My Notes
Search
CTRL + K
My Notes
Search
CTRL + K
Chaos & Non-Linear Dynamics
1.1 Basic Concepts and Geometric Approach
1.2 Linear System v.s Nonlinear System
1.3 Fundamental Theorem for the Flow
2.1 Linear Systems and Matrix Exponentials
2.2 Canonical 2x2 Matrices
3.1 1D Non-Linear Systems
3.2 General Concepts for Nonlinear Dynamics
3.3 Stability of Fixed Points
4.1 Periodic Orbits
4.2 Conservative Systems
4.3 Dissipative System
5.1 Local Bifurcations
5.2 Global Bifurcation
6.1 Iteration of Maps
6.2 Pointcaré Map and Periodic Stability
7.1 Chaos
7.2 Conjugacy and Examples
Chaos & Non-Linear Dynamics
Complex Analysis
1.1 Complex Number Algebra
1.2 Geometry of Complex Numbers
1.3 Spherical Representation
2.1 Limits, Derivative, Continuity of Complex Functions
2.2 Cauchy Riemann and Results
2.3 Polynomials and Rational Functions
2.4 Power Series
2.5 Abel's Limit Theorem
3.1 Trig Functions
3.2 Exponential, Log, Multivalued Functions
4.1 Metric Spaces in Complex
4.2 Conformal Maps
4.3 Mobius Transformations
Complex Analysis
Information Theory
Entropy
Intro to Real Analysis
1. The Real Numbers
2. Sequences
3. Series
4. Topology
5. Function Limits & Continuity
6. The Derivative
7. Sequence of Functions
8. Series of Functions
9. Power Series
10. Integral
Linear Algebra
Sections
Basis
Coordinate Representation
Diagonalizability
fdvs
Inner Product Space
Internal Direct Sums
Isometry
Isomorphisms
Linear Combination and Span
Linear Independence
Linear Transformations
Norm
Projection
Subspace test
Vector Space Axioms
Vector Space Properties
Linear Algebra
Numerical Analysis
1.1 Accuracy
1.2 Taylor Polynomials
1.3 Speed
2.1 Bisection Method
2.2 Fixed Point Iteration
2.3 Fixed Point Iteration Convergence
2.4 Newton's Method
2.7 Bracketing
3.2 Lagrange Polynomials
3.3 Newton Polynomials
4.1 Rudiments of Numerical Calculus
4.2 Undetermined Coefficients
5.1 Osculating Polynomials
Numerical Analysis
PDEs
1.1 PDEs Basics
1.2 First-Order Linear Equations
1.3 Types of Second-Order Equations
Statistics
Bayesian Statistics
1. Logic Probability and Uncertainty
2. Bayes Inference for Discrete Random Variables
3. Bayesian Inference on Binomial Proportion
4. Bayesian Inference on Poisson
5. Bayesian Inference on Normal Distribution
6. Hypothesis Testing
7. Bayesian Simple Linear Regression
8. Bayesian Analysis of Variance from Normal Likelihood
10. Jeffreys' Prior
11. Posterior Using Gibbs' Sampler
Bayesian Statistics
Regression Analysis
1. Simple Linear Regression
2. MLE in Simple Regression Model
3 Non-central Chi-Squared Theorems
4. Centred Model & Anova Derivations
5. SLR Confidence & Prediction Intervals
6. SLR Matrix Representation
7. Correlation and Hypothesis Testing
8. Intro to Multiple Linear Regression
9. MLR Hypothesis Testing
Anova Steps
Least Squares Vectorization
Regression Analysis
Statistical Learning
1. Introduction
2. K-nn Regression
3. Linear Models
Statistical Learning
Vector Calc
Sections
Arc Length
Basic Topology in Euclidean Spaces
Change of Variables
Differentiation
Double Integral Over a Rectangle
Double Integral Over Elementary Regions
Green's Theorem
Implicit Function Theorem
Limits and Continuity
Line Integral
Local Extremums of Real-Valued Functions
Path Integral
Surfaces and Stokes Theorem
Types of Functions
Vector Fields
Vector Calc
Welcome
Vector Space Properties
based on
Vector Space Axioms
Let
V
be a vector space, with
u
,
v
,
w
∈
V
and
c
∈
R
:
If
u
+
v
=
u
+
w
then
v
=
w
c
v
=
0
if and only if
c
=
0
or
v
=
0
(
−
1
)
v
=
−
v
(
−
c
)
v
=
−
(
c
v
)
=
c
(
−
v
)
The zero vector is unique
If
v
∈
V
its additive inverse
−
v
is unique