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In each of 21 through 23:(a) Draw a direction field for

Elementary Differential Equations and Boundary Value Problems | 10th Edition | ISBN: 9780470458310 | Authors: William E. Boyce ISBN: 9780470458310 168

Solution for problem 22 Chapter 2.1

Elementary Differential Equations and Boundary Value Problems | 10th Edition

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Elementary Differential Equations and Boundary Value Problems | 10th Edition | ISBN: 9780470458310 | Authors: William E. Boyce

Elementary Differential Equations and Boundary Value Problems | 10th Edition

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Problem 22

In each of 21 through 23:(a) Draw a direction field for the given differential equation. How do solutions appear tobehave as t becomes large? Does the behavior depend on the choice of the initial value a?Let a0 be the value of a for which the transition from one type of behavior to another occurs.Estimate the value of a0.(b) Solve the initial value problem and find the critical value a0 exactly.(c) Describe the behavior of the solution corresponding to the initial value a0.2y y = et/3, y(0) = a

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Biology of Plants Exam III Review Guide Topics 1. Evolution of Angiosperms A. Basic angiosperm cladogram B. Unique characteristics of angiosperms: 1. Flowers 2. Close carpels (ovaries) 3. Double fertilization leading to endosperm formation 4. 3-nucleate mature microgametophyte 5. 8-nucleate mature megagametophyte (usually) 6. Stamens with two pairs of pollen sacs 7. Presence of sieve tubes and companion cells in phloem C. Synoecious, dioecious, monoecious 1. Synoecious: perfect flowers 2. Dioecious: male and female flowers on different plants 3. Monoecious: male and female flowers on same plant D. Characteristics of all basal angiosperms and magnoliids discussed in class: 1. Basal Angiosperms: these lineages were originally regarded as “dicots”- but actually arose before the monocot/eudicot split a. Examples: family Amborellaceae, family Nymphaeales, and family Austroballeyales E. Characteristics of monocots and eudicots 2. Flowers and fruits A. The evolution of the flower (stamens, carpels, petals, etc.) and trends in floral evolution 1. Everything is a modified leaf 2. Sepals and petals evolved as sterile leaves associated with sporophylls a. Sporophylls containing microsporangia (microsporophylls) evolved into stamens 3. Sporphylls containg megasporangi (megasporophylls) evolved into carpels 4. Trends in flower evolution a. Evolution towards few flower parts that are definite in number b. Flower axis shortened, spiral arrangement of floral organs no longer evident, floral parts often fused c. Ovary superior inferior d. Distinct calyx and corolla e. Radial symmetry bilateral symmetry B. Various pollination syndromes 1. Insect pollination syndromes (type of insect, flower color, flower odor, nectar guides) a. Beetles= dull, strong and fruity or spicy, none b. Flies= dull red/brown, strong and foul (ex. Like carrion), none c. Bees= variable but not solid red, usually sweet, present d. Moths= white or pale/variable, strong and sweet, none e. Butterflies= variable/pink, moderately strong and sweet, present C. Parts of the fruit: endocarp, seed, fleshy mesocarp, exocarp D. Basics of fruit dispersal 1. Wind dispersal a. Small and lightweight seeds; may have curbed wings, inflated sacs, plumes, wooly hairs; of whole plant may roll on ground 2. Mechanical Ejection of Seeds a. Ballistic 3. Water dispersal a. Some fruits contain trapped air to help them float (stay buoyant) 3. Embryogenesis A. Sequence of early cell divisions in that give rise to embryo and suspensor 1. First division of the embryo is asymmetrical and transverse apical and basal a. Apical cell will become embryo b. Basal cell will become suspensor c. 3-cell proembryo—apical cell has divided again transversely 2. Embryo proper is now at the 4-cell stage; two more mitotic divisions have occurred; all four of these cells contribute to the final embryo 3. Asymmetrical division f the zygote has just occurred— resulting in apical and basal cells 4. 