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Differential Equations

26 ready-made sets. Every one writes a new problem with new numbers each time you open it, scores each part of your answer separately, and shows the full worked solution.

1.1Introduction to ODEs & Direction FieldsRead an autonomous equation without solving it: equilibria, a sign chart, stability, and slopes straight off the direction field.1.2Solutions to Some ODEsThe constant-coefficient first-order template, solved once as a constant plus an exponential, and what the sign of the rate decides about the long run.1.3Classification of Differential EquationsOrder, linear versus nonlinear, and the substitutions that turn a proposed solution into a characteristic polynomial.2.1First-Order Linear EquationsIntegrating factors in the right order: standard form first, then the factor, then the product rule, then one integration.2.2Separable EquationsSeparate, integrate, apply the initial condition early, pick the right branch, and state the interval of validity.2.3Modeling with First-Order ODEsMixing tanks, Newton's law of cooling and falling bodies with drag — rate in minus rate out before any calculus.2.4Existence & Uniqueness (first order)When the theorem guarantees a unique solution near a point, and what its silence does and does not mean.2.5Population DynamicsLogistic growth, threshold models and constant harvesting, all read off the shape of one parabola.2.7Euler MethodsStepping along the direction field by hand, the improved Euler correction, and why global error is one order worse than local.3.1Linear Homogeneous 2nd-Order ODEsCharacteristic roots, real and distinct, with initial conditions — and reading long-run behavior off the largest root.3.2Linear Independence & the WronskianWronskians, fundamental sets, Abel's theorem, and finding the largest interval on which a solution is guaranteed.3.3Complex RootsNegative discriminant, Euler's formula, and the split between the decay rate and the frequency.3.4Repeated RootsOne root, two solutions — where the extra factor of t comes from and how it changes the initial-condition algebra.3.5Method of Undetermined CoefficientsPick the right trial form, repair it when it collides with the homogeneous solution, then solve for the constants.3.7Free Mechanical VibrationsMass, spring and damper: natural frequency from a hanging stretch, amplitude and phase, and the three damping cases.3.8Forced Mechanical VibrationsTransient versus steady state, the amplitude formula, beats, and why resonance needs zero damping.6.1Laplace TransformsWorking the transform table instead of the definition, plus the first shifting theorem.6.2Solving IVPs with Laplace TransformsTransform the IVP, split with partial fractions or complete the square, and read the answer off the table.6.3Step FunctionsThe unit step as a switch: writing piecewise forcing in step form, and the second shifting theorem both ways.6.4Discontinuous Forcing FunctionsIVPs whose forcing switches on or off, solved in one pass instead of interval by interval.7.1Linear Systems of ODEsTurning a high-order equation into a first-order system, and reading the companion matrix back again.7.2Linear Algebra ReviewDeterminants, invertibility and independence — the six equivalent statements that eigenvalue work keeps using.7.3Eigenvalues and EigenvectorsTrace and determinant to the characteristic polynomial, and what the sign pattern says about the phase portrait.7.5Homogeneous Linear SystemsEigenvalues and eigenvectors to the general solution, initial conditions, and what the phase portrait looks like.7.6Complex EigenvaluesComplex eigenvalues, real solutions from Euler's formula, and the spiral sink / source / centre split.7.7Repeated EigenvaluesOne eigenvalue, one eigenvector: generalised eigenvectors and the improper node.

General Biology

15 sets, 267 cards, built to a real university syllabus. Each card is scheduled on its own, so the ones you keep missing come back sooner than the ones you know.

