User contributions for Rice
From Rice Wiki
22 May 2024
- 15:0015:00, 22 May 2024 diff hist +105 N Method of undetermined coefficients Created page with "Category:Differential Equations Glorified name for guess and find coefficients of second order ODEs." current
- 05:1005:10, 22 May 2024 diff hist +96 Second order linear ODE →Constant coefficient, homogeneous
- 05:0905:09, 22 May 2024 diff hist +493 N Reduction of order Created page with "Category:Differential Equations The '''reduction of order''' technique allows one to find a second solution to a differential equation when one solution is already found. Take a linear second order constant coefficient homogeneous ODE (see Second order linear ODE) with one repeated-root solution. Add u(t) as follows <math> y(t)=u(t)e^{2t} </math> Substituting into the ODE, and you get <math> u'' = 0 </math> Integrating up, and you get u in the form <math>..." current
- 00:2300:23, 22 May 2024 diff hist +91 Euler's formula No edit summary current
- 00:2100:21, 22 May 2024 diff hist +321 Second order linear ODE →Constant coefficient, homogeneous
21 May 2024
- 23:5023:50, 21 May 2024 diff hist +61 N Euler's formula Created page with "Category:Mathematics <math> e^{it}=\cos t+i\sin t </math>"
- 23:4923:49, 21 May 2024 diff hist +250 Second order linear ODE →Solutions
- 23:3323:33, 21 May 2024 diff hist +84 Second order linear ODE →Fundamental set of solutions
- 23:0423:04, 21 May 2024 diff hist +146 General existence theorem No edit summary
- 22:5722:57, 21 May 2024 diff hist +36 General existence theorem No edit summary
- 22:5722:57, 21 May 2024 diff hist +227 N General existence theorem Created page with "Every Second order linear homogeneous ODE with continuous coefficients has a fundamental set of solutions. This is proven by handpicking a set of initial conditions such that the Wronskian is 1."
- 22:5322:53, 21 May 2024 diff hist +167 Second order linear ODE →Constant coefficient, homogeneous
- 22:5022:50, 21 May 2024 diff hist +331 Wronskian No edit summary
- 22:2822:28, 21 May 2024 diff hist +123 Wronskian No edit summary
- 22:1722:17, 21 May 2024 diff hist +103 Second order linear ODE →Constant coefficient, homogeneous
- 22:0022:00, 21 May 2024 diff hist −352 Abel's theorem No edit summary
20 May 2024
- 15:4615:46, 20 May 2024 diff hist +75 ISA →RISC current
- 15:3415:34, 20 May 2024 diff hist +36 ISA →RISC
- 15:3415:34, 20 May 2024 diff hist +266 ISA →CISC
- 15:2915:29, 20 May 2024 diff hist +236 ISA →Accumulator
- 15:2515:25, 20 May 2024 diff hist +153 ISA →Stack
- 15:2215:22, 20 May 2024 diff hist +225 N ISA Created page with "Category:Computer Architecture '''Instruction set architecture (ISA)''' = Stack = Zero address architecture, where operands are on stack inside CPU. It has the downside of being slow due to DRAM being slower than SRAM."
- 15:1115:11, 20 May 2024 diff hist +123 N Addressing mode Created page with "Category:Computer Architecture Immediate, direct, indirect, register, register direct, register indexed. Review later." current
19 May 2024
- 19:4919:49, 19 May 2024 diff hist +331 N Wronskian Created page with "Category:Differential Equations The '''Wronskian''' of n equations is the determinant of the following matrix <math> \begin{vmatrix} f_1(x) & f_2(x) & \cdots & f_n(x) \\ f_1'(x) & f_2'(x) & \cdots & f_n'(x) \\ \vdots & \vdots & \ddots & \vdots \\ f_1^{(n-1)}(x) & f_2^{(n-1)}(x) & \cdots & f_n^{(n-1)}(x) \end{vmatrix} </math>"
- 19:0519:05, 19 May 2024 diff hist +414 N Abel's theorem Created page with "Category:Differential Equations '''Abel's theorem''' in linear differential equations states that for any second order linear homogeneous ODE, <math> y'' + p(t)y'+q(t)y=0 </math> Given <math>y_1, y_2</math> as particular solutions to the ODE, then the Wronskian of the two solutions can be described in terms of the ODE's coefficients as <math> W(t)=Ce^{\int p(x)dx} </math>"
- 18:5918:59, 19 May 2024 diff hist −96 Second order linear ODE No edit summary
18 May 2024
- 21:0621:06, 18 May 2024 diff hist +25 Hyperparameter optimization →Other techniques current
- 21:0621:06, 18 May 2024 diff hist +585 N Hyperparameter optimization Created page with "Category:Machine Learning Aspects of an ML model is controlled by hyperparameters. '''Hyperparameter optimization''' is an iterative process that attempts to find the best hyperparameters for a given model. = Grid search = '''Grid search''' (aka. grid search cross validation) computes all possible combinations of hyperparameters based on your input (possible values for each hyperparameter). The model is then trained and validated, and the best performance resul..."
