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    Spreadsheet Tutorial 3 - Column Graphs, Error Bars, and Standard Error of the Mean
    Generate a column or bar graph with standard error bars.

    Keywords: Resources @ HHMI - BioInteractiveScientific ProcessStatistics and MathScientific MethodologyHigh School

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    Spreadsheet Data Analysis Tutorial Series
    This series of self-paced tutorials show how to analyze data using a spreadsheet program.

    Keywords: Resources @ HHMI - BioInteractiveScientific ProcessStatistics and MathScientific MethodologyHigh School

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    Cell Cycle and Mitosis
    This module introduces activities that allow students to walk through the cell cycle and mitotic cell division processes. As part of the activities, students learn about and apply knowledge of...

    Keywords: introductory biologyQuantitative reasoningInterdisciplinary STEMquantitative biologyinterdisciplinaryquantitative skillscell functioncell cyclemitosisCell DivisionMitotic Indexcalculating meanstumorNIQBC2. Data and GraphsC4. mathematical modelsC3. Statistical Analysisstandard errormitotic phaseinterphase

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    2019-Hu-Treinen-One-step_method_for_modelling_longitudinal_data_with_differential_equations
    This study proposes a new approach to estimate the parameters in differential equation models used to describe non-linear trajectories of longitudinal data.

    Keywords: simulationparameter estimationshoppingfittingbehaviour

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    2018-Adeniji-EtAl-InverseProblemHolling-TannerModel
    We consider the inverse problem of parameter identification of nonlinear system of ODEs for a specific case of complete information about solution of the Holling-Tanner model for finite number of...

    Keywords: goal functionabsolute error curvesinvers methodholling-Tanner model

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    2-005-LinearizeItAll-TechniqueNarrative
    Linear approximations are often used to simplify nonlinear ordinary differential equations (ODEs) for ease in analysis. The resulting linear approximation produces an ODE where closed form...

    Keywords: computationerrorTorricelli's Lawdata fittinglinear approximation

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    2-001-NumericalMethodsComparisons-TechniqueNarrative
    This material teaches the basics of numerical methods for first order differential equations by following graphical and numerical approaches. We discuss the order of accuracy of the methods and...

    Keywords: Euler's methodimproved Euler's methodRK3 methodsRK4 methodsorder of accuracyabsolute errorCPU time

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    Avian Censys Analysis
    This Swirl course uses ecological data of bird counts and habitat variables to estimate inter-observer variability and the relationship of birds with habitat variables.

    Keywords: ecologyregressionaverageserror estimates

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    Value of Mistakes
    This module familiarizes students with brain research describing our physiological response to mistakes, and how making mistakes is a useful part of learning.

    Keywords: growth mindsetmath attitudesResources @ BIOMAAPmistakesvalue of mistakes

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    Teacher Guide: Math and Statistics
    Topics include measures of average (mean, median, and mode), variability (range and standard deviation), uncertainty (standard error and 95% confidence interval), Chi-square analysis, student...

    Keywords: Resources @ HHMI - BioInteractiveStatistics and Mathteacher guide

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    The Impact of Climate Change on Sea Hare Respiration
    In this lesson, students interpret graphs of sea hare respiration. Then, students view and reflect on an interview with environmental scientist Dr. Richelle Tanner, who collected the data in the...

    Keywords: graph interpretationclimate changefmnBioGraphIrepresentation in STEMsea hare

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    9-002-GroundWaterFlow-ModelingScenario
    The goals of this project are to compare a conceptual one-dimensional groundwater flow model to observations made in a laboratory setting, and to discuss the differences.

    Keywords: sgroundwater flowDarcy's Lawheat equationaquiferhydraulic headFourier's Lawsand tank

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    2014-Vance-Eads-Sensitivity Analysis of a Three-Species Nonlinear Response Omnivory Model with Predator Stage Structure
    We investigate a three-species nonlinear response omnivory model incorporating stage structure in the top predator. The model consists of four coupled ordinary differential equations involving...

    Keywords: stage structuresensitivity analysismortalityomnivoreomnivory modelsearch rates

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    1-097-SwimmingPool-ModelingScenario
    This project involves the dynamics of chlorine concentration during regular swimming pool maintenance cycles. Students will have the opportunity to use both analytic and numerical methods.

    Keywords: concentrationcchlorinenumerical errorswimming poolhorineerreor

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    3-085-SimplePendulum-ModelingScenario
    Thestudent is asked to derive and solve a differential equation that gives the position (angle

    Keywords: Newton's Second Law of Motionpendulumkinetic energypotential energyConservation of Energytinitial conditionssmall angle approximationTaylor polynomialpercent error

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    5-080-SpaceFlightRecolonize-ModelingScenario
    This project is a combination of differential equations, multi-variable calculus, and vector calculus with use of technology to model colonization of a new planet. Students solve a system of...

    Keywords: optimizationsum of square errorsvector calculusLagrange multipliersline integrals

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    6-029-TumorGrowth-ModelingScenario
    This modeling scenario guides a student familiar with single ordinary differential equation (ODE) models towards the development of a more complex system of two ODEs for describing the evolution of...

    Keywords: Pop_Growth Pilotlogisticcomparmenttumorsynthetic datasum of squares error

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    Adapted Value of Mistakes
    This module is adapted from BIOMAAP materials on the value of mistakes and application of growth mindset in a microbiology lab.

    Keywords: growth mindsetmath attitudesResources @ BIOMAAPmistakesvalue of mistakes

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    Phenotypic plasticity and predation
    Students predict changes to tadpole morphology and coloration after considering characteristics of the predator species and the prey themselves then test their own hypotheses (typically with...

    Keywords: RExcelimage analysisgraphingt-testsfrequency histogramsdata visualizationANOVAhypothesis formulationpredator-prey interactionsphenotypic plasticity

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    1999-Khorasheh-Ahmadi-Gerayeli-Application of Direct Search Optimization for Pharmacokinetic Parameter Estimation
    For simple pharmacokinetic compartmental models, analytical solution to the governing differential equations provide a mean to evaluate the associated rate constants. Such methods, however, can not...

    Keywords: sum of square errorsleast squarespharmacokineticslineteicscompartmental modelsdirect search

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