Mathematics for Game Development

  1. Calculus for Motion and Physics
    1. Calculus Foundations
      1. Functions
        1. Function Notation
          1. Domain and Range
            1. Function Types
              1. Graph Interpretation
              2. Limits
                1. Limit Definition
                  1. Limit Properties
                    1. One-Sided Limits
                      1. Limits at Infinity
                      2. Continuity
                        1. Continuous Functions
                          1. Discontinuous Functions
                            1. Types of Discontinuities
                          2. Differentiation
                            1. Derivative Concept
                              1. Rate of Change
                                1. Slope Interpretation
                                  1. Instantaneous vs Average Rate
                                  2. Derivative Rules
                                    1. Power Rule
                                      1. Product Rule
                                        1. Quotient Rule
                                          1. Chain Rule
                                          2. Derivatives of Common Functions
                                            1. Polynomial Functions
                                              1. Trigonometric Functions
                                                1. Exponential Functions
                                                  1. Logarithmic Functions
                                                  2. Motion Applications
                                                    1. Position Functions
                                                      1. Velocity from Position
                                                        1. Acceleration from Velocity
                                                          1. Higher-Order Derivatives
                                                        2. Integration
                                                          1. Integral Concept
                                                            1. Area Under Curves
                                                              1. Accumulation
                                                                1. Antiderivatives
                                                                2. Integration Techniques
                                                                  1. Basic Integration Rules
                                                                    1. Substitution Method
                                                                      1. Integration by Parts
                                                                      2. Definite vs Indefinite Integrals
                                                                        1. Fundamental Theorem of Calculus
                                                                          1. Evaluation Methods
                                                                          2. Motion Applications
                                                                            1. Position from Velocity
                                                                              1. Velocity from Acceleration
                                                                                1. Displacement Calculations
                                                                                2. Numerical Integration
                                                                                  1. Euler Method
                                                                                    1. Algorithm
                                                                                      1. Error Analysis
                                                                                        1. Stability Issues
                                                                                        2. Improved Euler Method
                                                                                          1. Runge-Kutta Methods
                                                                                            1. Verlet Integration
                                                                                              1. Position Verlet
                                                                                                1. Velocity Verlet
                                                                                                  1. Advantages for Physics
                                                                                                  2. Integration Method Comparison
                                                                                                    1. Accuracy
                                                                                                      1. Stability
                                                                                                        1. Computational Cost

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                                                                                                  6. Trigonometry in Games

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                                                                                                  8. Physics Simulation