Robotics and Mechatronics

  1. Foundational Mathematics and Physics
    1. Linear Algebra
      1. Vectors
        1. Vector Operations
          1. Vector Spaces
            1. Dot Product and Cross Product
            2. Matrices
              1. Matrix Operations
                1. Matrix Inversion
                  1. Determinants
                  2. Transformations and Rotations
                    1. Rotation Matrices
                      1. Euler Angles
                        1. Quaternions
                          1. Homogeneous Coordinates
                          2. Eigenvalues and Eigenvectors
                            1. Computation Methods
                              1. Physical Interpretation
                                1. Applications in Robotics
                              2. Calculus
                                1. Differential Calculus
                                  1. Derivatives
                                    1. Partial Derivatives
                                      1. Chain Rule
                                      2. Integral Calculus
                                        1. Definite and Indefinite Integrals
                                          1. Integration Techniques
                                          2. Vector Calculus
                                            1. Gradient
                                              1. Divergence
                                                1. Curl
                                                  1. Line and Surface Integrals
                                                  2. Differential Equations
                                                    1. Ordinary Differential Equations
                                                      1. First-Order ODEs
                                                        1. Second-Order ODEs
                                                          1. Solutions and Stability
                                                        2. Classical Mechanics
                                                          1. Statics
                                                            1. Forces and Moments
                                                              1. Equilibrium Conditions
                                                                1. Free Body Diagrams
                                                                2. Dynamics
                                                                  1. Newton's Laws of Motion
                                                                    1. Kinetic and Potential Energy
                                                                      1. Momentum and Impulse
                                                                        1. Rotational Dynamics
                                                                        2. Work and Energy Principles
                                                                          1. Work-Energy Theorem
                                                                            1. Conservation of Energy
                                                                              1. Power and Efficiency
                                                                            2. Probability and Statistics
                                                                              1. Basic Probability Theory
                                                                                1. Probability Distributions
                                                                                  1. Conditional Probability
                                                                                    1. Bayes' Theorem
                                                                                    2. Statistical Inference
                                                                                      1. Estimation
                                                                                        1. Hypothesis Testing
                                                                                          1. Confidence Intervals
                                                                                          2. Random Variables
                                                                                            1. Discrete Variables
                                                                                              1. Continuous Variables
                                                                                                1. Expectation and Variance
                                                                                                  1. Covariance and Correlation

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                                                                                              1. Introduction to Robotics and Mechatronics

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                                                                                              3. Mechanical Systems in Robotics