Math Documents of Gilles Cazelais

Basic Math

• A Proof of Pythagoras Theorem
• Basic graphs
• Geometry formulas
• Graph of y=asin(bx+c)
• Inscribed angle in a circle
• Interior angles in a triangle
• Inverse trig functions
• Linear combination of Sine and Cosine
• Polar graphs
• Proof of Law of Sines and Law of Cosines
• Proof of sum and difference identities
• Trigonometric formulas
• Unit circle
• Unit circle trigonometry

Calculus

• Single Variable Calculus

  • Area between curves
  • Basic introduction to Calculus (~260 kB)
  • Centroids
  • Convergence of series
  • Curve sketching examples
  • Derivatives formulas
  • Fundamental Theorem of Calculus
  • Harmonic series
  • Indeterminate forms of limits
  • Integration formulas
  • Integration by parts
  • Integration problems (with answers)
  • Inverse trig functions
  • Linear approximations
  • Maclaurin series
  • Maclaurin series of sin x
  • Newton's method
  • Partial fractions
  • Perimeter of an ellipse
  • Simpson's rule
  • Substitution method
  • Tabular method examples
  • The trapezoidal rule
  • Three equivalent definitions of e
  • A proof that e is irrational
  • A proof that pi is irrational
  • Dirichlet's test of convergence

• Multivariable Calculus

  • Coordinate systems
  • Double integrals
  • Double integrals in polar coordinates
  • Integral of exp(-x²)
  • Second derivative test
  • Space curves with MATLAB
  • Surface plots with MATLAB
  • Surface plots examples

Differential Equations

• Constant coefficients and Cauchy-Euler equations
• Direction Fields
• First order equations
• Laplace transforms book (~309 kB)
• Method of Undetermined Coefficients
• Table of Laplace transforms
• Introduction to the phase plane (~146 kB)

Discrete Mathematics

• Basic set operations
• Big-O examples
• Binomial theorem
• Block stacking problem
• Chinese remainder theorem
• Counting problems
• Dijkstra's algorithm example
• Euclid's algorithm
• Extended Euclid's algorithm
• Fibonacci sequence and the golden ratio
• Linear congruence
• Logical equivalences
• Logical implications
• Logical simplifications
• Methods of proof examples
• Prim's algorithm example
• RSA cryptography
• RSA example
• Solving recurrence relations
• Sieve of Eratosthenes (~147 kB)
• Twelve coins problem
• Zero power zero

Linear Algebra

• Balancing chemical equations
• Distance between two lines
• Review of Eigenvalues and Eigenvectors
• Solution of a linear system

Probability and Statistics

• Basics of Probability
• Birthday problem
• Collector's problem
• Chi-Square table
• Chi-Square Distribution
• Descriptive Stats example
• Discrete Random Variables
• Estimation of Parameters
• Hypotheses tests
• Large sample estimation of parameters
• Large sample Tests of Hypotheses
• Normal distribution table
• Poker hands
• Regression Analysis
• Rolling dice
• Sampling_distributions
• Small sample inference
• t-Distribution table

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