Core Math Crossword Puzzle

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Across

7. Cofactor expansion is also known as _______ expansion
10. A ________ matrix is a square matrix whose non diagonal entries are all zeros
12. ________ and Feebas’ story taught us that “one must take risks in love”
13. A(BC) = (AB)C
14. Like oscillations, ________ motion has damped and undamped DEs
18. The _____ Theorem states that an n x n real matrix is symmetric if and only if it is orthogonally diagonalizable
19. Describes a function that is injective AND surjective
20. As Prof. Su often says, “You can’t ____ me from…”
22. A fancier way of saying “onto”
25. A linear transformation that is both one-to-one and onto
28. “Are you kidding, does this really ____?” - Prof. Jakes
31. A center is a ______ equilibrium point
32. The set of all vectors that are orthogonal to a subspace is the orthogonal __________ of that subspace
33. Where all of our Core math courses took place
34. The type of problem that contains a DE and a boundary condition
36. The _________ multiplicity of an eigenvalue is the dimension of its corresponding eigenspace
39. In Math 19, we learned about single variable and multi variable ________
42. According to Prof. Jakes, ________ functions are the “peas and carrots” of DEs
43. The ___-Schwarz Inequality is |u・v| ≤ ||u|| ||v||
44. In __________ ODEs, the independent variable does not appear explicitly
45. An online space where we asked questions and collaborated with each other (in Math 19 & Math 82)
48. The type of phase portrait that we obtain when the eigenvalues have real AND imaginary components
50. The ______________ polynomial is a polynomial in λ obtained when expanding det(A − λI)
53. Every higher order DE can be written as a ______ of first-order DEs
55. Two vectors are __________ to each other if their dot product equals zero
56. The first type of proof that we learned how to write (in Core math)
67. The ____ of a set of matrices is the set of all linear combinations of the matrices
68. We use this website to submit our homework
70. An ___________ set is an orthogonal set of unit vectors
72. The last name of the other very important Darryl in Math 82
73. Wolfram ___________ is a useful computational tool in Math 82
75. “The child of a theorem”
76. The ____ functions “even have their own Wikipedia page” - Prof. Yong & Prof. Jakes
77. A quantity that has both magnitude and direction
78. The ______ form of a first-order, linear ODE is y’(x) + p(x)y(x) = q(x)
83. The type of phase portrait that we obtain when the eigenvalues only have imaginary components
84. “Math 73, _______ to see”
85. A ________ is closed under addition and scalar multiplication
87. 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
90. The number of problem sets that we had in Math 82
91. _____’s Method is a numerical tool that we used to approximate solutions to DEs
92. The highest rank that we reached in Prof Yong’s Spelling Bee game
93. We can solve a non-separable, first-order, linear ODE using the ___________ factor method
95. The sum of the entries on the main diagonal of a matrix
97. The type of phase portrait that we obtain when both eigenvalues are real and have the same sign
99. In ___ ODEs, the dependent variable and its derivatives only occur linearly
102. “______ is a rebellious lover.”
103. Prof. Jakes’ way of asking if something makes sense is saying this word twice
104. Everyone’s least favorite problem from (Math 82) Homework 4 was the _________ problem
107. The Greek letter that we use to denote the fundamental matrix
108. An unforced DE is also called a ___________ DE
110. The highest number of derivatives that appears in an ODE
113. y₁y₂’ − y₂y₁’
115. The professors that taught Math 82 during the summer of 2021 were Prof ____ and Prof Jakes
116. We call two matrices row __________ if and only if they can be reduced to the same row echelon form
119. The instrument that Prof. Zinn-Brooks played in the Math 73 Music Video
120. This type of ODE has a non-zero term that either depends only on the independent variable or is a non-zero constant
122. Prof. Yong played us an adorable video of this animal at the end of each break
125. A saddle is an ________ equilibrium point
127. An undamped oscillator is an example of a ____________ system
128. The ____ space is the subspace that contains solutions of the homogeneous linear system Ax = 0
129. An n x n matrix A is ______________ if there is a diagonal matrix D such that A is similar to D
130. When x₀ is singular, we use the _________ method
131. The Greek letter that we use for eigenvalues and in the characteristic polynomial/equation
132. The Greek letter that we use for writing long sums
133. A square matrix is __________ if and only if its determinant does not equal 0
134. An ____________ system of linear equations has no solution

