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MZB125 Exam - Coggle Diagram

- - - - Product rule
  - - - Linear approximation for root finding
    - - Estimating experimental uncertainties of dependent variables
- - - - Horizontal line test
- - - - Forces
      - Newton's Laws
      - Moment of Force (torque)
  - - - Justifying why scalar product
      - Example
        
        Law of Cosines
      - Orthogonal projections
    - - Direction of vector product
        
        Right-hand rule
      - Norm of the vector product
- - - - Designing matrices by column to perform wanted transformations
      - Rotation Matrix
      - Scaling Matrix
      - Non-commutatitivity of transformations
      - Inverse transformations & invertible matrices
      - Looking at Matrix products more
      - Examples
        
        Image Processing
        
        Projected Shadows
  - - - Image Processing & Computer Graphics
      - Robotics & Kinematics
      - Networks
      - Transition Matrices in probability & statistics
      - Quantum Mechanics
      - Systems of Linear equations, Scientific Computing
      - Tensoiral physical properties
- - - - Trajectory of mass falling by Gravity
  - - - Integration by Substitution
        
        Change of Integration Variable
        
        When looks similar derivative in there
        
        Composite function & products
      - Integration by Parts
        
        For products
  - - - Toughness
      - Anti-derivative of exp (-x^2)
      - Area between 2 curves
- - - - Complex Roots
        
        Roots of Quadratic Equation
      - Fundamental Theorem of Algebra
    - - Cartesian (standard form)
        
        Complex Conjugate
      - Polar Form
        
        Modulus
        
        Argument
      - Eulers Formula
        
        Euler's Identity
      - The Complex Plane
        
        De Moivre's Formula
    - - Stability of dynamnical Systems
        
        Bifurcation
        
        Control Theory
      - Making Solutions Real
      - Electrical Circuits
      - Transmission & reflection of electromagnetic Waves
      - Aeorplane Wings & the Magnus Effect
      - Schoedigners equation of Quantum Mechanics