Chapter 1: Introduction to the course. Review of MATLAB. Review of Calculus. Round-off Errors and Computer Arithmetic. Algorithms and Convergence.
Chapter 2: Solutions of Equations in One Variable: The Bisection Method, Fixed-Point Iteration, Newton’s Method and Its Extensions, Error Analysis for Iterative Methods, Accelerating Convergence, Zeros of Polynomials and Müller’s Method.
Chapter 3: Interpolation and Polynomial Approximation: Interpolations and the Lagrange Polynomial, Divided Differences, Hermite Interpolation, Cubic Spline Interpolation.
Chapter 4: Numerical Differentiation and Integration: Numerical Differentiation, Richardson’s Extrapolation, Elements of Numerical Integration, Composite Numerical Integration, Romberg Integration, Adaptive Quadrature Methods, Gaussian Quadrature, Multiple Integrals, Improper Integrals.
Chapter 5: Initial-Value Problems for Ordinary Differential Equations: The Elementary Theory of Initial-Value Problems, Euler’s Method, Higher-Order Taylor Methods, Runge-Kutta Methods, Higher-Order Equations and Systems of Differential Equations, Error Control and the Runge-Kutta-Fehlberg Method, Multistep Methods, Stability, Stiff Differential Equations.
Chapter 6: Direct Methods for Solving Linear Systems: Linear Systems of Equations, Pivoting Strategies, Linear Algebra and Matrix Inversion, The Determinant of a Matrix, Matrix Factorization, Special Types of Matrices.
All in-class MATLAB codes:
Organized by textbook sections: