Chemical Engineering 132A
Analytical Methods of Chemical Engineering
Professor Mike Gordon, Fall 2011
Homework #5: Due Wed. 30 November 2011
The last one!
(1) Set up the solution to the problems below. Setting up means you should apply the BCs/ICs and
all
ChE 10: Introduction to Chemical Engineering
Midterm Exam 1
Wednesday, October 31, 2012
Name: _SOLUTION_
Grade:
Problem 1
_ / 40
Problem 2
_ / 40
Problem 3
ver. A
_ / 20
Extra Credit _ / 5
TOTAL
_ / 100
Instructions: You have 50 minutes to complete this e
Chemical Engineering 132A
Analytical Methods of Chemical Engineering
Professor Mike Gordon, Fall 2011
Mathematica Assignment #3
Commands for today
Series[f[x],cfw_x,a,n]
Power series of order n for f(x) about the point x=a
5
Sum[f[n],cfw_n,0,5]
f ( n)
No
Chemical Engineering 132A
Analytical Methods of Chemical Engineering
Professor Mike Gordon, Fall 2011
Mathematica Assignment #1
If you do not finish during recitation,
turn in your completed assignment by Monday, 3 October 2011.
1) Define the following fu
ChE132a: Analytical Methods of Chemical Engineering
Professor Mike Gordon, Fall 2011
Homework #4: Due Wed. 16 Nov. 2011
(1) PGA p. 503
#1, 5, 6, 9
Explicitly write out an expression for the Fourier coefficients
(2) PGA p. 503
#10, 14, 19 Use Mathematica t
ChE132a: Analytical Methods of Chemical Engineering
Professor Mike Gordon, Fall 2011
Homework #3: Due Wed., 26 Oct. 2011
(1) PGA
p. 160-161
#2, 4 (work the integrals by hand); 15, 17, 22, 24, 27, 31, 45, 48
(2) Solve the following ODEs using Laplace trans
ChE132a: Analytical Methods of Chemical Engineering
Professor Mike Gordon, Fall 2011
Homework #2: Due Friday 14 Oct. 2011
(1) PGA
(2) PGA
(3) PGA
p. 43
p. 59
p. 71
#24, 25, 27, 30, 34, 41
#10, 13, 19; use the method of undetermined coefficients
#1, 2; use
ChE132a: Analytical Methods of Chemical Engineering
Prof. Mike Gordon, Fall 2011
Homework #1
Due: Wednesday, 5 October 2011
(1) PGA
p. 6
#1-8, 11, 13
(2) PGA
p.11-12
#3, 11
(3) PGA
p. 16
#3, 11
(4) PGA
p. 20
#3, 6, 9
OVER
(6) [counts double] Time to think
Chemical Engineering 132A
Analytical Methods of Chemical Engineering
Professor Mike Gordon, Fall 2011
Mathematica Assignment #4
Commands for today
LaplaceTransform[f[t],t,s]
InverseLaplaceTransform[F[s],s,t]
HeavisideTheta[t]
DiracDelta[t]
Apart[expr]
Lap
Chemical Engineering 132A
Analytical Methods of Chemical Engineering
Professor Mike Gordon, Fall 2011
Mathematica Assignment #5: Fourier Series
1) Which of the following functions are orthogonal on the domain [-L,L]?
