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MATH1013 (3 beyond boundedness and definite (3.4 L'Hopital's Rule,…

- - - - absolute & local extrema
      - Fermat's Thm, extreme value Thm, Rolle's Thm
      - locate the absolute extrema; solve applied optimization problems
    - - existence of zero
    - - continuous Defn, differentiable Defn
      - differentiable & continuous Thm;
        Maybe continuous but indifferentiable
      - algebraic properties of continuous funcions: just plug in
      - polynomial & rational functions are continuous
      - composition of continuous functions :star:
  - - - increasing & strictly increasing :question:
    - - inflection point
        defn: f continuous & concavity change at a
    - - horizontal
      - vertical
      - oblique
    - - f
        
        domain
        
        intercepts
        
        asymptotes
      - f'
        
        increasing/decreasing intervals
        
        local max/min
      - f''
        
        concave upward/downward
        
        inflexion
  - - - Mean Value Thm
      - directly plug in the base point(zeroth order apprx)
    - - increment vs differential
    - - upper bond of error committed
- - - - supplementary integration formulas :star:
    - - integral sign, integrand, constant
    - - Riemann sum
      - properties & further properties of definite integral
      - continuous --> integrable
    - - area between two curves
  - - - reduction formula
    - - fundamental theorem of algebra
      - integration by partial fractions
        
        single factors
        
        repeated factors
- - - - ODE
      - PDE
  - - - Bernoulli: nonlinear-->linear
      - Leibniz: linear-->seperable
  - - - R
        
        distinct
        
        repeated
      - C
- - - - argand plane
      - polar form
      - geometric interpretation of multiplication and division of complex numbers
    - - the n-th roots
      - De Moivre Thm
      - Euler's Formula and Complex Exponent :question:
- - - - limit exists
      - algebraic properties of limits
    - - upper/lower bond :question:
      - take the absolute value
    - - algebraic properties of limits of composite functions
      - chain rule
  - - - conclusions to remember :star:
    - - general rule
      - inverse+trigonometry
- - - - mxn matrix, aij
      - n-column vectors, n-row vectors
      - zero matrix, square matrix, diagonal entries, identity matrix
      - matrix equality, transpose, sum and difference of matrices, scalar multiplication
      - properties of matrix addition and scalar multiplication
    - - defn
      - properties
    - - rotation matrix
      - powers of square matrices
    - - invertible
      - properties of inverse matrices
  - - - ad-bc
      - det In
    - - inverse of 2x2, 3x3 invertible matrix