2: Derivatives of inverse trigonometric functions
8.0: Continuity, by limits
8.1: Discontinuity, amendable or not
8.1.0: Example, sin(x)/x
9.0: The constant e
9.1: e is irrational
10.0: Integration, What Is It
10.1: Integration, historical landmarks
10.1.1: Archimedes on parabola
10.1.2: Fermat on power functions
10.6: Mean value theorem for integration
10.7: Fundamental theorem of calculus
10.8: Anti-derivatives of power functions
10.9: Integration by subsitutions
10.10: Integration by parts
10.11: Improper Integrals
11.2: Second Derivative and Motion
12.0: Real Numbers, What Is It
27.0: Complex Plane
30.0: Infinite Series
30.6: Tayler Expansion
30.6.1: Sine/Cosine Expansion
30.6.2: Historical Note
30.7: Sum of 1 over n squared
30.8: Fourier Series
Created: Apr 7, 1997