This Git repo contains meticulous and conscientiously written notes on mathematics courses I have taken. I hope you will have fun!
Numerical Algorithms
Chapter | Section |
---|---|
1. Systems of Linear Algebraic Equations | Matrices |
Equivalent systems of equations | |
Invertibility of a matrix | |
Homogeneous systems of equations | |
3. Iterative techniques in Matrix Algebra | Spectral radius |
Convergent matrices | |
Solving some fun engineering problems using iterative methods | |
4. Interpolation | Cubic Spline interpolation in Python |
Real Analysis
Chapter | Section |
---|---|
1. Basic Notions | Natural numbers |
Sets | |
Functions |
Functional Analysis
Measure Theory
Vector Calculus
Chapter | Section |
---|---|
2. Differentiation in several variables | Functions of several variables |
Undergraduate Probability theory
Chapter | Section |
---|---|
1. The sample space | The empirical background |
Sample Space, Events | |
Discrete sample space |
Ordinary Differential Equations
Chapter | Section |
---|---|
1. Vector Spaces | Introduction |
Vector spaces | |
Subspaces | |
Sums and Direct Sums | |
4. The general theory of linear differential equations | Linear differential operators |
Linear differential equations | |
Linear first order differential equations | |
Existence and uniqueness of solutions | |
Dimension of the solution space | |
The Wronskian | |
Abel's Formula | |
5. Equations with constant coefficients | Introduction |
Linear homogeneous equations of order two | |
Homogeneous equations of arbitrary order | |
Non-homogeneous equations, variation of parameters and Green's function | |
Variation of parameters and Green's function extended to non-homogeneous equations of arbitrary order |
Partial Differential Equations
A first course in PDEs
Chapter | Section |
---|---|
1. What are Partial Differential Equations | Brief Historical Comments |
Introduction | |
Classical Solutions |