6-celled proembryo; apical cell has divided twice, basal cell once 5. Globular embryo with distinct protoderm 6. Torpedo stage embryo with three primary meristems are visible; later in plant development, cell division will be restricted to apical meristems and cambia B. Formation of the protoderm, ground meristem and procambium – and the tissues to which each will eventually give rise 1. Concentrically arranged as cell layers (radial polarity) is starting to emerge embryo has formed the protoderm 2. Protoderm will eventually give rise to the epidermis 3. Subsequent vertical cell divisions will give rise to the ground meristem and procambium 4. Primary meristem primary tissues a. Protoderm dermal tissues (epidermis) b. Ground meristem ground tissues (parenchyma, collenchyma, schlerenchyma) c. Procambium vascular tissues (primary xylem and primary phloem) C. Embryo anatomy D. Seed anatomy of eudicots and monocots E. Characteristics of the Orchidaceae and the Asteraceae 1. Asteraceae: “flower is actually made up of hundreds of tiny flowers bunched together; often divided into ray flowers and disk flowers; each has an inferior ovary with two fused carpels a. Flower head matures over a period of days, so individual flowers are pollinated by different donors 2. Orchidaceae 4. Seed germination A. Mechanisms of seed dispersal: characteristics of seeds dispersed by wind, water, animals, etc. B. Mechansisms of seed dormancy: cold stratification, scarification, leaching of inhibitors, etc. 1. Seed coat must eventually be ruptured to permit entry of water and oxygen 2. Cold stratification: seed requires a period of sustained low temperatures before it will germinate; seed must be exposed to temps less than 5-7C for many days; this prevents germination in warm days of autumn or during brief winter warm spells 3. Scarification: mechanical damage; seed must be abraded before it can germinate; wears away the seed coat, allowing water and O2 to enter and germination to begin; abrasion in soil, digestion in animal, microbial degradation 4. Breaking mechanisms: sustained low temperature; mechanical damage to seed coat; sustained rainfall washes away inhibitors in seed coat (desert plants); light required (ex: early successional trees) C. Process of germination from imbibing water to emergence of first foliage leaves 1. Imbibing: a. Seed takes up water b. Enzymes in the seed are activated c. New enzymes synthesized d. Seed swells, develops pressure, ruptures seed coat e. Aerobic respiration can take place when seed coat is broken f. Embryo cells begin to divide and grow again 2. Epigeous germination: cotyledons above ground level epi=above; hypocotyl is elongated and bent—this “hook” pushes up through the soil, pulling the cotyledons with it a. Example: common bean b. Seedling gets to use cotyledons for photosynthesis 3. Hypogeous germination: cotyledons remain underground hypo=below a. It is the epicotyl rather than the hypotcotyl that forms the hook b. Example: acorns/oaks c. Protects cotyledons from predation d. Plus can be heavy and hard to pull out of ground 5. Meristems and primary tissues A. What is a meristem What are apical and lateral meristems and where are they found in the plant body 1. Meristem: region of undifferentiated, dividing cells 2. Apical meristems: found at root and shoot tips; give rise to primary tissues 3. Lateral meristems (cambia): cylindrical vascular and cork cambia; give rise to secondary tissues B. Initials and derivatives 1. Apical Meristems intitials and derivatives a. Initials: divide and maintain the meristem as a continuous source of new cells b. Derivatives: become new body cells i. May divide a few more times before undergoing differentiation ii. Give rise to three “primary meristems”—partly differentiated tissues that remain meristematic for some time before differentiating into specific cell types protoderm, ground meristem, procambium C. Tissues and tissue systems 1. What are the 3 primary tissue systems of the plant Dermal tissues (epidermis), ground tissues (parenchyma, collenchyma, schlerenchyma), vascular tissues (primary xylem and phloem) 2. Axial and radial polarity of plant tissues (established early in embryogenesis) D. Ground tissue: functions and characteristics of parenchyma, collenchyma and schlerenchyma 1. Parenchyma (most common): most numerous cells in the plant body a. Cortex and pith of stems; cortex of roots; mesophyll of leaves and petals; flesh of fruits; vertical stands in primary xylem and phloem; rays in secondary xylem b. Functions: photosynthesis, storage, and secretion c. Cell features: i. Capable of cell division ii. Capable of de-differentiation iii. Thin, primary walls iv. Function in photosynthesis, storage, secretion, and regeneration 2. Collenchyma: cells support young, growing plant organs a. Mainly found as strands or a continuous cylinder just under the epidermis in young stems, petioles and large leaf veins b. Living, elongated cells running parallel to the length of organ c. Heavy cellulose PRIMARY cell walls which are thickened at the corners d. Intercellular air spaces are absent or very small e. The cells contain living protoplasm and they