Topics covered: Basic concepts and methods in numerical analysis: Solution of equations in one variable; Polynomial interpolation and approximation; Numerical differentiation and integration; Initial-value problems for ordinary differential equations; Direct methods for solving linear systems.
Dates: See UC Berkeley Summer Sessions C – Eight-Week Session
Course format: Fully remote – no physical presence required. You will need a computer with a reliable internet connection for online meetings, and the ability to produce and submit PDFs of your written work.
Units: Four (4) semester credits. This course satisfies the same prerequisites and major requirements as the standard version of Math 128A.
Prerequisites: Math 53 and Math 54, or equivalent. Basic programming experience is helpful (e.g., Math 98, Math 124, CS61A, Engin 7, or equivalent). An introductory MATLAB tutorial will be provided on bCourses at the start of the course.
Required textbook: R. L. Burden and J. D. Faires, Numerical Analysis, 10th edition, Cengage Learning, 2015. ISBN-13: 978-1305253667. Note: The 9th edition is also supported.
Assignments and exams: Weekly homework and quizzes, four programming assignments, one midterm, and a final exam.
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.
Organized by textbook sections: