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Math Documents

Basic Math

A Proof of Pythagoras theorem
Basic graphs
Basics of complex numbers
Complex numbers on the calculator
Geometry formulas
Geometry supplement
Graph of y=a sin(bx+c)
Graphing with Desmos
Examples of graphs of y=a sin(bx+c)
Inscribed angle in a circle
Interior angles in a triangle
Inverse trig functions
Linear combination of Sine and Cosine
Plotting with SAGE
Polar graphs
Proof of Law of Sines and Law of Cosines
Proof of sum and difference identities
Trigonometric formulas
Proof of the quadratic equation
Unit circle
Unit circle trigonometry

Calculus

Area between curves
Basic introduction to Calculus
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)
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
Visualizing solids of revolution with GeoGebra

Multivariable Calculus

Coordinate systems
Double integrals
Double integrals in polar coordinates (1)
Double integrals in polar coordinates (2)
Integral of exp(-x^2)
Second derivative test
Space curves with MATLAB
Surface plots with MATLAB
Surface plots examples
Vector Fields

Differential Equations

Constant coefficients and Cauchy-Euler equations
Direction Fields
First order equations
Laplace transforms book
Linear combination of Sine and Cosine
Method of Undetermined Coefficients
Practice questions
Table of Laplace transforms
Introduction to the phase plane

Linear Algebra

Balancing chemical equations
Distance between two lines
Fundamental theorem of invertible matrices
Gauss-Jordan elimination
Linear Algebra with MATLAB
Review of Eigenvalues and Eigenvectors
Solution of a linear system

Discrete Mathematics

Basic set operations
Big-O examples
Binomial theorem
Block stacking problem
Chinese remainder theorem
Counting problems
Dijkstra's algorithm
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
RSA cryptography
RSA example
Solving recurrence relations
Sieve of Eratosthenes
Twelve coins problem
Zero power zero

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 Tests of Hypotheses
Normal distribution table
Poker hands
Regression Analysis
Rolling dice
Sampling distributions
Statistics graphs
Statistics on the Calculator
Small sample inference
t-Distribution table

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