2. Differentiation

  1. 2.1. Symbolic Differentiation
    1. 2.1.1. Notation
      1. 2.1.1.1. Exercises
    2. 2.1.2. Examples
      1. 2.1.2.1. Newton's solver
        1. 2.1.2.1.1. Exercises
      2. 2.1.2.2. Kinematics
        1. 2.1.2.2.1. Exercises
    3. 2.1.3. Gradient
      1. 2.1.3.1. Exercises
    4. 2.1.4. Derivative Rules
    5. 2.1.5. Differentiating Division, Log, Sqrt, ...
      1. 2.1.5.1. Exercises
    6. 2.1.6. Abstract Vector Spaces
  2. 2.2. Automatic Differentiation
    1. 2.2.1. Forward Mode
      1. 2.2.1.1. autodiff vs fun_trans
      2. 2.2.1.2. Relation to Dual Numbers
      3. 2.2.1.3. Exercises
    2. 2.2.2. Reverse Mode
      1. 2.2.2.1. Exercises
  3. 2.3. Function Transformation
    1. 2.3.1. Implementing Forward Mode AD
    2. 2.3.2. Lambda Theorems
      1. 2.3.2.1. Exercises
    3. 2.3.3. Function Theorems
    4. 2.3.4. User Defined Functions
    5. 2.3.5. Free Variable Theorems
      1. 2.3.5.1. Exercises
    6. 2.3.6. Morphism Theorems
    7. 2.3.7. Compositional vs Simple Form
    8. 2.3.8. High Order Functions
      1. 2.3.8.1. Exercises