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muscle Temporalis Origin: temporal bone Insertion: coronoid process & ramus of the mandible Action: elevates and contracts mandible for chewing Masseter muscle Origin: zygomatic arch Insertion: mandible Action: elevates mandible (closes mouth) Orbicularis oculi Origin: medial wall of orbit, frontal and maxillar bones Insertion: circular path around orbit Action: blinking, squinting, forceful closing of eyelids Levator palpebrae superioris Origin: root of orbit (lesser wing of sphenoid bone) Insertion: skin of upper eyelid Action: opens eyelid Orbicularis oris muscle Origin: muscle fibers/fibrous tissue surrounding opening of mouth Insertion: skin at corner of mouth Action: kissing, compresses lips against teeth, shapes lips in speech Platysma muscle Origin: pectoralis major & deltoid fascia Insertion: mandible, muscles around mouth, skin on lower face Action: Opens and widens Mouth, most superficial muscle Sternocleidomastoid muscle Origin: clavicle & manubrium of sternum Insertion: mastoid process Action: flexes neck forward Scalenes muscle Origin: transverse process of C1 - C7 Insertion: first and second ribs Action: helps breath by elevating upper ribs, flexes head, rotates head side to side (bobbing for apples muscle) Digastric muscle Origin: mastoid notch of temporal bone, mandible Insertion: hyoid bone Action: Retracts mandible, ELEVATES HYOID BONE Stylohyoid muscle Origin: styloid process of temporal bone Insertion: hyoid bone Action: ELEVATES HYOID BONE Mylohyoid muscle Origin: mandible Insertion: hyoid bone Action: forms floor of mouth, ELEVATES HYOID BONE Sternohyoid muscle Origin: clavicle & manubrium of sternum Insertion: hyoid bone Action: DEPRESSES HYOID BONE Sternothyroid muscle Origin: sternum Insertion: thyroid cartilage of larynx Action: DEPRESSES HYOID BONE Omohyoid muscle Origin: superior border of scapula Insertion: body of hyoid bone Action: DEPRESSES HYOID BONE Thyrohyoid muscle Origin: thyroid cartilage of larynx Insertion: hyoid bone Action: DEPRESSES HYOID BONE Pectoralis major Origin: medial clavicle, costal cartilage (costals 1-7) Insertion: Intertubercular sulcus of humerus Action: flex upper arm, adducts upper arm across chest Pectoralis minor Origin: Anterior ribs 3 - 5 Insertion: coracoid process of scapula Action: downward rotation, abduction Serratus anterior Origin: all ribs Insertion: medial border of scapula ction: abduction, and upward rotation Internal intercostal muscles Origin: superior ribs 2-12, and margin of sternum Insertion: inferior margin of next higher rib Action: Forcefully contracts and retracts ribs, to assist in forceful inspiration External intercostal muscles Origin: inferior margin of ribs 1-11 Insertion: superior margin of next lower rib Action: Elevates ribs to assist in forceful inspiration Diaphragm muscle rigin: Xiphoid process of sternum, ribs 7-12, lumbar vertebra Insertion: Central tendon of diaphragm Action: Prime mover of inspiration. Trapezius muscle Origin: occipital bone & spines of C7 & all Thoracic vertebrae Insertion: Spine of scapula, acromion, and lateral 1/3rd of clavicle Action: stabilizes,raises, retracts, elevates, & rotates scapula, extend head Latissimus dorsi muscle Origin: T6 - T12, all Lumbar ver., sacrum, ilium, inferior four ribs Insertion: Intertubercular groove of humerus Action: extends, adducts, medially rotates upper arm Rhomboid major muscle Origin: spinous processes of T2 - T5 Insertion: Medial border of scapula Action: Retracts scapula and braces shoulder, fixes scapula during arm movements Rhomboid minor muscle Origin: spinous processes of C7 - T1 Insertion: Medial border of scapula Action: Retracts scapula and braces shoulder, fixes scapula during arm movements Iliocostalis part of erector spinae muscle Origin: ribs 3-12, thoracic and lumbar vertebrae Insertion: mastoid process, cervical, and thoracic vertebrae, and all ribs Action: extension and lateral flexion of vertebral column Longissimus part of erector spinae muscle Origin: ribs 3-12, thoracic and lumbar vertebrae Insertion: mastoid process, cervical, and thoracic vertebrae, and all ribs Action: extension and lateral flexion of vertebral column Spinalis part of erector spinae muscle Origin: ribs 3-12, thoracic and lumbar vertebrae Insertion: mastoid process, cervical, and thoracic vertebrae, and all ribs Action: extension and lateral flexion of vertebral column Rectus abdominis muscle Origin: pubic crest & symphisis Insertion: xiphoid process & ribs 5 - 7 Action: flexes vetebral column, child birth, stabilizes pelvis during walking External oblique muscle Origin: Ribs 5-12 Insertion: Iliac crest, pubic symphysis, superior pubis Action: aids in flexing rectus abdominis, aids muscles in trunk rotation, aids in side bends Internal oblique muscle Origin:iliac crest Insertion: Ribs 10-12, costal cartilage 7-10, pubis Action: aids in flexing rectus abdominis, aids muscles in trunk rotation, aids in side bends Transversus abdominis muscle Origin: last six ribs & iliac crest Insertion: xiphoid process, linea alba & pubis Action: compresses abdomen Linea alba Origin: sternum Insertion: pubic symphisis Action: forms midline Anconeus muscle Origin: lateral epicondyle of humerus Insertion: olecranon process of ulna Action: extension at elbow, abducts forearm during pronation Biceps brachii muscle Origin: scapula Insertion: radius Action: flex supinated forearm Brachialis muscle Origin: anterior humerus Insertion: coronoid process and tuberosity of ulna Action: prime mover of elbow flexion Brachioradialis muscle Origin: lateral distal humerus Insertion: styloid process of radius Action: flexes forearm (pronated) Coracobrachialis muscle Origin: coracoid process of scapula Insertion: medial mid-humerus Action: adduction & flexion of arm at shoulder joint Deltoid muscle Origin: clavicle & scapula Insertion: deltoid tuberosity of humerus Action: abducts upper arm, rotate arm at shoulder joint Teres major muscle Origin: inferior angle of scapula Insertion: intertubercular sulcus of humerus Action: extends, adducts, medially rotates arm Teres minor muscle Origin: lateral posterior scapula Insertion: tubercle Greater of humerus Action: lateral rotation at shoulder Supraspinatus muscle Origin: supraspinous fossa of scapula Insertion: Greater tubercle of humerus Action: assists deltoid in abducting arm Infraspinatus muscle Origin: infraspinous fossa of scapula Insertion: Greater tubercle of humerus Action: laterally rotates and adducts arm at shoulder joint Levator scapulae muscle Origin: Vertebrae C1-C4 Insertion: superior angle and medial border of scapula Action: elevates, rotates scapula downward Subscapularis muscle Origin: subscapular fossa of scapula Insertion: Lesser tubercle of humerus Action: medially rotates arm at shoulder joint Triceps brachii muscle Origin: humerus, scapula Insertion: Olecranon process of ulna Action: extends forearm ` Pronator teres muscle Origin: humerus & ulna Insertion: radius Action: pronates forearm Flexor carpi radialis muscle Origin: epicondyle of humerus Insertion: 2nd & 3rd metacarpals Action: flexes and adducts hand Palmaris longus muscle Origin: humerus Insertion: palmar fascia Action: Synergist for wrist flexion Flexor carpi ulnaris muscle Origin: humerus & ulna Insertion: Pisiform, hamate, 5th metacarpal anteriorly Action: flexes and abducts hand Flexor digitorum superficialis muscle Origin: humerus Insertion: distal phalanges 2-4 Action: flexes phalanges Flexor pollicis longus muscle Origin: anterior radius Insertion: distal phalanx of pollex Action: flexes pollex Flexor digitorum profundus muscle Origin: ulna Insertion: distal phalanges 2-4 Action: flexes phalanges Pronator quadratus muscle Origin: anterior distal ulna Insertion: anterior distal radius Action: pronates forearm, hold radius and ulna together Extensor carpi radialis longus muscle Origin: humerus Insertion: 2nd metacarpal Action: extends and abducts hand Extensor carpi radialis brevis muscle Origin: humerus Insertion: 3rd metacarpal Action: extends and abducts hand Extensor digitorum muscle Origin: humerus Insertion: distal phalanx of phlanges 2-4 Action: extends fingers and hand Extensor carpi ulnaris muscle Origin: humerus & ulna Insertion: 5th metacarpal Action: extends and adducts hand Abductor pollicis longus muscle Origin: radius, ulna Insertion: 1st metacarpal Action: abducts and extends thumb Extensor pollicis longus muscle Origin: ulna Insertion: distal phalanx of the pollex Action: extends thumb, abduction at wrist Extensor pollicis brevis muscle Origin: ulna Insertion: distal phalanx of the pollex Action: extends thumb, abduction at wrist Supinator muscle Origin: upper ulna, humerus Insertion: upper radius Action: supinates forearm Iliopsoas muscle Origin: ilium, T12 - L5 Insertion: iliacus, lesser trochanter, femur Action: flexion at hip psoas major Origin: Bodies and intervertebral discs of T12-L5 Insertion: Lesser Trochanter of femur Action: Flexes thigh at hip Iliacus Origin: Iliac