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 |
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