1.1Life, Domains and the CellProperties of life, levels of organisation, the three domains, prokaryotic vs eukaryotic cells, and why cells stay small.1.2Atoms, Bonds and the Chemistry of WaterAtomic structure, isotopes, the four bond types, electronegativity, the emergent properties of water, and pH with buffers.1.3The Four MacromoleculesDehydration synthesis and hydrolysis, then carbohydrates, lipids, proteins and nucleic acids, their monomers, bonds and functions.1.4Membrane Structure and TransportThe fluid mosaic model, membrane fluidity and proteins, then diffusion, osmosis, tonicity, active transport and bulk transport.1.5Organelles and the Endomembrane SystemEukaryotic organelles, the endomembrane pathway in order, the cytoskeleton, cell surfaces, and the endosymbiotic theory.1.6Cell Communication and Cell JunctionsHow cells send, receive and act on chemical signals, and the junctions that hold tissues together and let neighbours talk.2.1DNA Structure and ReplicationThe experiments that identified DNA, the chemistry of the double helix, and the enzymes that copy it semiconservatively.2.2Transcription, Translation and the Genetic CodeFrom gene to protein: making RNA, processing it, reading codons and building a polypeptide on the ribosome.2.3Mutations, Gene Regulation and BiotechnologyHow DNA sequence changes affect proteins, how cells switch genes on and off, and the lab tools built on both.2.4The Cell Cycle, Mitosis and MeiosisChromosome vocabulary, the phases of the cell cycle, how mitosis and meiosis differ, and where variation and aneuploidy come from.2.5Mendelian Genetics and Inheritance PatternsSegregation, independent assortment, crosses and ratios, then the extensions: codominance, epistasis, sex linkage, linkage and pedigrees.3.1Energy, Enzymes and ATPThermodynamics as biologists use it, free energy and coupling, ATP as the energy currency, and how enzymes and inhibitors work.3.2Cellular Respiration and FermentationRedox and electron carriers, the four stages with their locations and yields, chemiosmosis and ATP synthase, and fermentation.3.3PhotosynthesisChloroplast structure and pigments, the light reactions, Calvin cycle stoichiometry, and the C3, C4 and CAM strategies.3.4VirusesViral structure and genomes, lytic and lysogenic cycles, animal virus entry and exit, retroviruses and HIV, prions, vaccines and spillover.

Psychology

15 sets, 270 cards, built to a real university syllabus. Each card is scheduled on its own, so the ones you keep missing come back sooner than the ones you know.

1.1The Science of PsychologyWhat psychology is, its four goals, the historical schools, the seven modern perspectives, the subfields, and why it is a science.1.2Research Methods and StatisticsScientific method, descriptive designs, sampling, correlation, experiments, descriptive and inferential statistics, and research ethics.1.3Biology and BehaviourNeurons, synapses and transmitters, the nervous system divisions, brain structure and imaging, hormones and behaviour genetics.1.4Sensation and PerceptionThresholds and adaptation, vision and hearing, the other senses, Gestalt organisation, depth cues, constancies and what illusions reveal.2.1Consciousness, Sleep and DrugsAttention and awareness, circadian rhythms, the sleep stages and disorders, theories of dreaming, hypnosis, and the three drug classes.2.2LearningClassical and operant conditioning, reinforcement schedules, cognitive influences on learning, and observational learning.2.3MemoryEncoding, storage and retrieval, the stages and types of memory, why we forget, and how memory reconstructs rather than replays.3.1Thinking, Language and IntelligenceConcepts and problem solving, the heuristics that bias judgement, how language develops, and what intelligence tests do and do not measure.3.2Motivation and EmotionTheories of motivation, hunger and belonging, the four classic theories of emotion, and what actually predicts happiness.3.3Lifespan DevelopmentDevelopment from conception to death: Piaget and Vygotsky, attachment and parenting, Erikson and Kohlberg, and what changes with age.3.4PersonalityPsychodynamic, humanistic, trait and social-cognitive accounts of personality, the tests built on them, and the evidence for each.4.1Social PsychologyAttribution, attitudes, conformity and obedience, group processes, prejudice, aggression, attraction, helping and conflict resolution.4.2Stress and Health PsychologyAppraisal, stressors, the physiology of stress, stress and disease, coping, perceived control and the evidence on managing stress.4.3Psychological DisordersDefining and classifying disorder, and the diagnostic features, causes and course of the major categories an introductory survey covers.4.4TherapyPsychodynamic, humanistic, behavioural and cognitive therapies, how outcomes are evaluated, and the biomedical treatments alongside them.

Other subjects

More ready-made packs are being built. Until then, any subject works the same way — upload what your course gave you and the agent writes the set from it.