sometimes contain chloroplasts f. *** Functions: support and strength in young, expanding tissue; sometimes photosynthesis 3. Schlerenchyma: strengthens and supports plant parts that are no long elongating a. Dead at maturity with thick secondary walls; lumen is very small or absent b. Fibers and schlereids*** c. Functions: support of mature tissues, hardness of seeds and nuts, may store starch E. Epidermis: location and cells types, including specialized cells like trichomes and guard cells A. Guard cells: how they regulate their osmotic potential in order to open and close B. Epidermis: constitutes the entire dermal system in leaves, flowers, fruits, young stems, and young roots a. Covers outer surface of primary tissues; mainly consists of close-packed relatively unspecialized cells gives mechanical protection; secretes waxy cuticle on aboveground plant parts b. Trichomes: hair-like outgrowths of individual epidermal cells; increase surface area for water and nutrient uptake from soil c. Guard Cells: present in pairs and control stomatal opening; contain chloroplasts F. Vascular tissue A. Xylem: understand how tracheids (gymnosperms and angiosperms) and vessel elements (angiosperms only) differ 1. Function: transport of water and minerals, support, food storage 2. Tracheids: in both gymno and angiosperms; longer and thinner; lack protoplasts and are therefore non- living at maturity 3. Vessel elements: shorter, wider; have perforation plate son their end walls; the primary water conducting cell of angiosperms B. Phloem: understand all cell types and their anatomy; know how gymnosperm and angiosperm phloem cells differ 1. Function: transport of sugars and many other compounds 2. Cell types: sieve elements, companion or albuminous cells (parenchyma), storage parenchyma, fibers, schlereids a. Sieve cells in gymnosperms long, slender, overlapping ends b. Sieve-tube elements in angiosperms shorter, wider than sieve cells; associated with companion cells; have sieve plates at the ends i. P protein fills the pores in the sieve plate of a wounded phloem cell c. Cluters of pores (sieve areas) connect adjacent sieve elements d. Albuminous cell: parenchyma cell in gymnosperm phloem that is spatially and functionally associated with a sieve cell 6. Roots A. Root functions: anchorage, absorption of water and nutrients, conduction, and storage B. Understand how the basic mechanisms of water and nutrient uptake differ 1. Most plants derive their water form rainfall in the upper soil layers 2. Nutrients come from litterfall and root turnover 3. Oxygen diffuses into the soil from the atmosphere C. Where roots are found in the soil and why: they grow where the resources are water, oxygen, and nutrients 1. Water, oxygen, and nutrients all enter the soil from above D. Root anatomy: axial and radial 1. Anatomy and function of endodermis/ Casparian strips a. Endodermis: the innermost cell layer of the cortex- and a barrier to apoplastic movement of water and solutes i. This layer is compactly arrange and lacks air spaces b. Each cell has a suberin “belt” surrounding it the casparian strip i. Casparian strips is a band-like portion of the primary cell wall and middle lamella that is impregnanted with suberin (waxy substance) and sometimes lignin it stops apoplastic movement of water and solutes E. Functions of the root cap 1. Root cap: is a mass of living parenchyma cells that protects the root apical meristem c. Functions: secretes mucilage; produces border cells; perceives and responds to gravity 2. Role of amyloplasts and auxin in gravitropism a. The wall the amyloplasts fall against correlates with how auxin is deconjugated and distributed F. Maturation of various root tissue systems: phloem matures first (why), then endodermis, then xylem G. Lateral root emergence: 1. Lateral roots emerge from the pericycle, as does the vascular cambium in roots that undergo secondary growth H. Root secondary development from vascular cambium – role of procambium and pericycle 1. Pericycle: surrounds the vascular cylinder—lateral roots arise from it; it is a meristematic tissue which, in woody plants, will give rise to a vascular cambium later in root developtment; also the site of lateral root formation 2. Vascular cambium forms from division within the procambium and the pericycle a. Formation of vascular cambium is initiated by divisions in the procambium cells between the primary phloem and parimary xylem 7. Stems A. Function and anatomy of the shoot apical meristem 1. Stems + Leaves = Shoot; More complex than root system; Nodes, internodes, leaves; Stems support and conduction 2. Shoot apical meristem had tunica-corpus organization a. Tunica: