Dimensionless variables

1. Using Dimensionless Variables
2. Laws of Physics in Dimensionless Variables

Getting Rid of some Units

1. 4 Examples
2. Deeper Understanding

Appendix

1. Cartesian Coordinates in Higher Dimensions
2. Spherical Coordinates in Higher Dimensions
3. Minkowski Space
4. General Coordinates

Cross Product

1. Physical Motivation and Main Properties
2. Expression in Terms of Components
3. Parity

Appendix

1. Vectors in N-dimensional Space
2. Abstract Linear Space and Wedge Product

Algebra

1. Quadratic Equations, Counting Roots and General Polynomials
2. The Square Root Function and Logarithm Function

Differentiation

1. Rules
2. Cauchy-Riemann Conditions
3. Harmonic Functions

Integration

1. Rules, Cauchy Integral Theorem
2. Residue & Meromorphic Functions
3. Cauchy Integral Formula, Roots

Conservation of Energy

1. Work and KE; Work and PE
2. Significance

Numerical Methods

1. General Formalism
2. Different Methods of Evaluation

Parameters

1. Dependence on Parameters
2. Differentiating with respect to Parameters

Definition of Work

1. Constant Force
2. Linearity
3. Variable Force, Line Integral

Dependence on Path?

1. Reduction to Closed Loops and Examples
2. Condition for Conservative Force

Force from PE

1. Force components in Terms of Partial Derivatives
2. Gradient Operator, Curl of Gradient is Zero

Dependence on Path?

1. Reduction to Closed Loops, Condition to be Independent
2. Stokes' Theorem

The Related Scalar Field

1. The Related Scalar Field
2. Some Applications

Torque and Analog Newton's Second Law

1. Torque and Analog of Newton's Second Law
2. Angular Momentum

Appendix

1. Verifying the Energy
2. Euler-Lagrange Equation

Two Theorems

1. Parallel Axes Theorem
2. Perpendicular Axes Theorem

Friction

1. Phenomenological Law, Limiting Friction and Coefficient of Friction
2. Examples

Rolling Down an Incline

1. Three Methods to Solve the Problem
2. Other Examples

Introduction

1. Right Hand Rule and Specifying a Rotation
2. Non-commutativity and Reducing to Special Case

Equation of Motion

1. Derivation and Applying to Non-rigid Body
2. Precession of a Top

Moment of Inertia

1. An Example
2. Derivation of Key Forumla
3. Properties of Key Formula

Introduction and Kinematics

1. Introduction and Kinematics
2. Graphical and Complex Representation

Solving Equation of Motion

1. Equation of Motion and Solution in Polar Form
2. Solution in Alternate Form and Matching Initial Condition

Linearity and Superposition

1. Linear and Superposition
2. Real Equation, Complex Solution and Linear with Constant Coefficients

Inhomogeneous Case

1. Defining the Problem and Splitting into Two Parts
2. Constant Coefficient, Constant Inhomogeneity and Harmonic Inhomogeneity
3. Impulsive Inhomogeneity

Introduction and Kinematics

1. The Model
2. Numerical Solution
3. Guessing a Solution
4. Checking the Solution

Different Cases of Damping

1. Under-damped and Over-damped
2. Critically Damped

Case with Damping

1. Complex Solution
2. Physical Solution
3. Comparison with Undamped Case and Work Done by External Force

Secular Solution

1. Zero Damping
2. Small Damping

Impulsive Force

1. Need for Another Method and Impulse
2. General Solution