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Numerical Analysis
Numerical Analysis
42 lessons across 14 topics
1. Numerical Error and Computation
1
Absolute And Relative Error
2
Floating-point Numbers
3
Propagation Of Error
2. Root-Finding I
4
Bisection Method
5
Convergence Concepts
6
Fixed-point Iteration
3. Root-Finding II
7
Newton’s Method
8
Practical Issues And Stopping Criteria
9
Secant Method
4. Interpolation I
10
Lagrange Form
11
Newton Divided Differences
12
Polynomial Interpolation
5. Interpolation II
13
Interpolation Error
14
Piecewise Interpolation
15
Spline Overview
6. Numerical Differentiation and Integration I
16
Finite Differences
17
Simpson’s Rule
18
Trapezoidal Rule
7. Numerical Integration II
19
Adaptive Quadrature Overview
20
Composite Methods
21
Error Bounds
8. Midterm 1 and Linear Systems I
22
Gaussian Elimination
23
Lu Factorization
24
Midterm 1
9. Linear Systems II
25
Conditioning
26
Iterative Methods
27
Jacobi And Gauss-seidel Methods
10. Approximation and Least Squares
28
Applications To Data
29
Best-fit Approximations
30
Overdetermined Systems
11. Numerical Solutions of ODEs I
31
Euler’s Method
32
Local And Global Error
33
Stability Considerations
12. Numerical Solutions of ODEs II
34
Improved Euler
35
Runge-kutta Methods
36
System Approximations
13. Advanced Topics (SLASH) Project Work
37
Optimization Overview
38
Pde Introduction
39
Student Project Development
14. Review and Synthesis
40
Comparing Methods
41
Efficiency Vs(dot) Accuracy
42
Final Review
