Karl Heinz Dovermann,   Professor


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Research Papers

Online Algebra Refresher - Information

Calculus without Limits (Lecture Notes for Applied Calculus)

Vectors and Plane Geometry (Lecture Notes for the first week in Math 241 or 251A)

Calculus Lecture Notes for Math 161

Common Math 241 Final Exams and Practice Materials

Office Phone Email
Keller Hall 405
(808) 956-4654 heiner@math.hawaii.edu
 
Fall 2015
Course title Course number Room Hours
Introduction to Linear Algebra Math 311 Keller 402 MWF 8:30 -- 9:20
Calculus III Math 243 Keller 303 MWF 10:30 -- 11:20
Surgery Theory Math 649 PSB 317 T 9:00 -- 10:15
Office hours
MWF 9:30-10:20 & R 9:00 -- 10:00
and by appointment


Announcement for Math 243 (Spring 2016):

  • Syllabus for Math 243
  • Look up your grades for Spring 2016: (Use your student ID#)
  • First exam with solutions
  • HW1, due Wednesday January 13th, Section 11.1, Problems 10, 16, 22, 38.
  • HW2, due Friday January 15th, Section 11.2, Problems 10, 18, 22, 24, 50.
  • HW3, due Wednesday January 20th, Section 11.3, Problems 12, 18, 42, 48.
  • HW4, due Friday January 22nd, Section 11.4, Problems 20, 24, 28, 30.
  • HW5, due Monday January 25th, Section 11.5, Problems 2, 4, 6, 20, 24, 36.
  • HW6, due Wednesday January 27th, Section 11.5, Problems 42, 48, 54, 60.
  • HW7, due Friday January 29th, Section 11.6, Problems 1-12, 16, 20, 24, 28, 32.
  • HW8, due Monday February 1st, Section 10.1, Problems 2, 6, 10, 16, 24, 28, 40.
  • HW9, due Wednesday February 3rd, Section 10.2, Problems 6, 8, 14, 16.
  • HW10, due Friday February 5th, Section 10.2, Problems 20, 22, 24, 26.
  • HW11, due Monday February 8th, Section 10.3, Problems 4, 8, 18, 24.
  • HW12, due Friday February 12th, Section 12.1 Problems 4, 8, 18, 24, 28.
  • HW13, due Wednesday February 17th, Section 12.2 Problems 6, 10, 24, 26.
  • HW14, due Wednesday February 24th, Section 12.3 Problems 4, 6, 10, 14.
  • HW15, due Friday February 26th, Section 12.4 Problems 2, 4, 10, 16.
  • HW16, due Wednesday, March 2nd, Section 12.5 Problems 6, 12, 19, 28.
  • HW17, due Friday March 4th, Section 12.6 Problems 2, 4, 6.
  • HW18, due Friday, March 11th, Section 13.1 Problems 2, 6, 13-18, 34, 42.
  • HW19, due Wednesday, March 30th, Section 13.3 Problems 4, 8, 12, 16, 24, 28, 42, 46.
  • HW20, due Friday, April 1st, Section 13.3 Problems 58, 64, 68, 70, 72.
  • Explain why you can use the cross product of the velocity and acceleration vector as normal vector to the osculating plane. (Extra credit)
  • HW21, due Monday, April 4th, Section 13.4 Problems 4, 8, 12, 16, 24, 28, 42, 46 (by Friday will be fine).
  • HW22, due Wednesday, April 6th, Section 13.5 Problems 2, 6, 8, 12.
  • HW23, due Monday, April 11th, Section 13.2 Problems 4, 10, 18, 34, 46. (I had picked these problems out, but had forgotten to post them.)
  • HW24, due Monday, April 11th, Section 13.6 Problems 8, 14, 24, 40.
  • HW25, due Friday, April 15th, Section 13.7 Problems 8, 18, 26, 30.
  • HW26, due Monday, April 18th, Section 13.7 Problems 32, 34, 40, 42.
  • HW27, due Wednesday, April 20th, Section 13.7 Problems 52, 56.
  • HW28, due Monday, April 25th, Section 13.8 Problems 40, 42.
  • Announcement for Math 311 (Spring 2016):

