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Mathematical Methods - Coggle Diagram

- - - - The x,y coordinate plane
        Has an equation that plots all the possible values of that make the equation hold true, this forms a shape or rather a family of shapes
        
        Functions
        
        Families:
        
        Polynomials
        
        Trigonometric
        
        Exponential/logarithmic
        
        Transformations:
        
        Can dilate, translate or reflect the function
        
        Using matrices, function notation
        
        Domain: The extent of all possible x-values
        Range: The extent of all possible y-values
- - - - Areas:
        
        Rectangles: b*h
        
        Triangles: (1/2)bh = (1/2)bc*sin(theta)
  - - - Sine, cosine and tangent
        SOHCAHTOA
    - - Symmetry properties(that yield the same result depending on base angle in first quadrant and sign of quadrant):
        
        Q1: theta
        
        Q2: pi-theta
        
        Q3: pi + theta
        
        Q4: 2*pi-theta
      - Signs:
        
        Sine is positive in Q1, 2 and negative in Q3, 4
        
        Cosine is positive in Q1, 4 and negative in Q2, 3
        
        Tangent is positive in Q1, 3 and negative in Q2, 4
- - - - Probability Distribution types:
        
        Discrete, can only take up specific values
        
        Continuous, can take up any possible value within given domain
        
        Discrete:
        
        Mean(Average), E(X) = sum(x*Pr(X=x))
        
        Median: Middle value(50th percentile)
        
        Mode: Most common value
        
        Variance: Average area of spread
        
        Standard deviation: Average distance from where the values would fall from the mean
        
        Binomial Distribution:
        
        Only two outcomes
        
        Has ,n, number of trials
        
        Each trial is independent
        
        Probability of success, p, is constant
        
        Continuous:
        
        Mean(Average), integral(x*Pr(X=x))
        
        Median: 50th percentile
        
        Mode: Most common value
        
        Variance: Average area of spread
        
        Standard deviation: Average distance from where the values would fall from the mean
        
        Normal Distribution:
        
        Symmetric on both sides
        
        Mean= Median = Mode
        
        Infinitely continuous
- - - - Derivatives
        
        Find the rate of change of a function
        
        Notation: d/dx, f'(x)
        
        Chain rule:
        
        For composite functions
        
        Product rule:
        
        For functions that are multiplied together
        
        Quotient rule:
        
        For functions that are divided by each other
      - Integrals
        
        Find the net change over a period given the rate of change
        
        Area under the graph
        
        Sum of infitesimally small geometric shapes
        
        Indefinite integrals:
        
        For integrating functions without limits
        
        To obtain the antiderivative
        
        Definite Integrals:
        
        To the find the change over a certain period, has limits