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What am I
doing here?
The main objective of this course
is to help you develop skill with a variety of commonly used
mathematical and numerical methods in physics in engineering. We will
focus on the practical rather than the theoretical aspects of each
technique, but there will naturally be some theory involved. The topics
include derivatives and partial derivatives, infinite series (including
Fourier series and Taylor series), vector calculus, complex numbers,
linear algebra, tensors, differential equations, and probability. There
will also be some examination of commonly used numerical techniques.
What do I
have to read?
The
textbook is: Mathematical Methods in the Physical Sciences, by
Mary Boas (3rd edition, Wiley). This book
is very readable. |
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Final Exam:
The final exam will be held on Monday, May 10, from 3:30 to 6:30pm, and
will be comprehensive.
Assignments:
Homework will be done primarily on CAPA this semester. However, some
assignments will require submission of MathCAD documents, or supporting
written work. Written work will be graded on clarity (a combination of
neatness and completeness) and accuracy. Be warned: an answer is not the
same as a solution. Assignments that are too hard to understand are also
too hard to grade, and will receive zeroes.
Some reminders about the minimum requirements for acceptable
assignments:
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·
Use exactly 8˝
´
11 inch paper. Do not use spiral ring paper. Use only one side of
each sheet.
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·
Put your name and the
assignment number on the top of each page.
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Staple your sheets
together. No paper clips, or torn or folded corners.
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Use pencil, not pen.
Erase mistakes instead of blotching them out.
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Work must progress
linearly down the page. Recopy solutions that are too nonlinear.
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·
Be careful with symbol
names. There may be more than one velocity in a problem, so they
can’t both be called “v”. Use subscripts when needed.
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·
Do not use
computational notation, such as ^, *, E, :=, etc.
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Use words and pictures
to supplement your equations. Isn’t that what you want when
you read?
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·
Work symbolically
rather than numerically whenever possible.
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Box your answers.
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What is the course schedule?
Here is a tentative hourly schedule of topics for the semester.
What is the course schedule?
Here is a tentative schedule of topics for the semester:
|
Class |
Date |
Topic |
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1 |
TWR Jan 19, 20, 21 |
Infinite Series [Ch. 1] |
|
2 |
Monday, January 25 |
Series II; Taylor series and
approximations of derivatives [Ch. 1] |
|
3 |
TWR Jan 26, 27, 28 |
Vector calculus I: dot,
cross, del, and grad [Ch. 6] |
|
4 |
Monday, February 1 |
Vector calculus II:
divergence, curl, Laplacian [Ch. 6] |
|
5 |
TWR, Feb 2, 3, 4 |
Numerics:
Plotting with MathCAD |
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6 |
Monday, February 8 |
Derivatives/Chain rule
[Review/Ch. 4] |
|
7 |
TWR, Feb 9, 10, 11 |
Complex analysis I [Ch. 2] |
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8 |
Monday, February 15 |
Complex analysis II [Ch. 2] |
|
9 |
TWR, Feb 16, 17, 18 |
Numerics:
General computing with MathCAD |
|
10 |
Monday,
February 22 |
Exam #1
(covers classes 1-8) |
|
11 |
TWR, Feb 23 |
Linear algebra I [Ch. 3] |
|
12 |
Monday, March 1 |
Linear algebra II [Ch. 3] |
|
13 |
TWR, Mar 2, 3, 4 |
Numerics:
Curve fitting |
|
14 |
Monday, March 8 |
Eigenvalues & Eigenvectors
[Ch. 3] |
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15 |
TWR, Mar 9, 10, 11 |
Tensors [Ch. 10] |
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Spring Break |
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16 |
Monday, March 22 |
Coordinate Transformations
[Ch. 10] |
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17 |
TWR, Mar 23, 24, 25 |
Multi-variable integration
review with Numerics [Review/Ch. 5] |
|
18 |
Monday, March 29 |
1st order
ordinary differential equations (separation of variables) [Ch.
8] |
|
19 |
TWR, Mar 30, 31, Apr 1 |
2nd order
ordinary differential equations (constant coefficients) [Ch. 8] |
|
20 |
Monday,
April 5 |
Exam #2
(covers classes 9-17) |
|
21 |
TWR, Apr 6, 7, 8 |
Numerics:
Differential equations (MathCAD RKadapt) |
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22 |
Monday, April 12 |
Fourier series I [Ch.7] |
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23 |
TWR, Apr 13, 14, 15 |
Fourier series II & Fourier Transforms [Ch. 7] |
|
24 |
Monday, April 19 |
Partial differential equations (heat equation) [Ch. 13] |
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25 |
WR, Apr 21, 22 |
Partial differential equations (wave equation)
[Ch. 13]
Note that the Tuesday section will not meet on April 20, due to
“Great Day”. Students in the Tuesday section are encouraged to
attend either the Wednesday or Thursday section that week. |
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26 |
Monday, April 26 |
Probability: interpreting a pdf, counting, “choosing” [Ch. 15] |
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27 |
TWR, Apr 27, 28, 29 |
Probability: common distributions (normal, binomial, poisson)
[Ch. 15] |
|
28 |
Monday, May 3 |
Statistics: standard
deviation [Ch.
15] |
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T, May 4 |
Review |
|
{29} |
Monday,
May 10 |
Final
Exam (comprehensive) 3:30 pm |
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