Dažu funkciju definēšana, lietojot diferenciālvienādojumus

6533b857fe1ef96bd12b48c9

RESEARCH PRODUCT

Dažu funkciju definēšana, lietojot diferenciālvienādojumus

Aleksejs Dovgaļuks

subject

hiperboliskais sinuss un kosinuss eksponentfunkcija Pedagoģija teorēma par lineāra homogēna diferenciālvienādojuma atrisinājuma eksistenci un vienīgumu Košī problēma trigonometriskais sinuss un kosinuss

description

Darbā ir apūkoti divi paņēmieni funkciju definēšanai: paņēmiens, kas balstās uz teorēmu par lineāra homogēna diferenciālvienādojuma atrisinājuma eksistenci un vienīgumu (Košī uzdevuma atrisinājums) un klasiskais vidusskolas vai matemātiskās analīzes paņēmiens. Darbā tiek aplūkotas sekojošas funkcijas: eksponentfunkcija, hiperboliskais sinuss un kosinuss un trigonometriskais sinuss un kosinuss. Liela uzmanība veltīta šo funkciju svarīgākajām īpašībām un formulu pierādījumiem ar abu paņēmienu palīdzību. Rezultātā jaunais paņēmiens ar diferenciālvienādojumu palīdzību tiek uzskatīts par salīdzinoši viegli uztveramu un izmantojamu, kuru var pielietot zinot tikai vienu teorēmu no diferenciālvienādojumu teorijas. Atslēgas vārdi: teorēma par lineāra homogēna diferenciālvienādojuma atrisinājuma eksistenci un vienīgumu, Košī problēma, eksponentfunkcija, hiperboliskais sinuss un kosinuss un trigonometriskais sinuss un kosinuss.

