Lectures in course MATH-251(a): Numerical analysis

Introduction to Numerical Analysis

Covers the basics of Numerical Analysis, emphasizing the importance of numerical methods in solving mathematical problems with computers.

Numerical Analysis: Jupyter Notebook Tutorial

Covers course organization, Jupyter Notebook for Python experimentation, algorithms, interpolation, solving equations, linear systems, and practical applications.

Floating Point Numbers: Representation and Errors

Introduces floating point number representation, round-off errors, and their impact on numerical computations.

Floating Point Representation in Computers

Covers the representation of real numbers in a computer using floating point representation and the dangers of significant digit cancellation.

Fixed Point Methods: Non-linear Equations

Covers fixed point methods for finding zeros of non-linear equations.

Nonlinear Equations: Bisection Method

Covers the bisection method for solving nonlinear equations with continuous functions and root finding examples in diode circuits.

Nonlinear Equations: Bisection and Fixed-Point Methods

Explores nonlinear equations, bisection, fixed-point methods, error control, and graphical interpretations of fixed points.

Electrical Circuit: Fixed Point Methods

Explores applying fixed point methods to solve electrical circuit equations and find diode voltage.

Higher Order Methods: Iterative Techniques

Covers higher order methods for solving equations iteratively, including fixed point methods and Newton's method.

Nonlinear Equations: Fixed-Point Methods, High-Order

Covers fixed-point methods and high-order techniques for solving nonlinear equations.

Newton's Method: Order 2

Explains Newton's method of order 2 for finding function zeros.

Nonlinear Equations: Methods and Convergence

Explores high-order fixed-point methods and Newton-Raphson method for solving nonlinear equations.

Newton Method: Data Interpolation

Covers the Newton method for finding zeros of functions using data interpolation.

Nonlinear Equations and Polynomial Interpolation

Introduces nonlinear equations and polynomial interpolation for curve fitting.

Viscosity and Data Interpolation

Covers viscosity calculation, data interpolation, and function integration using evenly distributed points.

Polynomial Interpolation: Curve Fitting

Explores polynomial interpolation for curve fitting, error analysis, and the Runge's phenomenon.

Curve Fitting: Polynomial Interpolation

Explores curve fitting via polynomial interpolation, stability, errors, and node distribution impact.

Error Analysis and Interpolation

Explores error analysis and limitations in interpolation on evenly distributed nodes.

Spline Interpolation: Definition and Error Analysis

Explains spline interpolation and error analysis in approximating data points using piecewise linear and spline methods.

Digital Derivation: Evaluation and Formulas

Explores digital derivation, function evaluation, and polynomial approximations for accurate measurements and evaluations.