Core Math Crossword Puzzle

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Across
  1. 2. A solution set is ___________ if its two solutions are linearly independent
  2. 6. Wolfram ___________ is a useful computational tool in Math 82
  3. 11. An undamped oscillator is an example of a ____________ system
  4. 12. We can use ________ expansion to compute the determinant of 3 x 3 matrices
  5. 14. A square matrix is __________ if and only if its determinant does not equal 0
  6. 16. The number of problem sets that we had in Math 82
  7. 18. An n x n matrix A is diagonalizable if and only if A has n linearly ___________ eigenvectors
  8. 19. The 2x2 zoology of phase portraits reminded us of the _____ emoji
  9. 21. We use the separation of variables method to solve first-order, _________ ODEs
  10. 22. A quantity that has both magnitude and direction
  11. 23. This type of circuit is mathematically similar to the mass-spring system with damping
  12. 28. An ___________ set is an orthogonal set of unit vectors
  13. 29. The instrument that Prof. Zinn-Brooks played in the Math 73 Music Video
  14. 34. The ___-Schwarz Inequality is |u・v| ≤ ||u|| ||v||
  15. 35. The dimension of a matrix’s null space
  16. 38. When using the Undetermined ___________ method to solve a forced, linear, constant-coefficient DE, we start by guessing a particular solution to the DE
  17. 39. The number of vectors in a basis for a subspace
  18. 40. An online space where we asked questions and collaborated with each other (in Math 19 & Math 82)
  19. 41. According to Prof. Jakes, ________ functions are the “peas and carrots” of DEs
  20. 42. The final step in the mathematical modeling process (based on Prof. Yong’s diagram)
  21. 43. We call two matrices row __________ if and only if they can be reduced to the same row echelon form
  22. 47. Describes a function that is injective AND surjective
  23. 50. An ____________ system of linear equations has no solution
  24. 51. “Very ______” - Prof. Karp
  25. 53. Another name for eᴬᵗ
  26. 54. The type of phase portrait that we obtain when the eigenvalues have real AND imaginary components
  27. 55. “Are you kidding, does this really ____?” - Prof. Jakes
  28. 56. The ________ Inequality is ||u + v|| ≤ ||u|| + ||v||
  29. 57. The dimension of a matrix’s row and column spaces
  30. 58. “______ is a rebellious lover.”
  31. 61. The Math 73 Music Video was a parody of “_____ the Sea” from The Little Mermaid
  32. 62. The ___________ matrix has columns that are linearly independent solutions of x’ = Ax
  33. 63. A center is a ______ equilibrium point
  34. 65. We can use elementary row operations to reduce a matrix into row _______ form
  35. 68. The last name of the other very important Darryl in Math 82
  36. 71. A technique that we use to solve nonlinear systems
  37. 74. y₁y₂’ − y₂y₁’
  38. 76. We find the ___________ points by setting x’ AND y’ equal to 0
  39. 77. In Math 19, we learned about single variable and multi variable ________
  40. 79. The Greek letter that we use to denote the fundamental matrix
  41. 80. Used as a prefix for “space”, “vector”, and “value”
  42. 83. The _____ Theorem states that an n x n real matrix is symmetric if and only if it is orthogonally diagonalizable
  43. 86. The _______-Grobman Theorem tells us when linearization is faithful
  44. 88. The _________ multiplicity of an eigenvalue is its multiplicity as a root of the characteristic equation
  45. 90. Cofactor expansion is also known as _______ expansion
  46. 91. The D in DE stands for ____________
  47. 92. Prof. Jakes always showed us a “ ___ of the day” after break
  48. 95. A fancier way of saying “onto”
  49. 96. x − x³/3! + x⁵/5! − ...
  50. 97. We can solve a non-separable, first-order, linear ODE using the ___________ factor method
  51. 98. To find the _________ of a matrix, we interchange the rows and columns of the matrix
  52. 101. Where all of our Core math courses took place
  53. 103. The ____ functions “even have their own Wikipedia page” - Prof. Yong & Prof. Jakes
  54. 104. We find the __________ by setting x’ OR y’ equal to 0
  55. 108. An online tool for graphing (useful for plotting level curves!)
