(b) a = 2;
b = 5;
x = a + (b-a) .* (0:40) ./ 40;
(c) x = a + (b-a) .* (0:40) ./ 40;
y = sin(x);
plot(x,y);
Matlab pukes if you try the .+ listed in the notes.For exercise 1.12, your expression may not be subtraction-free. Alternatively, you can find a Big-O(x5) approximation.
Catalog Description. 174. Numerical Methods in Science and Engineering (4) Floating point arithmetic, linear equations, interpolation, integration, differential equations, nonlinear equations, optimization, least squares. Students may not receive credit for both Math. 174 and Physics 105 or MAE 153 or 154. Students may not receive credit for Math. 174 if Math. 170 A,B, or C has already been taken. Prerequisites: Math. 21D (2DA) and Math. 20F (2EA).
Course Description. This course serves as an introduction to applied numerical mathematics. Numerical analysis, roughly speaking, is concerned with finding approximate numerical solutions to problems for which we lack sufficient data or have no analytic solution: for example, we will explore methods of finding approximate roots of functions for which we have no closed form solution; we will examine algorithms which approximate the integral of a “black box” function; we will use iterative solvers to find the approximate solutions to linear systems; we will use the method of least squares to find the “best” function to approximate a set of data points.
Grading Policy. Grading will be based upon performance in eight homeworks, three quizzes, two single hour exams and a comprehensive final. The final quarter grade is subdivided as follows: Homework: 15%,Quizzes: 15%; Exams: 35%; Final: 35%.
Homeworks will be collected in the discussion section. The TA has discretion regarding accepting homework by proxy or via his/her mailbox. It is my expectation that the TA will cover homework during the discussion section, allowing students to make some changes to their homework before submitting same. It is also my expectation that the TA will not accept late homework. Students are encouraged to work together on homeworks (but prohibited from doing so on quizzes and exams). However, each student must hand in their own homework, with their own name. Moreover, students should list on their homework who they worked with.
Quizzes will be administered in the discussion section; the material on the quizzes will be similar to that of the assigned homeworks. The purpose of the quizzes is not to make you miserable, rather to make you review the material between the exams. The first quiz will be returned before the cutoff date for ‘drop without a W,’ i.e., the end of the fourth week.
The midterm exams will be administered in class, on Monday, October 25, and Friday, November 19. The final is Thursday, December 6 at 3:00pm. If you have known conflicts with any of these exams, you must alert me of this before Friday October 1. Legitimate, documented excuses for missing an exam will be dealt with individually.
The two midterm exams account for 35% of the final grade. Your better score of the two midterms will be worth 20% of your grade, while your lesser score will be worth 15%. This is supposed to skew scores upwards, and decrease the effects of a “bad day.”
Final scores will be converted into letter grades as follows:
| Final Score | Final Grade |
| at least 90% | A- or better |
| at least 80% | B- or better |
| at least 70% | C- or better |
| at least 60% | D or better |
Students are expected to adhere to the University’s policy on academic integrity.
Course Schedule. The lecture schedule is tentative, but the homework and exam schedules are exact. Section numbers refer to the course notes.
| week 0 | F Sep 24 | Syllabus & Taylor’s Theorem §1.1 |
| M Sep 27 | Subtractive cancellation, Linear Algebra Review §1.2,1.3 |
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| W Sep 29 | Introduction to octave/Matlab §2.1-2.4 |
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| week 1 | W Sep 29 (disc.) | octave/Matlab demo? |
| F Oct 01 | Linear Equations §3.1 |
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| M Oct 04 | Linear Equations §3.1,3.2 |
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| W Oct 06 | Linear Equations §3.2,3.3 |
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| week 2 | W Oct 06 (disc.) | HW 1 : §1 # 1,2,4,5,8,9,11,12,13,14
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| F Oct 08 | Linear Equations §3.4 |
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| M Oct 11 | Linear Equations §3.4 |
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| W Oct 13 | Rootfinding §4.1 |
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| week 3 | W Oct 13 (disc.) | HW 2 : §1 # 15,16,17,19,21,22,23
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| F Oct 15 | Rootfinding §4.2 |
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| M Oct 18 | Rootfinding §4.3 |
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| W Oct 20 | Interpolation §5.1 |
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| week 4 | W Oct 20 (disc.) | HW 3 : §3 # 8
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| F Oct 22 | Interpolation §5.2 |
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| M Oct 25 | exam 1 covering §1.1-1.3,3.1-3.4,4.1-4.3 |
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| W Oct 27 | Spline Interpolation §6.1, 6.2 |
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| week 5 | W Oct 27 (disc.) | HW 4 : §4 # 8
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| F Oct 29 | Spline Interpolation §6.3 |
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| M Nov 01 | Derivatives §7.1 |
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| W Nov 03 | Derivatives §7.2 |
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| week 6 | W Nov 03 (disc.) | HW 5 : §5 # 11
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| F Nov 05 | Quadrature §8.1 |
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| M Nov 08 | Quadrature §8.2 |
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| W Nov 10 | Quadrature §8.3 |
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| week 7 | W Nov 10 (disc.) | HW 6 : §7 # 4,5,6
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| F Nov 12 | Quadrature §8.4 |
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| M Nov 15 | Least Squares §9.1 |
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| W Nov 17 | Least Squares §9.2 |
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| week 8 | W Nov 17 (disc.) | HW 7 : §8 # 6,7,9,10
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| F Nov 19 | exam 2 covering §5.1,5.2,6.1-6.3,7.1,7.2,8.1-8.4 |
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| M Nov 22 | ODEs §10.1 |
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| W Nov 24 | ODEs §10.1,10.2 |
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| week 9 | W Nov 24 (disc.) |
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| F Nov 26 | Thanksgiving-No Meeting |
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| M Nov 29 | ODEs §10.3 |
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| W Dec 01 | ODEs §10.3 |
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| week 10 | W Dec 01 (disc.) | HW 8 : §9 # 6
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| F Dec 03 | final exam review |
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| finals | Th Dec 9 | Comprehensive Final Exam. 3:00p-6:00p |