Chapter 1

Calculus and Vector Algebra

Limits and continuity

medium • 1 min read

First-order differential equations

medium • 2 min read

Vector addition and multiplication

medium • 3 min read

Scalar and vector triple products

medium • 4 min read

Applications of vectors in physics

medium • 5 min read

Chapter 2

Orthogonal Curvilinear Coordinates

Cylindrical coordinate system

medium • 1 min read

Spherical polar coordinates

medium • 2 min read

Scale factors and basis vectors

medium • 3 min read

Jacobians and transformation

medium • 4 min read

Applications in electromagnetism

medium • 5 min read

Chapter 3

Vector Calculus

Gradient of a scalar field

medium • 1 min read

Divergence and curl of vectors

medium • 2 min read

Line, surface, and volume integrals

medium • 3 min read

Gauss's divergence theorem

medium • 4 min read

Stokes' theorem and applications

medium • 5 min read

Chapter 4

Ordinary Differential Equations

Second-order linear ODEs

medium • 1 min read

Homogeneous with constant coefficients

medium • 2 min read

Non-homogeneous ODEs

medium • 3 min read

Wronskian

medium • 4 min read

Applications to harmonic oscillators

medium • 5 min read

Chapter 5

Partial Differential Equations

Method of separation of variables

medium • 1 min read

Wave equation in 1D and 2D

medium • 2 min read

Heat equation

medium • 3 min read

Laplace equation basics

medium • 4 min read

Boundary value problems

medium • 5 min read

Chapter 6

Probabilities and Statistics

Basic concepts of probability

medium • 1 min read

Random variables and expected value

medium • 2 min read

Binomial distribution

medium • 3 min read

Poisson distribution

medium • 4 min read

Normal (Gaussian) distribution

medium • 5 min read