Homework Math240-002: DONAGI

Assignment #1: Due in recitation, week of January 19.

  • (8.1) Matrix Algebra 3,12,13,15,18,23,28,33,36,38
  • (8.2) Systems of Linear Algebraic Equations 5,7,9,20

    Assignment #2: Due in recitation, week of January 26.

  • (8.3) Rank of a Matrix 1,5,9,13,16,17
  • Old exams: Fall 2006 No. 2, Fall 2007 No. II. Fall 2005 Nos. 9, 10(a), 10(b).

    Assignment #3: Due in recitation, week of Feb 2.

  • (8.4) Determinants 3,7,21,29
  • (8.5) Properties of Determinants 4,7,12,15,21,31,33,37,39
  • (8.6) Inverse of a Matrix 1,5,9,11,21,25,27,49,51

    Assignment #4: Due in recitation, week of Feb 9.

    Part I: Do the core problems:

  • (8.8) The Eigenvalue Problem 1,6,7,15,21,26
  • (8.9) Powers of matrices 3,7,9,14,17
  • (8.12) Diagonalization 5,15,19,37

    Part II: Mock midterm exams.

    The material for these mock tests is taken from the "Math 240 old final exams" . Please time yourself: you should be able to complete the first two tests in 25 minutes each, including some time for checking your answers. The third test should take 35 minutes. In other words, you have 5 minutes per problem! It is crucial that you work fast. If it takes you longer than 5 minutes per problem, you must practice working faster. Use the first test to help you identify topics with which you need more practice or some help. Make sure you work on these topics before attempting the second test, and again before attempting the third test. Please work on these tests as soon as you can, so that you will be able to get help if needed during office hours.

  • Mock test #1: Spring 07: 1,2,3,8,9
  • Mock test #2: Fall 06: 1,2,3,4
  • Mock test #3: Fall 07: 2,4,5,11 and Spring 08: 1,3,4

    Assignment #5: Due in recitation, week of Feb 16.

  • (3.1) Preliminary Theory: Linear Equations 1,3,7,15,18,22, 31,33,36
  • (extra credit) For which positive integers d and n is there a real n x n matrix A whose d-th power equals -I? (To get the extra credit you need to give a full justification of your answer.)
  • (extra credit) Let v be a non zero row vector, v^T its transpose, and consider the n x n matrix A:=v^T v. What is the rank of A? What are its eigenvalues? Is it diagonalizable? Describe a maximal linearly independent set of eigenvectors for A. (To get the extra credit you need to give a full justification of your answer.)

    Assignment #6: Due in recitation, week of Feb 23.

  • (3.2) Reduction of order 1,3,11,14
  • (3.3) Homogeneous Linear Equations with Constant Coefficients 3,15,37
  • (10.1) Preliminary Theory 5,7,13,19,25
  • (10.2) Homogeneous Linear Systems 5,11,21
  • (10.2) Homogeneous Linear Systems 16 (extra credit)

    Assignment #6: Due in recitation, week of Mar 2.

  • (3.4) Undetermined Coefficients 1,6,17,25,27,33
  • (3.8) Linear Models: Initial Value Problems 3,7,17,25,31
  • (10.3) Solutions by Diagonalization 1,5,10
  • (10.4.1) Undetermined Coefficients 3,6,10
  • Extra credit: (3.8) problem 43
  • Extra credit: find a formula for the determinant of the n by n matrix A with entries a_{i,j}=(x_i)^(j-1). Give a clear and convincing explanation for your formula. When does it vanish?

    Assignment #7:

    Part I: Due in recitation, week of Mar 16. Do the core problems:

  • (3.6) Cauchy-Euler Equation 1,9,11,15,27
  • (5.1) Solutions about Ordinary Points 3,9,11,15,21,31
  • (5.2) Solutions about Singular Points 5,11,15,21,27,33
  • (5.3) Special Functions 1,5,9,11,15,18,25,33,44

    Part II: Mock midterm exam. (Will not be collected.)