year	journal	country	edition	language
2022-01-01

https://dspace.lu.lv/dspace/handle/7/59971

PEPhysical Sciences and Engineering
- PE2Fundamental Constituents of Matter
  - PE2_1Theory of fundamental interactions
  - PE2_2 Phenomenology of fundamental interactions
  - PE2_3Experimental particle physics with accelerators
  - PE2_4Experimental particle physics without accelerators
  - PE2_6Nuclear, hadron and heavy ion physics
  - PE2_8Gas and plasma physics
  - PE2_5Classical and quantum physics of gravitational interactions
  - PE2_7Nuclear and particle astrophysics
  - PE2_9 Electromagnetism
  - PE2_10Atomic, molecular physics
  - PE2_11Ultra-cold atoms and molecules
  - PE2_18Equilibrium and non-equilibrium statistical mechanics: steady states and dynamics
  - PE2_14Lasers, ultra-short lasers and laser physics
  - PE2_17Metrology and measurement
  - PE2_16Non-linear physics
  - PE2_12Optics, non-linear optics and nano-optics
  - PE2_13Quantum optics and quantum information
  - PE2_15Thermodynamics
- PE1Mathematics
  - PE1_1Logic and foundations
  - PE1_6Geometry and global analysis
  - PE1_8Analysis
  - PE1_7Topology
  - PE1_9Operator algebras and functional analysis
  - PE1_10ODE and dynamical systems
  - PE1_12Mathematical physics
  - PE1_11Theoretical aspects of partial differential equations
  - PE1_13Probability
  - PE1_14Mathematical statistics
  - PE1_15Generic statistical methodology and modelling
  - PE1_4 Algebraic and complex geometry
  - PE1_19Scientific computing and data processing
  - PE1_2Algebra
  - PE1_20Control theory, optimisation and operational research
  - PE1_21Application of mathematics in sciences
  - PE1_22Application of mathematics in industry and society
  - PE1_5Lie groups, Lie algebras
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  - PE1_16Discrete mathematics and combinatorics
  - PE1_17Mathematical aspects of computer science
  - PE1_3Number theory
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  - PE3_1Structure of solids, material growth and characterisation
  - PE3_2Mechanical and acoustical properties of condensed matter, lattice dynamics
  - PE3_3Transport properties of condensed matter
  - PE3_4Electronic properties of materials, surfaces, interfaces, nanostructures
  - PE3_6Macroscopic quantum phenomena, e.g. superconductivity, superfluidity, quantum Hall effect
  - PE3_5Physical properties of semiconductors and insulators
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  - PE3_7Spintronics
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  - PE6_11Machine learning, statistical data processing and applications using signal processing (e.g. speech, image, video)
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  - PE6_4Theoretical computer science, formal methods, automata
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- PE7Systems and Communication Engineering
  - PE7_1Control engineering
  - PE7_2Electrical engineering: power components and/or systems
  - PE7_7Signal processing
  - PE7_8Networks, e.g. communication networks and nodes, Internet of Things, sensor networks, networks of robots
  - PE7_9Man-machine interfaces
  - PE7_5(Micro- and nano-) electronic, optoelectronic and photonic components
  - PE7_6Communication systems, wireless technology, high-frequency technology
  - PE7_3Simulation engineering and modelling
  - PE7_10Robotics
  - PE7_4(Micro- and nano-) systems engineering
  - PE7_12Electrical energy production, distribution, applications
  - PE7_11Components and systems for applications (in e.g. medicine, biology, environment)
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  - PE8_4Computational engineering
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  - PE8_8Propulsion engineering, e.g. hydraulic, turbo, piston, hybrid engines
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  - PE8_14Automotive and rail engineering; multi-/inter-modal transport engineering
  - PE8_10Manufacturing engineering and industrial design
  - PE8_12Naval/marine engineering
- PE9Universe Sciences
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  - PE9_7The Milky Way
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  - PE9_11Gravitational wave astronomy
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- PE10Earth System Science
  - PE10_2Meteorology, atmospheric physics and dynamics
  - PE10_7Physics of earth’s interior, seismology, geodynamics
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  - PE10_16Ozone, upper atmosphere, ionosphere
  - PE10_15Geomagnetism, palaeomagnetism
  - PE10_17Hydrology, hydrogeology, engineering and environmental geology, water and soil pollution
  - PE10_18Cryosphere, dynamics of snow and ice cover, sea ice, permafrosts and ice sheets
  - PE10_20Geohazards
  - PE10_19Planetary geology and geophysics
  - PE10_21Earth system modelling and interactions
  - PE10_14Earth observations from space/remote sensing
  - PE10_11Geochemistry, cosmochemistry, crystal chemistry, isotope geochemistry, thermodynamics
  - PE10_13Physical geography, geomorphology
  - PE10_12Sedimentology, soil science, palaeontology, earth evolution
- PE11Materials Engineering
  - PE11_2Engineering of metals and alloys
  - PE11_1Engineering of biomaterials, biomimetic, bioinspired and bio-enabled materials