outermost layer(s) of cells; cells divide anticlinically b. Corpus: beneath the tunica layer(s); cells divide in various planes and add bulk to the developing shoot 3. Shoot apical meristem gives rise to the same three primary meristems found in the root: ground, procambium, and protoderm B. Three types of stem vascular organization and where they are found 1. Stem structure 1: non-monocot seed plants a. Vascular tissues form a relatively continuous cylinder within ground tissue b. There is a clear division of cortex and pith c. Parenchyma tissue connects the cortex and pith in narrow bands (interfascicular region) 2. Stem structure 2: most common (but not in monocots) a. Discrete vascular bundles b. Vascular bundles are arranged in a cylinder c. Cortex and pith are distinct—and connected by wide interfascicular regions 3. Stem structure 3: found in most monocots and some herbaceous eudicots a. The vascular bundles occur in multiple rings of bundles—or – scattered throughout the ground tissue b. Ground tissue is not separated into cortex and pith C. Stem anatomy: 1. Eudicot Stem: discrete vascular bundles; arranged in cylinder (separates from pith); separated from one another by wide bands of ground tissue 2. Monocot Stem: a. The vascular bundles occur in: i. More than one ring of bundles ii. Or are scattered throughout the ground tissue b. Ground tissue is not distinguished as cortex and pith 8. Leaves A. Basic eudicot leaf anatomy: 1. Epidermis a. Stoma: mainly found on lower leaf surfaces; allow entry of CO2 and exit of O2****; water vapor can cool leaf but excessive water loss is a problem b. Stomatal apparatur: pore (opening) bordered by 2 sasuace-shaped guard cells have chloroplasts and control water loss by opening/closing pore 2. Mesophyll: middle of leaf; most photosynthesis takes place here; in non-monocots divded into 2 regions: a. Palisaede: uppermost region, compactly arranged parenchyma; 80% of chloroplasts are here b. Spongy: lower region; loosely arranged parenchyma; abundant air spaces 3. Veins: vascular bundles; xylem and phloem—various sizes scattered throughout mesophyll a. Largest vein= long axis of the leaf called midvein i. Midvein + ground tissue = midrib b. Xylem= top; phloem= bottom c. Surrounded by jacket of thicker-walled parenchyma cells that are compactly arranged= bundle sheath i. Bundle sheath: surrounds the veins; assures that no part of the vascular tissue is exposed to air in the intercellular spaces B. Why have compound leaves a. Minimizes wind damage to large leaves b. They are easier to cool in hot water C. Needle leaf anatomy D. Arid climate leaf modifications: in arid regions—dry, wide temperature ranges (very cold at night, very hot during day), high light intensity 1. Xerophytes: a. Thick, leathery leaves b. Stomata sunken below the surface in special depressions (reduce loss of water through transpiration)= stomatal crypt******** c. Succulent, water-retaining leaves or no leaves at all (stems take over photosynthesis=cladophylls) d. Or dense, hairy coverings on leaves E. Monocot leaf anatomy 1. Parallel veins; usually don’t have the mesophyll differentiated into palisade and spongy layers 2. Shade leaves: thinner per unit weight, larger, fewer hairs, fewer chloroplasts 3. Sun leaves: thicker per unit weight, smaller, more hairs, more chloroplasts F. Hydrophyte leaf modifications: aquatic; plant like; water lilies 1. Hydrophyte leaves: large air spaces; stomata only on upper surface of floating leaves; submerged leaves; no stomata at all; schlereid G. Thorns, spines and prickles – what are the differences 1. Thorns: modified stem—arise from above leaf 2. Spines: modified leaf/stipule (below the leaves) 3. Prickles: outgrowth of epidermis or cortex (not modified anything) H. Unusual leaves: carnivorous plants, reproductive leaves, bracts, food storage leaves 1. Carnivorous/Insectivorous plants: over 200 species; grow mostly in swampy areas and bogs; certain needed elements, like nitrogen, may not be sufficient in the soil for the plants; some elements like nitrogen are furnished when soft parts of insects and other small organisms are trapped by specialized leaves and are broken down and digested; all have chlorophyll; can develop normally without insects if they are given the nutrients they need 2. Reproductive plants: asexual reproduction a. Examples: walking fern, Kalanchoe “mother of thousands” 3. Bracts: modified/specialized leaves found associated with reproductive structure (like flowers or flower stalks) a. Example: Poinsetiia—flowers themselves have NO petals; Dogwood BIOL 3080 Exam 3 Terms - Quiescent center: region of intials divides actively early in root development