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Numerical Analysis I
Numerical Analysis: Intro and Error Analysis
Number Representation and Precision
Nonlinear Equations: Bisection Method
Fixed-Point Iteration for Nonlinear Equations
Newton's Method and Secant Method
Lagrange Polynomial Interpolation
Newton's Divided Differences Interpolation
Interpolation
Interpolation
Numerical Differentiation
Newton-Cotes Formulas for Integration
Composite Trapezoidal & Simpson's Rules
Gaussian Quadrature for Numerical Integration
Euler's Method for Initial Value Problems
Higher-Order Taylor Methods for ODEs
Initial Value Problems: Runge-Kutta Methods
Scientific Computing: Software & Applications
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Numerical Analysis I
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|e_1| \leq \frac{(b-a)^3}{12n^2} \max|f''(x)|
|e_2| \leq \frac{(b-a)^5}{180n^4} \max|f^{(4)}(x)|
||ax - b||
||a||
ฮด
ฮดt
ฮดx
ฮต (Machine Epsilon)
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A
A priori error estimation
A-stability
Absolute convergence
Absolute error
Absolute stability
Acceleration methods
Acceleration techniques
Accuracy
Adams-Bashforth Method
Adams-Moulton Method
Adaptive algorithms
Adaptive Error Control
Adaptive interpolation techniques
Adaptive Methods
Adaptive Quadrature
Adaptive quadrature techniques
Adaptive runge-kutta
Adaptive Runge-Kutta 4th Order
Adaptive Step Size
Adaptive step size control
Adaptive step size methods
Adaptive techniques
Addition
Addition Rule
Additive Taylor methods
Aerodynamic profiles
Aitken's Delta Squared Method
Aitken's ฮดยฒ
Algorithm
Algorithm efficiency
Algorithm Instability
Algorithm stability
Anderson Acceleration
Approximate integration
Approximate solution
Approximation
Approximation error
Approximation of area under a curve
Approximation of Integrals
Approximation Theory
Area under a curve
Asymptotic Analysis
Asymptotic behavior
Asymptotic Expansion
Augustin-Louis Cauchy
Automatic differentiation
B
B-spline
Backward difference
Backward difference formula
Backward differentiation formulas
Backward error analysis
Backward euler
Backward euler method
Backward stability
Banach Fixed-Point Theorem
Barycentric form
Barycentric interpolation
Barycentric weights
Basin of Attraction
Basis functions
Basis polynomials
Benchmarking
Big O Notation
Bisection Method
Black-box systems
Bolzano's Theorem
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