  - PE11_3Engineering of ceramics and glasses
  - PE11_4Engineering of polymers and plastics
  - PE11_5Engineering of composites and hybrid materials
  - PE11_6Engineering of carbon materials
  - PE11_7Engineering of metal oxides
  - PE11_8Engineering of alternative established or emergent materials
  - PE11_9Nanomaterials engineering, e.g. nanoparticles, nanoporous materials, 1D & 2D nanomaterials
  - PE11_10Soft materials engineering, e.g. gels, foams, colloids
  - PE11_11Porous materials engineering, e.g. covalent-organic, metal-organic, porous aromatic frameworks
  - PE11_12Semi-conducting and magnetic materials engineering
  - PE11_13Metamaterials engineering
  - PE11_14Computational methods for materials engineering
LSLife Sciences
- LS1Molecules of Life: Biological Mechanisms, Structures and Functions
  - LS1_2Biochemistry
  - LS1_1Macromolecular complexes including interactions involving nucleic acids, proteins, lipids and carbohydrates
  - LS1_3DNA and RNA biology
  - LS1_4Protein biology
  - LS1_5Lipid biology
  - LS1_6Glycobiology
  - LS1_11Chemical biology
  - LS1_12Protein design
  - LS1_13Early translational research and drug design
  - LS1_14Innovative methods and modelling in molecular, structural and synthetic biology
  - LS1_10Synthetic biology
  - LS1_8Structural biology
  - LS1_9Molecular mechanisms of signalling processes
  - LS1_7Molecular biophysics, biomechanics, bioenergetics
- LS2Integrative Biology: from Genes and Genomes to Systems
  - LS2_1Genetics
  - LS2_3Epigenetics
  - LS2_2Gene editing
  - LS2_4Gene regulation
  - LS2_5Genomics
  - LS2_6Metagenomics
  - LS2_7Transcriptomics
  - LS2_8Proteomics
  - LS2_9Metabolomics
  - LS2_10Glycomics/Lipidomics
  - LS2_11Bioinformatics and computational biology
  - LS2_12Biostatistics
  - LS2_14Genetic diseases
  - LS2_16Innovative methods and modelling in integrative biology
  - LS2_13Systems biology
  - LS2_15Integrative biology for personalised medicine
- LS4Physiology in Health, Disease and Ageing
  - LS4_1Organ and tissue physiology and pathophysiology
  - LS4_4Endocrinology
  - LS4_3Physiology of ageing
  - LS4_2Comparative physiology
  - LS4_5Non-hormonal mechanisms of inter-organ and tissue communication
  - LS4_6Microbiome and host physiology
  - LS4_7Nutrition and exercise physiology
  - LS4_8Impact of stress (including environmental stress) on physiology
  - LS4_9Metabolism and metabolic disorders, including diabetes and obesity
  - LS4_10The cardiovascular system and cardiovascular diseases
  - LS4_11Haematopoiesis and blood diseases
  - LS4_12Cancer
  - LS4_13Other non-communicable diseases (except disorders of the nervous system and immunity-related diseases)
- LS3Cell Biology, Development, Stem Cells and Regeneration
  - LS3_4Cell junctions, cell adhesion, the extracellular matrix, cell communication
  - LS3_5Cell signalling and signal transduction, exosome biology
  - LS3_6Organelle biology and trafficking
  - LS3_7Mechanobiology of cells, tissues and organs
  - LS3_8Embryogenesis, pattern formation, morphogenesis
  - LS3_9Cell differentiation, formation of tissues and organs
  - LS3_10Developmental genetics
  - LS3_11Evolution of developmental strategies
  - LS3_12Organoids
  - LS3_3Cell behaviour, including control of cell shape, cell migration
  - LS3_13Stem cells
  - LS3_14Regeneration
  - LS3_15Development of cell-based therapeutic approaches for tissue regeneration
  - LS3_17Theoretical modelling in cellular, developmental and regenerative biology
  - LS3_16Functional imaging of cells and tissues
  - LS3_1Cell cycle, cell division and growth
  - LS3_2Cell senescence, cell death, autophagy, cell ageing
- LS5Neuroscience and Disorders of the Nervous System
  - LS5_1Neuronal cells
  - LS5_3Neural development and related disorders
  - LS5_5Neural networks and plasticity
  - LS5_10Ageing of the nervous system
  - LS5_11Neurological and neurodegenerative disorders
  - LS5_12Mental disorders
  - LS5_7Sensory systems, sensation and perception, including pain
  - LS5_13Nervous system injuries and trauma, stroke
  - LS5_14Repair and regeneration of the nervous system
  - LS5_15Neuroimmunology, neuroinflammation
  - LS5_16Systems and computational neuroscience (e.g. modelling, simulation, brain oscillations, connectomics)
  - LS5_18Innovative methods and tools for neuroscience
  - LS5_17Imaging in neuroscience
  - LS5_9Neural basis of cognition (e.g. learning, memory, attention, emotions, speech)
  - LS5_6Neurovascular biology and blood-brain barrier
  - LS5_8Neural basis of behaviour (e.g. sleep, consciousness, addiction)
  - LS5_4Neural stem cells
  - LS5_2Glial cells and neuronal-glial communication
- LS6Immunity, Infection and Immunotherapy
  - LS6_1Innate immunity
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  - LS6_3Regulation of the immune response
  - LS6_4Immune-related diseases
  - LS6_5Biology of pathogens (e.g. bacteria, viruses, parasites, fungi)
  - LS6_7Mechanisms of infection
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  - LS6_8Biological basis of prevention and treatment of infection
  - LS6_9Antimicrobials, antimicrobial resistance
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- LS7Prevention, Diagnosis and Treatment of Human Diseases