Down

1. In this type of iteration, xₙ is an approximate solution to the DE
2. The _______-Grobman Theorem tells us when linearization is faithful
3. An online tool for graphing (useful for plotting level curves!)
4. This type of circuit is mathematically similar to the mass-spring system with damping
5. Math 19, Math 73, and Math 82 are collectively known as ____ math
6. Prof. Yong’s garage door is an example of a ______ oscillator
8. A technique that we use to solve nonlinear systems
9. The number of vectors in a basis for a subspace
11. ________ functions are infinitely differentiable
12. Matrix ______________ is not commutable
15. The Math 73 Music Video was a parody of “_____ the Sea” from The Little Mermaid
16. x − x³/3! + x⁵/5! − ...
17. A Greek letter that is commonly used with trig and polar coordinates
21. The type of problem that contains a DE and an initial condition
23. In addition to being important in calculus, the ______ series are useful for solving DEs (especially when using the power series method)
24. As Prof. Orrison often says, “Change of ___________ is very important in math”
26. The password for Prof. Jakes’ (Math 82) Zoom meeting
27. The corollary of ____’s Theorem says that the Wronskian of two solutions to a DE are either always zero or never zero
29. An ________ point is the opposite of a singular point
30. We can use elementary row operations to reduce a matrix into row _______ form
35. We find the __________ by setting x’ OR y’ equal to 0
37. 1 − x²/2! + x⁴/4! − ...
38. The _________ multiplicity of an eigenvalue is its multiplicity as a root of the characteristic equation
40. The Gram-____ Process is an algorithm that we use to construct an orthogonal basis of a subspace of Rⁿ
41. We can use ________ expansion to compute the determinant of 3 x 3 matrices
46. Used in Math 82 to describe a collection of phase portraits (although more commonly used to refer to the study of animals)
47. A _____ for a subspace is a set of vectors that spans the subspace and is linearly independent
49. The solution to a forced DE consists of a homogeneous solution and a __________ solution
51. A vector space that has no finite basis is _____-dimensional
52. To find the _________ of a matrix, we interchange the rows and columns of the matrix
54. We use the characteristic polynomial/equation to find the ___________ of a matrix
57. A matrix of first-order partial derivatives that is often used for the linearization of nonlinear DEs
58. We learned about this type of polynomial of degree N while exploring power series
59. The ___________ matrix has columns that are linearly independent solutions of x’ = Ax
60. The _________ numbers are 1, 1, 2, 3, 5, 8, …
61. A square matrix is _________ if it equals its own transpose
62. The last name of the author who wrote our Math 73 textbook
63. Another name for eᴬᵗ
64. Prof. Jakes always showed us a “ ___ of the day” after break
65. “Very ______” - Prof. Karp
66. Our best guess to the solution of a DE (what we substitute into the DE to solve it)
67. When the determinant of A is negative, we’re in “______ city!”
69. We use the separation of variables method to solve first-order, _________ ODEs
71. An acronym for the type of differential equations that we focused on in Math 82
74. Our homework can either be handwritten or typed in _____
79. The ________ Inequality is ||u + v|| ≤ ||u|| + ||v||
80. A __________ system of linear equations has at least one solution
81. For a 2 x 2 matrix, we know this as “ad − bc”
82. The dimension of a matrix’s null space
86. An acronym for the epidemic model that we explored further in Math 82 (and were introduced to in Bio 52)
88. When we solve a DE using power series, we find a _________ relation for the coefficients of a solution to the DE
89. When we had questions in Math 73, we could post them on ______
94. The second step in the mathematical modeling process (based on Prof. Yong’s diagram)
96. The broken furnace problem in (Math 82) Homework 6 relies on ______’s Law of Cooling
98. The D in DE stands for ____________
100. When using the Undetermined ___________ method to solve a forced, linear, constant-coefficient DE, we start by guessing a particular solution to the DE
101. A square matrix is invertible if and only if ____ is not one of its eigenvalues
103. The 2x2 zoology of phase portraits reminded us of the _____ emoji
105. We find the ___________ points by setting x’ AND y’ equal to 0
106. A solution set is ___________ if its two solutions are linearly independent
109. A quantity that only has magnitude (no direction)
111. The dimension of a matrix’s row and column spaces
112. An n x n matrix A is diagonalizable if and only if A has n linearly ___________ eigenvectors
114. The maximal interval over which a solution to a DE exists and satisfies the DE is the domain of _________
117. The final step in the mathematical modeling process (based on Prof. Yong’s diagram)
118. Statements that have been proven to be true (we reference these in the proofs that we write)
121. We can use the _________ of parameters method to solve second-order, linear, forced ODEs
123. The third step in the mathematical modeling process (based on Prof. Yong’s diagram)
124. Everyone’s favorite type of proof from Math 19 is the _______-delta proof
126. Used as a prefix for “space”, “vector”, and “value”