  56. 113. In addition to being important in calculus, the ______ series are useful for solving DEs (especially when using the power series method)
  57. 116. An acronym for the epidemic model that we explored further in Math 82 (and were introduced to in Bio 52)
  58. 117. This type of ODE has a non-zero term that either depends only on the independent variable or is a non-zero constant
  59. 118. The first type of proof that we learned how to write (in Core math)
  60. 122. An unforced DE is also called a ___________ DE
  61. 123. An n x n matrix A is ______________ if there is a diagonal matrix D such that A is similar to D
  62. 126. The ____ of a set of matrices is the set of all linear combinations of the matrices
  63. 127. Like oscillations, ________ motion has damped and undamped DEs
  64. 128. A(BC) = (AB)C
  65. 129. The Greek letter that we use for eigenvalues and in the characteristic polynomial/equation
  66. 130. When we had questions in Math 73, we could post them on ______
  67. 131. The ______ form of a first-order, linear ODE is y’(x) + p(x)y(x) = q(x)
  68. 132. A _____ for a subspace is a set of vectors that spans the subspace and is linearly independent
Down
  1. 1. A square matrix is invertible if and only if ____ is not one of its eigenvalues
  2. 3. Our best guess to the solution of a DE (what we substitute into the DE to solve it)
  3. 4. The sum of the entries on the main diagonal of a matrix
  4. 5. Prof. Yong played us an adorable video of this animal at the end of each break
  5. 6. The password for Prof. Jakes’ (Math 82) Zoom meeting
  6. 7. The maximal interval over which a solution to a DE exists and satisfies the DE is the domain of _________
  7. 8. Our homework can either be handwritten or typed in _____
  8. 9. We learned about this type of polynomial of degree N while exploring power series
  9. 10. The professors that taught Math 82 during the summer of 2021 were Prof ____ and Prof Jakes
  10. 13. The _________ numbers are 1, 1, 2, 3, 5, 8, …
  11. 15. Statements that have been proven to be true (we reference these in the proofs that we write)
  12. 17. For a 2 x 2 matrix, we know this as “ad − bc”
  13. 20. An ________ point is the opposite of a singular point
  14. 24. A ________ is closed under addition and scalar multiplication
  15. 25. Used in Math 82 to describe a collection of phase portraits (although more commonly used to refer to the study of animals)
  16. 26. A __________ system of linear equations has at least one solution
  17. 27. The Gram-____ Process is an algorithm that we use to construct an orthogonal basis of a subspace of Rⁿ
  18. 30. A matrix of first-order partial derivatives that is often used for the linearization of nonlinear DEs
  19. 31. In this type of iteration, xₙ is an approximate solution to the DE
  20. 32. The highest number of derivatives that appears in an ODE
  21. 33. “Math 73, _______ to see”
  22. 36. A vector space that has no finite basis is _____-dimensional
  23. 37. The second step in the mathematical modeling process (based on Prof. Yong’s diagram)
  24. 44. We use the characteristic polynomial/equation to find the ___________ of a matrix
  25. 45. The type of problem that contains a DE and a boundary condition
  26. 46. The _________ multiplicity of an eigenvalue is the dimension of its corresponding eigenspace
  27. 48. The ______________ polynomial is a polynomial in λ obtained when expanding det(A − λI)
  28. 49. “The child of a theorem”
  29. 52. When x₀ is singular, we use the _________ method
  30. 59. Everyone’s favorite type of proof from Math 19 is the _______-delta proof
  31. 60. The highest rank that we reached in Prof Yong’s Spelling Bee game
  32. 61. A saddle is an ________ equilibrium point
  33. 64. When we solve a DE using power series, we find a _________ relation for the coefficients of a solution to the DE
  34. 66. The type of phase portrait that we obtain when the eigenvalues only have imaginary components
  35. 67. The last name of the author who wrote our Math 73 textbook
  36. 69. An acronym for the type of differential equations that we focused on in Math 82
  37. 70. Prof. Yong’s garage door is an example of a ______ oscillator
  38. 72. The type of problem that contains a DE and an initial condition
  39. 73. In ___ ODEs, the dependent variable and its derivatives only occur linearly
  40. 75. Prof. Jakes’ way of asking if something makes sense is saying this word twice
  41. 77. The set of all vectors that are orthogonal to a subspace is the orthogonal __________ of that subspace
  42. 78. We can use the _________ of parameters method to solve second-order, linear, forced ODEs
  43. 81. We use this website to submit our homework
  44. 82. An n x n matrix A is _______ to an n x n matrix B if there is an invertible n x n matrix P such that P⁻¹AP = B
  45. 84. Math 19, Math 73, and Math 82 are collectively known as ____ math
  46. 85. ________ and Feebas’ story taught us that “one must take risks in love”
  47. 87. A Greek letter that is commonly used with trig and polar coordinates
  48. 89. 1 − x²/2! + x⁴/4! − ...
  49. 93. In __________ ODEs, the independent variable does not appear explicitly
  50. 94. Everyone’s least favorite problem from (Math 82) Homework 4 was the _________ problem
  51. 99. ________ functions are infinitely differentiable
  52. 100. _____’s Method is a numerical tool that we used to approximate solutions to DEs
  53. 102. Matrix ______________ is not commutable
  54. 103. The corollary of ____’s Theorem says that the Wronskian of two solutions to a DE are either always zero or never zero
  55. 105. The broken furnace problem in (Math 82) Homework 6 relies on ______’s Law of Cooling
  56. 106. A square matrix is _________ if it equals its own transpose
  57. 107. Every higher order DE can be written as a ______ of first-order DEs
  58. 109. As Prof. Su often says, “You can’t ____ me from…”
  59. 110. When the determinant of A is negative, we’re in “______ city!”
  60. 111. A linear transformation that is both one-to-one and onto
  61. 112. Two vectors are __________ to each other if their dot product equals zero
  62. 114. As Prof. Orrison often says, “Change of ___________ is very important in math”
  63. 115. A ________ matrix is a square matrix whose non diagonal entries are all zeros
  64. 119. The Greek letter that we use for writing long sums
  65. 120. The solution to a forced DE consists of a homogeneous solution and a __________ solution
  66. 121. The third step in the mathematical modeling process (based on Prof. Yong’s diagram)
  67. 124. The type of phase portrait that we obtain when both eigenvalues are real and have the same sign
  68. 125. The ____ space is the subspace that contains solutions of the homogeneous linear system Ax = 0
  69. 126. A quantity that only has magnitude (no direction)