  • Syllabus for Math 311
  • Look up your grades for Spring 2016: (Use your student ID#)
  • First Math 311 exam with solution.
  • Second Math 311 exam with solution.
  • A first exam for Math 311
  • Another first exam for Math 311
  • A second exam for Math 311
  • Another second exam for Math 311
  • A final for Math 311
  • Another final for Math 311
  • Another final for Math 311
  • HW1, due Wednesday January 13th, Section 1.1, Problems 16, 24, 32 (you are the graphing utility), 72, 88.
  • HW2, due Friday January 15th, Section 1.2, Problems 10, 12, 14, 18, 22, 36, 64.
  • HW3, due Wednesday January 20th, Section 2.1, Problems 6, 8, 12, 16, 30, 54.
  • HW4, due Friday January 22nd, Section 2.2, Problems 10, 20, 24, 44, 66.
  • HW5, due Monday January 25th, Section 2.3, Problems 12, 22, 30, 44, 48.
  • HW6, due Wednesday January 27th, Section 2.3, Problems 54, 58 and Section 2.4 Problems 30, 60.
  • HW7, due Friday January 29th, Section 3.1, Problems 12, 18, 30, 40.
  • HW8, due Monday February 1st, Section 3.2, Problems 24, 28, 36, 50, 56.
  • HW11, due Monday February 8th, Section 3.5, Problems 6, 11, 30, 64.
  • HW12, due Friday February 12th, Section 4.2, Problems 26, 30 and Section 4.3, Problems 4, 20, 30.
  • HW13, due Friday February 19th, Section 4.4, Problems 2, 12, 16, 20, 32, 38.
  • HW14, due Wednesday February 24th, Section 4.5, Problems 81, 82. Also show: If V is a finite dimensional vector space, and L a linearly independent subset of V, then L is a subset of a basis.
  • HW15, due Friday February 26th, Section 4.6 Problems 10, 18, 50, 70.
  • HW16, due Wednesday March 2nd, Section 4.6 Problems 53, 58, 59.
  • HW17, due Monday March 7th, Section 5.1 Problems 114, 115. Show that the formula for the cosine of an angle between two vectors is equivalent to the assertion in the Theorem of Cosines.
  • HW18, due Wednesday March 9th, Section 5.3 Problems 10, 20, 32, 42. Also, using the integral from -1 to 1 as inner product, orthonormalize 1, x, x^2, x^3.
  • HW19, due Wednesday March 16th, Section 6.3 Problems 52, 62, 68, 70. Show that the inverse of a bijective linear map is linear.
  • HW20, due Monday, March 28th: Show that row equivalence, column equivalence, and their combination are in fact equivalence relations. Find the equivalence classes of the combined row and column relation.
  • HW20a, due Friday, April 1st, Show that the image of a linearly independent set under an injective linear map is again linearly independent.
  • HW21, due Monday, April 4th, Section 7.1, Problems 12, 16, 22, 28. (I know I am late posting the assignment, so Wednesday will be fine.)
  • HW22, due Wednesday April 6th, Section 7.2 Problems 6, 14, 39, 49 (Friday will be fine, we have not covered all relevant material in class yet).
  • HW23, due Monday April 11th, Show: A matrix is diagonalizable if and only if the sum of the geometric multiplicities of the eigen values equals the size of the matrix.
  • HW24, due Wednesday April 13th, Repeat the quiz: Define what it means that a map in linear, show that L(p) = p''-3p'+2p defines a linear map from V to itself. Here V is the vector space spanned by B = {e^x, xe^x, e^(2x), xe^(2x)}. Find the matrix of L with respect to the basis B. Find the kernel of L.
  • HW25, due Wednesday April 20th, Show that unitary equivalence of matrices defines an equivalence relation.
  • HW26, due Monday April 18th, Show: A complex matrix is unitarily equivalent to an upper triangular matrix.
  • HW27, due Monday April 25th, Show: If the columns of a matrix A are linearly independent, then the rank of A equals the rank of A^t A.
  • Announcement for Math 242 Sections 1 & 2 (Fall 2009):


    Announcement for Math 241 (Fall 2014):