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Graduate practice chapters
641–650 of 650 matching chapters · Page 33 of 33
Clear filtersGraduate · Chapter 641
Smoothing a weak derivative · Smoothing width ε=0.9; Corner location b=-0.25
Evaluate at x=0.6. Find the smooth derivative, the sign-function representative of the weak derivative, and the pointwise smoothing error. Givens: Smoothing width ε=0.9; Corner location b=-0.25.
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Open practice chapterGraduate · Chapter 642
Critical norm scaling · Final spatial factor λ=2.25; Lebesgue exponent p=2.5
Evaluate at the current scale λ=1.75. Find the norm-scaling exponent, the Lᵖ norm ratio, and the spatial volume ratio. Givens: Final spatial factor λ=2.25; Lebesgue exponent p=2.5.
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Open practice chapterGraduate · Chapter 643
Conditional expectation by groups · First group baseline a=2.5; Second group baseline b=1
Use the completed group estimates at the animation endpoint. Find E[X|G] on both groups, E[X], and the mean squared prediction error. Givens: First group baseline a=2.5; Second group baseline b=1.
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Open practice chapterGraduate · Chapter 644
Contraction estimates · Contraction slope q=0.6; Constant b=-1.5
Use n=7 iterations. Find the fixed point, seventh iterate, and exact absolute error from the fixed point. Givens: Contraction slope q=0.6; Constant b=-1.5.
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Open practice chapterGraduate · Chapter 645
Smoothing a weak derivative · Smoothing width ε=0.95; Corner location b=0
Evaluate at x=0.6. Find the smooth derivative, the sign-function representative of the weak derivative, and the pointwise smoothing error. Givens: Smoothing width ε=0.95; Corner location b=0.
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Open practice chapterGraduate · Chapter 646
Coercivity in a finite model · First diagonal entry a=1.8; Second diagonal entry b=3
Use θ=6π/5 radians. Find vᵀAv and the sharp lower and upper bounds over all unit directions. Givens: First diagonal entry a=1.8; Second diagonal entry b=3.
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Open practice chapterGraduate · Chapter 647
Critical norm scaling · Final spatial factor λ=2.5; Lebesgue exponent p=3
Evaluate at the current scale λ=1.9. Find the norm-scaling exponent, the Lᵖ norm ratio, and the spatial volume ratio. Givens: Final spatial factor λ=2.5; Lebesgue exponent p=3.
Question · Worked solution · Animated example
Open practice chapterGraduate · Chapter 648
Conditional expectation by groups · First group baseline a=3; Second group baseline b=1.5
Use the completed group estimates at the animation endpoint. Find E[X|G] on both groups, E[X], and the mean squared prediction error. Givens: First group baseline a=3; Second group baseline b=1.5.
Question · Worked solution · Animated example
Open practice chapterGraduate · Chapter 649
Contraction estimates · Contraction slope q=0.7; Constant b=-1
Use n=7 iterations. Find the fixed point, seventh iterate, and exact absolute error from the fixed point. Givens: Contraction slope q=0.7; Constant b=-1.
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Open practice chapterGraduate · Chapter 650
Smoothing a weak derivative · Smoothing width ε=1; Corner location b=0.25
Evaluate at x=0.6. Find the smooth derivative, the sign-function representative of the weak derivative, and the pointwise smoothing error. Givens: Smoothing width ε=1; Corner location b=0.25.
Question · Worked solution · Animated example
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