    The material for this mock test is taken from the "Math 240 old final exams" . This test is for your benefit, and will not be collected or graded. Please complete it by Wednesday, March 18. We will go over it in class on March 19. As previously, please time yourself: you should be able to complete this 11-problem test in an hour, including some time for checking your answers. In other words, you have 5 minutes per problem. It is crucial that you work fast. If it takes you longer than 5 minutes per problem, you must practice working faster. You can get such prctice with the old exams included in next week's assignment. (These _WILL_ be collected and graded.)

  • Mock test: Fall 07: 1,3,9,14 and Spring 08: 9-15.

    Assignment #8: Due in recitation, week of Mar 23.

    The material for these mock tests is taken from the "Math 240 old final exams" . Please time yourself: you should be able to complete the first test in 50 minutes, including some time for checking your answers. The second test should take 80 minutes. In other words, you have 5 minutes per problem. It is crucial that you work fast. If it takes you longer than 5 minutes per problem, you must practice working faster. Use the first test to help you identify topics with which you need more practice or some help. Make sure you work on these topics before attempting the second test. Please work on these tests as soon as you can, so that you will be able to get help if needed during office hours.

  • Mock test #1: Fall 06: 9,10,13-15; and Spring 07: 5,6,14,15. (9 problems, 50 minutes.)
  • Mock test #2: Fall 05: 6-7,13,14, free response 2,4; and Spring 06: 2-4,7-9,13. (13 problems, 75 minutes.)

    Assignment #9: Due in recitation, week of Mar 30.

    This week's assignment consists of review of material from Math 114. We will spend a few minutes going over it in class on Tuesday, but you should be able to do the assignment on your own right away. Charlie will go over it again in recitation if necessary.

  • (9.1) Vector Functions 3,7,13,15,17,23, 25,29,33,39
  • (9.4) Partial Derivatives 13,27,33,39,49, (review) 53
  • (9.5) Directional Derivatives 1,11,16,23,27,31 (review)
  • (9.6) Tangent Planes and Normal Lines(review) 1,15,25,30

    Assignment #10: Due in recitation, week of Apr 6.

  • (9.7) Divergence and Curl 1,9,13,27,33,39
  • (9.8) Line Integrals(review) 1,2,7,19,21,23,28
  • (9.9) Independence of Path(review) 1,3,5,7,10,21,25,27
  • (9.10)Double Integrals(review) 1,11,13,23,29,35,40

    Assignment #11: Due in recitation, week of Apr 13.

  • (9.11)Double Integrals in Polar Coordinates(review) 1,5,8,20,25,28,32
  • (9.12)Green’s theorem(review) 1,5,10,13,18,21,24,26,29
  • (9.13)Surface integrals 1,5,11,19,27,33,37
  • (9.14)Stokes’ Theorem 1,3,5,11,15,17
  • (9.15)Triple Integrals (review) 1,4,7,9,12,13,15,19,21

    Assignment #12: Due in recitation, week of Apr 20.

  • (9.16)Divergence Theorem 3,7,11,15,17
  • (9.17)Change of Variables in Multiple Integrals (review) 1,3,5,11,17,25
  • Mock test #1: F08 #4-7, F07 #6,8,10,13,15.
  • Mock test #2: S08 #5-8, S07 #4, 10-13.

    Assignment #13: This is the last assignment for the year. It consists of four mock tests. Please try to work them out under realistic exam-type time limits: 120 minutes per test. The deadline is extended through Friday, May 1.

  • Mock test #1: Fall 2002
  • Mock test #2: Fall 2004
  • Mock test #3: Spring 2005
  • Mock test #4: Fall 2008

    To help you prepare for the final exam, you may optionally want to also try some of the remaining old tests:

  • Mock test #5: Spring 2003
  • Mock test #6: Fall 2003
  • Mock test #7: Spring 2004