- 20:5720:57, 18 May 2024 diff hist +158 Dropout regularization No edit summary current
- 20:2420:24, 18 May 2024 diff hist 0 Dropout regularization No edit summary
- 20:2320:23, 18 May 2024 diff hist +411 N Dropout regularization Created page with "Category:Machine Learning '''Dropout regularization''' behaves quite differently than other regularization techniques. Instead of penalizing large weights in the loss function, it adds a layer that randomly ignores neurons at every full-pass. Dropout regularization is controlled by hyperparameter '''dropout rate'''. For example, a dropout rate of 0.2 means that 20% of input neurons will be ignored."
- 20:2020:20, 18 May 2024 diff hist +72 Regularization →Techniques current
- 19:5919:59, 18 May 2024 diff hist +2 Ridge regression No edit summary current
- 19:5819:58, 18 May 2024 diff hist +30 N Ridge Regression Rice moved page Ridge Regression to Ridge regression current Tag: New redirect
- 19:5819:58, 18 May 2024 diff hist 0 m Ridge regression Rice moved page Ridge Regression to Ridge regression
- 19:5719:57, 18 May 2024 diff hist +738 Regularization Removed redirect to Lasso regression Tag: Removed redirect
- 19:4919:49, 18 May 2024 diff hist +39 N Overfit Redirected page to Curve fitting#Overfitting current Tag: New redirect
- 19:4819:48, 18 May 2024 diff hist +27 N Curve Fitting Rice moved page Curve Fitting to Curve fitting current Tag: New redirect
- 19:4819:48, 18 May 2024 diff hist 0 m Curve fitting Rice moved page Curve Fitting to Curve fitting current
- 19:4719:47, 18 May 2024 diff hist +30 N Regularization Rice moved page Regularization to Lasso regression Tag: New redirect
- 19:4719:47, 18 May 2024 diff hist 0 m Lasso regression Rice moved page Regularization to Lasso regression current
- 00:3400:34, 18 May 2024 diff hist +680 N Superposition principle Created page with "Category:Differential Equations The '''superposition principle''' is actually a broad category of principles that widely apply to homogeneous linear stuff. I'll discuss this in the context of differential equations. Consider a linear operator on functions, L <math> L[y]=y''+py'+qy </math> It can be (pretty easily) proven that <math> L[y_1+y_2]=L[y_1]+L[y_2] </math> and <math> L[cy]=cL[y] </math> Then, given two homogeneous solutions <math> L[y_1]=L[y_2]=..." current
- 00:2300:23, 18 May 2024 diff hist +489 Existence-uniqueness No edit summary current
- 00:1100:11, 18 May 2024 diff hist +87 Initial value problem No edit summary current
- 00:0900:09, 18 May 2024 diff hist +102 Second order linear ODE →General solution
- 00:0800:08, 18 May 2024 diff hist +103 Initial value problem No edit summary
17 May 2024
- 21:2621:26, 17 May 2024 diff hist +259 N Initial value problem Created page with "Category:Differential Equations The '''initial value problem (IVP)''' is a very common class of problem in Differential Equations. As the name suggests, in an IVP, an initial value is given along with a differential equation. <math> y(t_0)= y_0 </math>"
- 21:2421:24, 17 May 2024 diff hist +34 N IVP Redirected page to Initial value problem current Tag: New redirect
- 21:2421:24, 17 May 2024 diff hist +813 N Numerical solutions of differential equations Created page with "Category:Differential Equations *Note that this is not tested in MAT22B Numerical solutions of IVPs involve using taylor series and the definition of derivatives: <math> \frac{dy}{dx}(x=x_0) = \lim_{h\rightarrow 0}\frac{y(x_0+h)-y(x_0)}{h} </math> Since we know one initial value of the function, we can use the above property to iteratively approximate the surrounding values with a small step (h). = Classification = Numerical solutions are evaluated by th..." current
- 21:0521:05, 17 May 2024 diff hist +90 Existence-uniqueness No edit summary
