Classical Mechanics

  1. Mathematical Preliminaries
    1. Units and Dimensional Analysis
      1. SI Units
        1. Base Units
          1. Meter
            1. Kilogram
              1. Second
              2. Derived Units
                1. Newton
                  1. Joule
                    1. Watt
                  2. Unit Conversion
                    1. Conversion Factors
                      1. Systematic Conversion Methods
                        1. Common Unit Conversions in Mechanics
                          1. Length Conversions
                            1. Mass Conversions
                              1. Time Conversions
                                1. Force Conversions
                              2. Dimensional Consistency
                                1. Checking Equations for Consistency
                                  1. Dimensional Homogeneity
                                    1. Buckingham Pi Theorem
                                    2. Order-of-Magnitude Estimates
                                      1. Fermi Problems
                                        1. Scaling Arguments
                                      2. Vector Algebra
                                        1. Scalars and Vectors
                                          1. Definitions and Differences
                                            1. Physical Quantities as Vectors
                                              1. Displacement
                                                1. Velocity
                                                  1. Force
                                                  2. Physical Quantities as Scalars
                                                    1. Mass
                                                      1. Energy
                                                        1. Temperature
                                                      2. Vector Addition and Subtraction
                                                        1. Graphical Methods
                                                          1. Head-to-Tail Method
                                                            1. Parallelogram Method
                                                            2. Analytical Methods
                                                              1. Component Addition
                                                                1. Algebraic Operations
                                                              2. Scalar (Dot) Product
                                                                1. Definition and Properties
                                                                  1. Geometric Interpretation
                                                                    1. Applications in Physics
                                                                      1. Work Calculations
                                                                        1. Projections
                                                                      2. Vector (Cross) Product
                                                                        1. Definition and Properties
                                                                          1. Right-Hand Rule
                                                                            1. Applications in Mechanics
                                                                              1. Torque
                                                                                1. Angular Momentum
                                                                              2. Components of a Vector
                                                                                1. Cartesian Components
                                                                                  1. Unit Vectors
                                                                                    1. i, j, k Notation
                                                                                    2. Vector Decomposition
                                                                                      1. Magnitude and Direction
                                                                                      2. Coordinate Systems
                                                                                        1. Cartesian Coordinates
                                                                                          1. Two-Dimensional Systems
                                                                                            1. Three-Dimensional Systems
                                                                                            2. Polar and Cylindrical Coordinates
                                                                                              1. Conversion Between Systems
                                                                                              2. Spherical Coordinates
                                                                                                1. Applications in Three Dimensions
                                                                                            3. Essential Calculus
                                                                                              1. Derivatives and Rates of Change
                                                                                                1. Physical Interpretation
                                                                                                  1. Velocity as Derivative of Position
                                                                                                    1. Acceleration as Derivative of Velocity
                                                                                                    2. Higher-Order Derivatives
                                                                                                      1. Chain Rule Applications
                                                                                                      2. Integrals and Summation
                                                                                                        1. Definite and Indefinite Integrals
                                                                                                          1. Area Under a Curve
                                                                                                            1. Physical Applications
                                                                                                              1. Displacement from Velocity
                                                                                                                1. Work from Force
                                                                                                              2. Differential Equations in Mechanics
                                                                                                                1. Ordinary Differential Equations
                                                                                                                  1. First-Order Equations
                                                                                                                    1. Second-Order Equations
                                                                                                                      1. Initial and Boundary Conditions
                                                                                                                        1. Solving Simple Equations of Motion
                                                                                                                          1. Constant Acceleration
                                                                                                                            1. Simple Harmonic Motion

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                                                                                                                      1. Introduction to Classical Mechanics

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                                                                                                                      3. Kinematics: The Description of Motion