Hint: directly integrate all possible
Chemical Engineering 132A
Analytical Methods of Chemical Engineering
Professor Mike Gordon, Fall 2011
Mathematica Assignment #6: Visualizing PDE Solutions
Commands for today
Sum[f[n],cfw_n,1,100]
ft=Table[f[n],cfw_n,1,100]
ft[5]
Chop[]
Animate[Plot[f[x,t]
Chemical Engineering 132A
Analytical Methods of Chemical Engineering
Professor Mike Gordon, Fall 2011
Mathematica Assignment #7: Visualizing PDE Solutions
Commands for today
Table[F[m,n],cfw_m,1,20,cfw_n,1,20]
make a 2D table for all combinations of m and
Chemical Engineering 132A
Analytical Methods of Chemical Engineering
Professor Mike Gordon, Fall 2011
Course Description
This course addresses the mathematical foundations of almost everything you will do as
Chemical Engineers. We will learn various techn
ChE132a: Analytical Methods of Chemical Engineering
Professor Mike Gordon, Fall 2011
Getting Started Mathematica Commands
f=5
f:= some expression
f[x_]:=some function of x
f[x_,y_,z_]:= some function of x,y,z
define f to be 5
define f to represent some ex
Chemical Engineering 132A
Analytical Methods of Chemical Engineering
Professor Mike Gordon, Fall 2011
Mathematica Primer
Mathematica is an extremely powerful software package that can numerically and
symbolically manipulate all kinds of mathematical expre
Chemical Engineering 132A
Analytical Methods of Chemical Engineering
Professor Mike Gordon, Fall 2011
Mathematica Assignment #2
If you do not finish during recitation, turn it in by Monday 10 Oct., 2011.
(4) Use DSolve[] to solve the following ODEs:
(5) S
CHEMICAL ENGINEERING 132A
Professor Todd Squires
Spring Quarter, 2007
Final Homework!
Due Friday, June 8 (Thurs., June 7 if you want it corrected before your nal on Monday)
Problem 1. A circular pipe of radius 1 contains solute with a concentration initia
CHEMICAL ENGINEERING 132A
Professor Todd Squires
Spring Quarter, 2007
Computer Lab Assignment 8
New Commands:
<GraphicsAnimation
Animate[Plot[f[x,t],cfw_x,0,1,PlotRange->cfw_0,1],cfw_t,0,10,.5]
as = Table[a[n],cfw_n,0,50]
a20 = as[20]
Like last week, were
CHEMICAL ENGINEERING 132A
Professor Todd Squires
Spring Quarter, 2007
Homework 5
Due Wednesday, May 30
Problem 1. p503, prob 2
Problem 2. p504, prob 50
Problem 3. p504, prob 51
Problem 4. Fluid Mechanics example. The equation for a uni-directional uid ow
CHEMICAL ENGINEERING 132A
Professor Todd Squires
Spring Quarter, 2007
Computer Lab Assignment 1
Introduction to Mathematica
Mathematica can be extremely helpful in doing mathematics for engineering. The following is a very brief tutorial
designed to help
Department of Chemical Engineering
University of California, Santa Barbara
Chemical Engineering
132A
Analytical Methods
in Chemical Engineering
Fall 2016
Homework #4
Homework due: Wednesday, 2 November 2016
1. Complete the solution of the following heat c
Department of Chemical Engineering
University of California, Santa Barbara
Chemical Engineering
132A
Analytical Methods
in Chemical Engineering
Fall 2016
Homework #3
Homework due: Wednesday, 19 October 2016
1. Find the Laplace transforms of the following
Chemical Engineering 132A
Analytical Methods of Chemical Engineering
Professor Glenn Fredrickson, Fall 2016
Homework #6: Due Wednesday 30 November 2016
Practical applications of PDEs!
(1) Hot fluid at 200C is transported across a plant site through a cast
Department of Chemical Engineering
University of California, Santa Barbara
Chemical Engineering
132A
Analytical Methods
in Chemical Engineering
Fall 2016
Homework #2
Homework due: Wednesday, 12 October 2016
1. Find the general solutions of the following h
Department of Chemical Engineering
University of California, Santa Barbara
Chemical Engineering
132A
Analytical Methods
in Chemical Engineering
Fall 2016
Homework #1
Homework due: Wednesday, 5 October 2016
1. In each case, indicate whether the equation is
Chemical Engineering 132A
Analytical Methods of Chemical Engineering
Homework #5: Due Wednesday 16 November 2016
(1) Set up the solution to the problems below. Setting up means you should apply the BCs/ICs and
construct the solution as a series, but leave
CHEMICAL ENGINEERING 132A
Professor Todd Squires Spring Quarter, 2007 Review for Midterm
(A) Be able to look at a differential equation and tell things about it. 1) Ordinary differential equation or Partial Differential Equation? P 2P P +u = t x2 x