but its rate of division slows later - Promeristem: the initials and their most recent derivatives in an apical meristem; the least differentiated part of an apical meristem - Aerenchyma: form when cortical cells undergo programmed cell death in response to low O2; contains large intercellular air spaces these air spaces form open conduits for gas flow from shoot to root - Endodermis: innermost cell layer of the cortex- a barrier to apoplastic movement of water and solutes - Casparian Strip: strips of adjacent cells align to create a waxy barrier to the movement of water and solutes from the cortex into the stele - Adventitious roots: arise from the stem - Pneumatophores: “air roots” of aquatic plants - Storage roots: enlarged to store sugars and starch; many important horticultural crops - Leaf epidermis – outermost layer of cells on the top and bottom of the leaf; secretes waxes that form the cuticle - Leaf cuticle – layer of leaf wax on the top and bottom of the leaf; seals the leaf off from the outside atmosphere and prevents uncontrolled water loss - Palisade mesophyll (also called palisade parenchyma) cells – primary photosynthestic cells of the leaf; there may be one or more layers of them; they contain large numbers of photosynthetic organelles called chloroplasts; these cells are positioned near the top surface of the leaf, underneath the epidermis. - Spongy mesophyll cells – irregularly-shaped chloroplast- containing cells; they have many air spaces among them; they also contribute to leaf phsotosynthesis - Air spaces – The interior of the leaf contains a great deal of air space, where CO , O2and2H O vapo2 are found - Vein – veins contain structural tissue that supports the leaf and vessels that move water and sugars through the leaf - Bundle sheath cells – a layer of compactly arranged cells that surrounds the xylem and phloem in a leaf vein - Xylem – water-conducting cells that bring water and minerals up from the rooots into the leaf; these cells are dead when functional - Phloem – sugar-conducting cells that transport sugar out of the leaf to other parts of the tree; these cells are alive when functional - Guard cells – two specialized cells that surround a pore (or stoma) in the leaf surface; they can open or close the pore, thereby changing the permeability of the leaf to water vapor and other gases. - Stoma (plural stomata or stomates)– a pore in the leaf surface; water vapor exits the leaf through the stomata, while CO enters 2 - Radicle: First root to emerge from seed - Cotyledon: seed leaf; may look different than later foliage leaves - Hypocotyl: area between radicle and cotyledon attachment point - Epicotyl: area above cotyledon attachment point and below next set of leaves - Plumule: portion of the seedling above the cotyledons Parts of the corn seed embryo: 1.Radicle: First root to emerge from seed; at its tip is root apical meristem 2.Coleorhiza: sheath enclosing the radicle 3.Cotyledon= scutellum (single cotyledon of a grass embryo, specialized to digest and absorb the endosperm 4.Plumule: shoot apical meristem and first foliage leaves 5.Coleoptile: sheath enclosing the plumule 6.Aleurone: outermost, protein-containing layer of endosperm

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Textbook: Elementary Differential Equations and Boundary Value Problems
Edition: 10
Author: William E. Boyce
ISBN: 9780470458310

The answer to “In each of 21 through 23:(a) Draw a direction field for the given differential equation. How do solutions appear tobehave as t becomes large? Does the behavior depend on the choice of the initial value a?Let a0 be the value of a for which the transition from one type of behavior to another occurs.Estimate the value of a0.(b) Solve the initial value problem and find the critical value a0 exactly.(c) Describe the behavior of the solution corresponding to the initial value a0.2y y = et/3, y(0) = a” is broken down into a number of easy to follow steps, and 88 words. Since the solution to 22 from 2.1 chapter was answered, more than 231 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 22 from chapter: 2.1 was answered by , our top Math solution expert on 12/23/17, 04:36PM. This full solution covers the following key subjects: . This expansive textbook survival guide covers 76 chapters, and 2039 solutions. Elementary Differential Equations and Boundary Value Problems was written by and is associated to the ISBN: 9780470458310. This textbook survival guide was created for the textbook: Elementary Differential Equations and Boundary Value Problems, edition: 10.

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In each of 21 through 23:(a) Draw a direction field for