# Numerical Methods for Physical Modeling Math 174/274 --- Winter 2021

## Announcements

 From now on, important announcements will be made on this section of the course website / syllabus.

The final grade will be composed by the best of the following two options: (a) 20% homework, 20% first midterm, 20% second midterm, and 40% final exam. (b) 20% homework, 20% best midterm, and 60% final exam. You must pass the final exam to pass the class.

Your course grade will be determined by your cumulative average at the end of the quarter, based on the following scale:

 A+ A A- B+ B B- C+ C C- 100 - 96.66 96.65 - 93.33 93.32 - 90.00 89.99 - 86.66 86.65 - 83.33 83.32 - 80.00 79.99 - 76.66 76.65 - 73.33 73.32 - 70

The above scale is guaranteed: for example, if your cumulative average is at least 73, then your final grade will be at least B. However, your instructor may adjust the above scale to be more generous.

## Course Calendar

The dates of the exams, holidays, and an outline of topics to be discussed in each week. This calendar is preliminary and may be subject to change as the quarter progresses.
Week Topics
1 Vectors and Matrices on Computer, Floating-point numbers, Linear Systems of Equations
Videos 1, 2, 3
2 Floating-point numbers, Triangular Systems of Equations, LU decomposition
Videos 4, 5, 6
18.01.2021. Martin Luther King, Jr. Holiday
3 Cholesky Decomposition
Video 7
Videos 8, 9
5 Nonlinear Systems of Equations: bisection method and Newton method
Videos 10, 11
6 Interpolation
Videos 12, 13, 14
15.02.2021. Presidents' Day Holiday
Videos 15, 16
8 Introduction to Ordinary Differential Equations, Theory of ODE
Videos 17, 18, 19, 20
9 Theory of ODE
Videos 21, 22, 23
10 Numerical solution of initial value problems
QR decomposition
Videos 24, 25, 26
FI
17.03.2021.
Final Exam. Details to be announced.

## Slides

Lecture 01 (Vectors and Matrices)
Lecture 02 (Floating-point numbers)
Lecture 03 (Linear Systems of Equations)

Lecture 04 (Floating-point numbers and rounding errors)
Lecture 05 (Triangular Matrices)
Lecture 06 (Gaussian elimination and LU decomposition)

Lecture 07 (Symmetric Positive-Definite Matrices and LU Decomposition)

Lecture 09 (Convergence of Gradient Descent)

Lecture 10 (Bisection Method)
Lecture 11 (Newton's Method)

Lecture 12 (Taylor Polynomials)
Lecture 13 (Lagrange Interpolation)
Lecture 14 (Hermite Interpolation)

Lecture 15 (Numerical Integration)