Resources (Updated 3/9)
Stewart Textbook Website (Calculus III)
Stewart Textbook Website (Calculus I & II)
Paul's Online Math Notes - Calculus I
Paul's Online Math Notes - Calculus II
Paul's Online Math Notes - Calculus III
Paul's Online Math Notes - Differential Equations
Announcements (Updated 6/11)
HERE is the take-home portion of the Final Exam.
There will be an optional Homework/Review Session Wednesday 6/10 at 11:00 AM (until around noon) in Room 735.
The "Blank Copies of Old Exams" folder above now contains Exams from this semester!
As agreed, you may take Part 2 of the Final Exam early on Friday 6/12 from 8:30 AM to 10:15 AM in Room 735. If you cannot make this time or the regularly scheduled time, please let me know ASAP.
The Final Exam will consist of two parts: Part 1 (Take-Home Problems) and Part 2 (In-Class Problems). Part 1 of the Final Exam will be available for download here on Thu 6/11 and is due Friday 6/12 at 12:40 PM. Part 2 of the Final Exam will be Friday 6/12 from 12:40 PM to 2:25 PM (Periods 5 & 6) in Room 631.
Exam 3 Solutions are posted below.
Exam 2 Solutions are posted below.
Quiz 10 (Take Home) is due at 9 AM on Mon 5/4. If you are going to be absent on that date, please scan and email it to me by that time.
Exam 2 will be on Wed 5/6 and will cover HW 9 through HW 17 (HW 17 is the final ODE homework).
Exam 1 Solutions are posted below.
Exam 1 will be on Wednesday 3/18.
Here are the Quiz 2 Solutions.
Welcome to Advanced Applied Math.
Homework (Updated 6/5)
(Note: You are responsible for all Homework posted and/or updated before 5:00 PM the school day before the due date. Due dates are subject to change, so please check them carefully.)
"ODE" denotes the Ordinary Differential Equations textbook
"FCA" denotes the Fundamentals of Complex Analysis textbook
Notes:
(1) Some of these ODE's are in differential form (i.e., the ODE has already been "multiplied" through by dx). To convert back to the more familiar Leibnitz form, just "divide" the ODE through by dx. Also consider regarding x as the dependent variable and "dividing" through by dy, which may result in an ODE which is easier to solve.
(2) Whenever possible, solve for an explicit solution (isolate the dependent variable), even though the answers in the textbook are often left in implicit form. You will generally be required to find explicit solutions on Exams and Quizzes.
(3) In the ODE Textbook (as well as in Wolfram Alpha, and many other places), "log" denotes the natural logarithm that we normally denote by "ln".
This is all of the remaining homework!
HW 27 (Complex Logarithms Part 2)
FCA Page 123 Problems 9, 10, and these Problems
Due Before the Final
HW 26 (Complex Logarithms Part 1)
FCA Page 123 Problems 1, 3, 4, 5, 6
Also, review the Solutions to Exam 3 and resolve anything that you do not understand!
Due Mon 6/8
HW 25 (Rational Functions)
FCA Page 108 Problems 11, 13, 14
Due Mon 6/1
HW 24 (Polynomials)
FCA Page 108 Problems 1, 2, 3, 4, 5
Due Wed 5/27 (Problems 1, 2, 3, 4)
Due Thu 5/28 (Problem 5)
Here is the Solution to HW 23 Problem 14.
HW 23 (Harmonic Functions)
FCA Page 84 Problems 1, 2, 3, 5, 6, 14
Due Fri 5/22
HW 22 (Cauchy-Riemann Equations)
FCA Page 77 Problems 1, 3, 5, 9, 10
Due Wed 5/20 (Problems 1, 3, 5)
Due Thu 5/21 (Problems 9, 10)
HW 21 (Analyticity)
FCA Page 70 Problems 4, 7, 9, 11, 13
Due Mon 5/18 (Problems 4, 7)
Due Wed 5/20 (Problems 9, 11, 13)
HW 20.5 (Admissibility)
Do these problems.
Due Fri 5/15
HW 20 (Limits and Continuity)
FCA Page 63 Problems 7, 11, 12, 13, 17, 21, 25
Due Wed 5/13 (Problem 7 Only).
