Computation has become one of the three legs of science and engineering: Theory, Experiment, and Computation. Scientific computing has been vitally important for studying a wide range of physical, engineering and social phenomenon. In this course we will study the mathematical foundations of well-established numerical algorithms and will cover classical topics in Numerical Analysis: the solution of linear and nonlinear equations, interpolation, numerical differentiation, numerical integration.

The course will focus on the analysis of numerical methods, but also require the students to implement a range of numerical methods using numerical software (Python). If you are not familiar with Jupyter or VScode, please come to the instructor's office for the introduction to Python during the office hours.

Knowledge of undergraduate linear algebra and calculus. Python will be used as the primary language and you will be expected to master it through the course.

You are encouraged to use LaTex editor (overleaf.com) for the homework but not required.

36% homework
30% midterm
30% final exam
4% attendance

We will cover the following sections:
1.3 Algorithms and Convergence
2.1 The Bisection Method
2.2 Fixed-Point Iteration
2.3 Newton's Method
2.4 Error Analysis
2.5 Zeros of Polynomials
3.1 The Lagrange Polynomials
3.2 Divided Differences
3.3 Hermite Interpolation
3.4 Cubic Spline
4.1 Numerical Differentiation
4.3 Numerical Integration
4.4 Composite Numerical Integration
4.7 Gaussian Quadrature
5.1 The Elementary Theory of Initial-Value Problems
5.2 Euler's Method
5.3 Higher-Order Taylor Methods
5.4 Runge-Kutta Methods
5.6 Multistep Methods
5.9 Higher-Order Equations and Systems of Differential Equations
5.10 Stability
8.1 Discrete Least Squares Approximation
8.2 Orthogonal Polynomials and Least Squares Approximation
8.3 Chebyshev Polynomials
8.4 Rational Function Approximations

No late homework will be accepted without an approved excuse.

No late homework will be accepted without an approved excuse.