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Introduction to Applied Mathematics for Scientists and Engineers (Math 427/527)

We will cover vector integral calculus, Fourier series and transforms, series solutions to differential equations, Sturm-Liouville problems, wave equation, heat equation, Poisson equation, analytic functions, and contour integration. This will be Chapters 5, 10, 11-14, and 17 (time- permitting).

Send me an e-mail

Please send me an e-mail at donnacalhoun@boisestate.edu so that I can compile an e-mail list for the class. At the very least, include a subject header that says "Math 427/527". You may leave the message area blank, if you wish, or send me a short note about what you hope to get out of this course.

Basic course information

Instructor Prof. Donna Calhoun
Time Tuesday/Thursday 1:30-2:45
Place TBA
Office Hours Wednesday 1:30-3:30
Prerequesites Math 275 and Math 333

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Required and suggested textbooks

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Lectures

Week #1 (Aug. 26)
Tuesday --  Review of First and Second order ODEs; 5.1 : Power Series
Thursday --  5.1 : Power Series
Week #2 (Sep. 2)
Tuesday --  Legendre Polynomials (Chapter 5.2)
Codes written or demonstrated in class :
sphere_polar.m
Thursday --  Method of Frobenius (Chapter 5.3)
Week #3 (Sep. 9)
Tuesday --  Forbenius Method (5.4)
Thursday --  Bessel functions (5.4-5.5)
Codes written or demonstrated in class :
plot_bessel.m
Week #4 (Sep. 16)
Tuesday --  Section 10.1 : Line Integrals
Thursday --  Section 10.2 : Path Independence of Line Integrals
Week #5 (Sep. 23)
Tuesday --  Chapter 10.4 : Green's Theorem
Thursday --  Chapter 10.4 : Green's Theorem (cont.)
Week #6 (Sep. 30)
Tuesday --  Chapter 10.5-10.7: Surfaces, surface integrals and Divergence Theorem
Thursday --  Chapter 10.9 : Stoke's Theorem
Week #7 (Oct. 7)
Tuesday --  11.1 : Fourier Series
Codes written or demonstrated in class :
Fourier_example.m
Thursday --  No class
Week #8 (Oct. 14)
Tuesday --  Review for midterm #1
Thursday --  Midterm #1
Week #9 (Oct. 21)
Tuesday --  Fourier Series (continued)
Thursday --  Chapter 11.2, 11.3 : Arbitrary Period. Even and Odd Functions. Half-Range Expansion
Week #10 (Oct. 28)
Tuesday --  Chapter 11.5 : Sturm-Liouville Problems. Orthogonal Functions
Thursday --  11.6 : Orthogonal Series. Generalized Fourier Series
Week #11 (Nov. 4)
Tuesday --  Section 11.7 : Fourier Integrals
Thursday --  Section 11.8 : Fourier Cosine and Sine Transforms
Week #12 (Nov. 11)
Tuesday --  11.9 : Fourier Transforms
Thursday --  11.9 : Fourier Transform (cont)
Week #13 (Nov. 18)
Tuesday --  Section 12.2 : Modeling : Vibrating string, wave equation; Section 12.3 : Solution by separation of variables. Use of Fourier Seris
Thursday --  Section 12.4 : D'Alembert's solution of the wave equation
Codes written or demonstrated in class :
wave.m
Week #14 (Dec. 2)
Week #15 (Dec. 9)

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Homework Assignments

Homework is due at the start of class on the due date listed

Homework #1

Due Sept. 10

Assignment :
hmwk1.pdf
Other resources :
prob2.m  -- Use this to start the numeric portion of Problem 2
prob5.m  -- Use this for the numeric portion of Problem 5
Updates to homework :
 --  (8/30/2019) Two more problems will be added
 --  (9/3/2019) Fixed two minor bugs in prob2.m homework file.
 --  (9/4/2019) Add two more homework problems, and second code.
 --  (9/5/2019) Fixed typo in homework problem 5; added plots
 --  (9/5/2019) Updated prob5.m Matlab code to include contour lines.
 --  (9/6/2019) Updated prob5.m Matlab code. White background better for printing.
Homework #2

Due Sept. 19

Assignment :
hmwk2.pdf
Other resources :
hmwk2.tex  -- Latex copy of the homework.
macros.tex  -- Macros needed to compile the homework.
eqn_wiki.png  -- Figure from Wiki page.
Updates to homework :
 --  (9/14/2019) Fixed a few typos; minor rearrangement of problems; some clarification.
 --  (9/14/2019) Added a few more comments on the units part of the last question.
 --  (9/15/2019) Fixed typo in equation in problem Problem 4.
Homework #3

Due Oct. 3

Assignment :
hmwk3.pdf
Other resources :
hmwk3.tex  -- Latex copy of the homework.
macros.tex  -- Macros files for homework
cyl_surf.m  -- Matlab code showing surface in Problem 7
Updates to homework :
 --  (9/18/2019) Only one problem so far; more to come
 --  (9/24/2019) Homework complete
 --  (9/25/2019) Fixed typo in Problem 7 (y=x^2 should read x=y^2)
 --  (9/25/2019) Changed notation for tangents and normals so it is consistent with the book.
 --  (9/25/2019) Updated Matlab script for Problem 7.
 --  (9/26/2019) Add w(x,y) function to Problem 4
Homework #4

Due Oct. 15

Assignment :
hmwk4.pdf
Other resources :
hmwk4.tex  -- Latex copy of the homework.
macros.tex  -- Macros files for homework
stokes.m  -- Matlab code for problems 3 and 4
Updates to homework :
 --  (10/6/2019) Two more problems on Fourier Analysis
 --  (10/10/2019) Added one problem Fourier series.
Homework #5

Due Oct. 31

Assignment :
hmwk5.pdf
Other resources :
hmwk5.tex  -- Latex copy of the homework.
macros.tex  -- Macros files for homework
Updates to homework :
 --  (10/28/2019) Fixed typo on problem 1 (remove term 1/2; include term 1/9)
 --  (10/28/2019) Fixed typo on problem 4 (Should be A_0, not a_0)
Homework #6

Due Nov. 21

Assignment :
hmwk6.pdf
Other resources :
hmwk6.tex  -- Latex copy of the homework.
macros.tex  -- Macros files for homework
Updates to homework :
 --  (11/18/2019) Fixed typo on problem 3 (add sqrt) and problem 4 (derive (7) from (1) and (8) from (2))
Homework #7

Due Dec. 3

Assignment :
hmwk7.pdf
Other resources :
hmwk7.tex  -- Latex copy of the homework.
macros.tex  -- Macros files for homework
Updates to homework :
 --  (11/26/2019) Added problem on the heat equation; minor edits to wave equation problem
 --  (12/3/2019) Fixed bug in problem 2(d) (remove 1/2 in each term).
Homework #8

Due Dec. 19

Assignment :
hmwk8.pdf
Other resources :
prob2.m  -- Code created in class
hmwk8.tex  -- Latex copy of the homework.
macros.tex  -- Macros files for homework
Updates to homework :
 --  (12/13/2019) Added one last problem on Laplace's equation in the sphere.
 --  (12/14/2019) Fixed typo in problem #3.
 --  (12/18/2019) Fixed minor bug in prob2.m file (Line 59) should read 'surf(xm,ym,u)'

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Midterm

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Grading policy

TBA

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