Due Thu 5/14 (Remaining Problems)
HW 19 (Functions of a Complex Variable)
FCA Page 56 Problems 1-5, 7b, 8b, 9b, 10d, 11d
Due Mon 5/11 (Problem 1 Only).
Due Wed 5/13 (Remaining Problems)
HW 18B (Planar Sets 2)
FCA Page 43 Problems 15-20 (all).
Due Mon 5/11
HW 18A (Planar Sets 1)
FCA Page 42 Problems 2-8 (We did not cover the definition of "bounded" it is on Page 42.); Problems 11, 12.
Due Fri 5/8
Please come to class on Mon 5/4 ready to present and discuss HW 14 - HW 17, as well as discuss any other questions or problems you may have.
HW 17 (Series Solutions Near an Ordinary Point)
ODE Page 546 Problems 3, 5, 7, 9, 11
Due Mon 5/4
HW 16 (Method of Variation of Parameters)
ODE Page 240 Problems 2, 3, 4, 5, 12, 15, 18, 20
Due Wed 4/29
HW PSR (Power Series Review)
Review the sections on "Power Series" & "Power Series and Functions" in Paul's Online Math Notes - Calculus II and write down any questions you may have.
Due Mon 4/27 & Wed 4/29
HW 15B (Complex Exponentials are Your Friends)
Do these Problems.
Due Fri 4/24
HW 15A (Method of Undetermined Coefficients)
ODE Page 231 Problems 3, 6, 7, 9, 11, 13, 15, 17, 19, 23, 30, 32
Due Thu 4/23
HW 14 (Linear Homogeneous ODE's with Constant Coefficients - No Restrictions on Roots of Characteristic Equation)
ODE Page 220 Problems 24, 25, 26, 27, 28, 29, 30, 33, 34, 35
Due Mon 4/20
Please come to class on Thu 4/16 ready to present and discuss HW 9A - HW 13.
HW 13 (Evaluating Complex Trig & Hyperbolic Functions)
FCA Page 115 Problem 5
(Note: exp(z) is simply an alternate notation for ez which avoids the need for superscripts)
Due Thu 4/16
HW 12 (Powers and Roots)
FCA Page 37 Problems 4, 5, 7, 9, 10, 11, 15, 16
Due Wed 4/15
HW SB2 (Return to 9th Grade Geometry)
Do this problem.
Due Mon 4/13
HW SB1 (More Fun with Finite Fields)
Do these problems.
Due Mon 4/13
HW 11B (Return to Calculus II)
FCA Page 32 Problem 23 (answers are in the back of the book)
Due Thu 4/2
HW 11A (Complex Exponentials)
FCA Page 31 Problems 1, 2, 3, 4, 7, 8, 11
Due Wed 4/1
HW 10C (Arg! Arg!)
Do these problems. Also do Problem 11 on Page 22 if you have not yet done so.
Due Mon 3/30
HW 10B (Arg!)
FCA Page 22 Problems 7 (e)-(h), 11, 12, 13
Also, do Problem 3 on Spring 2014 Exam I. Please give the problem a serious attempt before checking the solution in the solutions section. There may be a similar problem on tomorrow's Quiz!
For Problem 11, you will need to use the fact that if z = x + i y, Arg(z) = tan-1(y/x) when x>0 (and only when x>0 !!!), together with the fact that tan-1 is odd. We will talk more about this tomorrow.
Due Fri 3/27
HW 10A (arg!)
FCA Page 22
Problem 4 (just mimic the induction argument we used in class to prove the similar identity for conjugate)
Problem 5 (if you choose to do the absolute value last, you will do a lot of unnecessary work)
Problem 6 ("cis(theta)" is a ridiculous abbreviation for "cos(theta) + i sin(theta)")
Problem 7 (a)-(d) only
Also, try to redo Problem 16 on Page 13 using a more ... "enticing" proof.
