Fundamentals of Calculus, Special Relativity and Quantum mechanics

Contents

Part 1

1. Basic calculus and other mathematical concepts
   1. Derivatives
   2. Integrals
   3. Logarithms
   4. Variances
   5. Dot product
2. Fundamentals of special relativity
   1. Lorentz transformation
   2. Relativistic velocity
   3. Relativistic mass and momentum
   4. Four-vectors

Part 2

1. Advanced mathematics and applications of the above-learnt
   1. Taylor series
   2. Chain rule
   3. Product rule
   4. Properties of logarithms
   5. Derivatives of e
   6. Euler's formula and identity
2. More special relativity and fundamentals of quantum mechanics
   1. Harmonic oscillator
   2. Photoelectric effect
   3. Energy-mass equivalence
   4. De Broglie wavelength
   5. Wave-particle duality

Part 3

1. Quantum mechanics
   1. Double-slit experiment
   2. Quantum tunnelling
   3. Wave equation
   4. Quantum states and superposition
2. Other mathematical concepts
   1. Inner product spaces and Hilbert spaces

Part 4

1. Advanced quantum mechanics
   1. Operators
   2. Schrodinger equation
   3. Heisenberg uncertainty principle

Part 5

1. Intuitive understanding of the Hawking Radiation