  - LS7_2Medical technologies and tools (including genetic tools and biomarkers) for prevention, diagnosis, monitoring and treatment of diseases
  - LS7_1Medical imaging for prevention, diagnosis and monitoring of diseases
  - LS7_5Applied gene, cell and immune therapies
  - LS7_4Regenerative medicine
  - LS7_3Nanomedicine
  - LS7_6Other medical therapeutic interventions, including transplantation
  - LS7_7Pharmacology and toxicology
  - LS7_8Effectiveness of interventions, including resistance to therapies
  - LS7_9Public health and epidemiology
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  - LS7_14Digital medicine, e-medicine, medical applications of artificial intelligence
  - LS7_15Medical ethics
  - LS7_13Palliative medicine
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- LS8Environmental Biology, Ecology and Evolution
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  - LS8_10Ecology and evolution of species interactions
  - LS8_12Microbial ecology and evolution
  - LS8_13Marine biology and ecology
  - LS8_14Ecophysiology, from organisms to ecosystems
  - LS8_15Theoretical developments and modelling in environmental biology, ecology, and evolution
- LS9Biotechnology and Biosystems Engineering
  - LS9_3Bioengineering of cells, tissues, organs and organisms
  - LS9_2Applied genetics, gene editing and transgenic organisms
  - LS9_4Microbial biotechnology and bioengineering
  - LS9_5Food biotechnology and bioengineering
  - LS9_6Marine biotechnology and bioengineering
  - LS9_7Environmental biotechnology and bioengineering
  - LS9_8Applied plant sciences, plant breeding, agroecology and soil biology
  - LS9_10Veterinary and applied animal sciences
  - LS9_9Plant pathology and pest resistance
  - LS9_11Biomass production and utilisation, biofuels
  - LS9_12Ecotoxicology, biohazards and biosafety
  - LS9_1Bioengineering for synthetic and chemical biology
SHSocial Sciences and Humanities
- SH2Institutions, Governance and Legal Systems
  - SH2_1Political systems, governance
  - SH2_2Democratisation and social movements
  - SH2_3Conflict resolution, war, peace building
  - SH2_4Legal studies, comparative law, law and economics
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  - SH2_8Political and legal philosophy
  - SH2_9Digital approaches to political science and law
- SH1Individuals, Markets and Organisations
  - SH1_6Banking, insurance
  - SH1_7Accounting, asset prices, auditing
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  - SH1_14Strategy, operation research
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  - SH1_3Development economics political economics
  - SH1_1Macroeconomics; monetary economics; economic growth, labour economics
  - SH1_4Finance; financial markets
  - SH1_16Quantitative economic history, economic systems, institutional economics
  - SH1_5Corporate finance; international finance
- SH3The Social World and Its Interactions
  - SH3_1Social structure, social mobility, social innovation
  - SH3_2Inequalities, discrimination, prejudice
  - SH3_3Aggression and violence, antisocial behaviour, crime
  - SH3_5Social attitudes and beliefs
  - SH3_4Social integration, exclusion, prosocial behaviour
  - SH3_7Social policies, welfare, work and employment
  - SH3_8Poverty and poverty alleviation
  - SH3_10Communication and information, networks, media
  - SH3_11Digital social research
  - SH3_9Social aspects of teaching and learning, curriculum studies, education and educational policies
  - SH3_12Social studies of science and technology
  - SH3_6Social influence; power and group behaviour
- SH4The Human Mind and Its Complexity
  - SH4_1Cognitive basis of human development, developmental disorders; comparative cognition
  - SH4_2Personality and social cognition; emotion
  - SH4_3Clinical and health psychology
  - SH4_4Neurocognitive psychology
  - SH4_5Attention, perception, action, consciousness
  - SH4_6Learning, memory; cognition in ageing
  - SH4_7Reasoning, decision-making; intelligence
  - SH4_8Language learning and processing (first and second languages)
  - SH4_11Pragmatics, sociolinguistics, linguistic anthropology, discourse analysis
  - SH4_9Theoretical linguistics; computational linguistics
  - SH4_10Language typology; historical linguistics
- SH6The Study of the Human Past
  - SH6_1Archaeological methods and theory, history of archaeology
  - SH6_2Prehistoric archaeology, archaeology of non-literate societies
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  - SH6_6Digital, computational, virtual and geospatial archaeologies
  - SH6_7Historiography, theory and methods of history, including the analysis of digital data
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  - SH6_11Global, transnational, and comparative history
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- SH5Texts and Concepts
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  - SH5_3Book studies
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  - SH5_2Theory and history of literature, comparative literature
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  - SH7_2Migration
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  - SH8_8Visual and performing arts, screen, arts-based research
  - SH8_9Digital approaches to anthropology, cultural studies and art