Due Thu 3/26
HW 9C (Welcome to Complex Analysis II)
FCA Page 13 Problems 7, 9, 11, 13, 16
Due Wed 3/25
HW 9B (Fun with Finite Fields)
Consider the set {0, 1, 2, 3, 4} with addition and multiplication defined "modulo 5", which means whenever you obtain a number greater than or equal to 5, divide by 5 and replace the number by the remainder, which will always be in {0, 1, 2, 3, 4}. For example: 2 + 4 = 6 = 1 (modulo 5); (3)(4) = 12 = 2 (modulo 5), etc. This, in fact, defines a Field with only 5 members.
a) Construct a 5 x 5 addition table for this Field.
b) Construct a 5 x 5 multiplication table for this Field.
c) Construct a 5 x 2 table listing the additive inverse and the multiplicative inverse for each member of the Field (for which they are defined).
d) Prove that the set {0, 1, 2, 3} with addition and multiplication defined "modulo 4" is, in fact, NOT a Field. (Hint: Repeat steps a), b), and c). What goes wrong?)
However there is a Finite Field with 4 elements with a different addition and multiplication table. Type "finite field of order 4" into Wolfram Alpha to see it.
Due Mon 3/23
HW 9A (Welcome to Complex Analysis I)
FCA Page 5 Problems 7, 9, 11, 13, 14, 17, 19, 20, 21, 23, 24, 25
Due Mon 3/23 (but do as much as possible for Fri 3/20)
Please come to class on Monday 3/16 ready to present and discuss homework problems.
HW MFO (Mixed First Order ODE's)
ODE Page 104 Problems Any/All. You are not responsible for finding integrating factors and/or substitutions for types of ODE's that we did not cover.
Due Mon 3/16
HW 11 (Linear Homogeneous ODE's with Constant Coefficients - Characteristic Equation has only Real Roots, Some Possibly Multiple)
ODE Page 220 Problems 14, 15, 16, 18, 19, 20, 21, 22
Due Fri 3/13
HW 10 (Linear Homogeneous ODE's with Constant Coefficients - Characteristic Equation has only Real Roots, All Distinct)
ODE Page 220 Problems 1-9 (all)
Due Thu 3/12
HW 9 (An Intro to Linear ODE's)
Do this problem.
Due Wed 3/11
HW 8 (Fun with Hyperbolic Functions)
Due Mon 3/9
HW 7 (Exact First Order ODE's)
ODE Page 79 Problems 5-17 odd. In Problem 7, "dy" should be outside the parentheses.
Due Thu 3/5 (But read the discussion of Exact Equations (ODE Pages 72-78) and do at least one problem for Wed 3/4. Note especially the Remark on Page 78 and the example following.)
HW 6 (Homogeneous First Order ODE's)
ODE Page 61 Problems 3, 5, 6, 8, 12-15 (solve explicitly for y in 12-15) (Hint: Problem 3 is much easier if x is regarded as the dependent variable and you let u = x/y)
Due Mon 3/2
HW 5 (Bernoulli Equation)
ODE Page 97 Problems 3, 7, 8, 22
Due Fri 2/27
HW 3B (Linear First Order ODE's - continued)
1) If you haven't already, solve explicitly for the solution y = f(x) in Problem 24 below and determine the domain of validity.
2) Do this problem.
Due Thu 2/26
HW 3A (Linear First Order ODE's)
ODE Page 97 Problems 1, 2, 5, 6, 9, 11, 13, 14, 17, 24 (Hint: Problem 24 is linear if x is regarded as the dependent variable)
Due Wed 2/25 (but please try a few over break!)
HW 2C
Find an explicit general solution to the ODE y' = r y (1 - y), where r is a constant.
Due Thu 2/12
HW 2B (Separable First Order ODE's)
ODE Page 55 Problems 10, 12, 18, 19, 20, 21
Due Wed 2/11
HW 2A (Separable First Order ODE's)
ODE Page 55 Problems 2, 3, 5, 7, 11, 17
Due Wed 2/11
HW 1 (Verifying Solutions to ODE's)
ODE Page 27 Problems 1-3; Page 37 Problems 1-4
Due Fri 2/6
Note: All Test Statistics are before adding make-up points (if applicable).
Exam 1
Statistics
Student Work
Exam 2
Statistics
Solutions (Correction: For Problem 5, the two exponentials in the last line should have a factor of 2 in the exponent.)
Student Work
Exam 3
Statistics
Student Work