crest Insertion: Lesser Trochanter of femur Action: Flexes thigh at hip Adductor magnus muscle Origin: inferior pubis and ischium Insertion: Adductor tubercle and linea aspera of femur Action: adducts and flexes, extends, lateral rotation of thigh at hip Adductor longus muscle Origin: inferior ramus of pubis Insertion: linea aspera of femur Action: adducts, flexes, & medially rotates thigh at hip Adductor brevis muscle Origin: inferior ramus of pubis Insertion: linea aspera of femur Action: adducts thigh Pectineus muscle Origin: superior ramus of pubis Insertion: femur Action: Adducts, flexes and medially rotates thigh Gracilis muscle Origin: inferior ramus of pubis Insertion: tibia Action: Flexes and medially rotates tibia at knee, adducts femur Rectus Femoris Origin: anterior inferior iliac spine, superior part of acetabulum Insertion: patella, tibia Action: extension at knee, flexion at hip Sartorius (Longest muscle in the body) Origin: iliac spine (ilium) Insertion: tibia flexion at knee, flexion & lateral rotation at hip, used in crossing legs Action: Vastus Intermedius Origin: femur Insertion: tibia, patella Action: knee extension Vastus Lateralis: Origin: femur Inserion: tibia, patella Action: knee extension Vastus Medialis Origin: femur Inserion: tibia, patella Action: knee extension Tensor fasciae latae muscle Origin: iliac crest (ilium), anterior superior iliac spine Insertion: Proximal Portion of the femur Action: Flexes & abducts thigh, rotates thigh medially, Stabilizes knee and trunk Gluteus maximus muscle Origin: iliac crest (ilium), sacrum, coccyx Insertion: gluteal tuberosity of femur, iliotibial band Action: extend thigh, lateral rotation Gluteus medius muscle Origin: iliac crest (ilium) Insertion: Greater trochanter of femur Action: abducts and medially rotates thigh Gluteus minimus muscle Origin: Gluteal lines on posterior ilium Insertion: Greater trochanter of femur Action: abducts and medially rotates thigh Biceps femoris ( long head, short head ) Origin: Ischial tuberosity & Linea aspera of femur Insertion: fibula Action: flexes knee, extends thigh Semitendinosus muscle Origin: Ischial tuberosity (ishium) Insertion: tibia Action: Flexes knee, Extension and rotation at hip Semimembranosus muscle Origin: Ischial tuberosity (ishium) Insertion: tibia Action: Flexes knee, Extension and rotation at hip Tibialis anterior muscle Origin: lateral condyle of tibia Insertion: 1st metatarsal & cuneiform bone Action: Dorsiflexes and inverts foot Extensor digitorum longus muscle Origin: lateral condyle of tibia & fibula Insertion: phalanges 2-5 Action: extends toes 2 -5, Dorsiflexes And everts foot Extensor hallucis longus muscle Origin: fibula Insertion: Distal phalanx of hallux Action: extends big toe (Hallux), Dorsiflexes/ inverts foot Fibularis (Peroneus) Longus Origin: fibula Insertion: 1st metatarsal & first cuneiform Action: Maintains plantar flexion and everts foot Fibularis brevis Fibularis (Peroneus) Brevis Origin: fibula Insertion: 5th metatarsal Action: Plantar flexes and everts foot Fibularis longus Gastrocnemius muscle Origin: femur Insertion: calcaneus Action: plantar flexes foot, flexes knee Soleus muscle Origin: Proximal fibula & tibia Insertion: calcaneus Action: Plantar flexion
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ASU >> SOLS >> BIO 201 (Spring, 2009)
Facial Muscles Spine Muscles Rib Muscles Neck Muscles Back Muscles Chest Muscles Upper Arm Muscles Lower Arm Muscles Upper leg Muscles Lower Leg Muscles Main Buccinator Main frontalis Main Corrugator supercilii Main Depressor anguli oris Ma...
ASU >> BIO >> BIO 201 (Spring, 2009)
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ASU >> BIO >> BIO 201 (Spring, 2009)
Label the structures marked on the lateral aspect of this human brain using the word bank that follows*: *Not all word will be used. Cerebral Cortex, Pituitary Gland, Corpus Callosum, Thalamus, Pons, Medulla olongata, Spinal Cord, Dura Mater, Frontal...
ASU >> BIO >> BIO 201 (Spring, 2009)
Answers Nervous System Study Guide Brain and Nervous System Terminology Lab 9 Matching Olfactory Occulomotor Vestibulocochlear Vagus Hypoglossal smell eye movement hearing and balance visceral organs tongue movement Optic Accessory Trigeminal...
ASU >> BIO >> BIO 201 (Spring, 2009)
Lateral View of the Sheep Brain Dorsal Horizontal Section Anterior Posterior Ventral Olfactory bulbs Optic nerves and chiasm Look for pituitary here Medulla Lateral View of the Sheep Brain Primary Motor Cortex Central Sulcus Primary Sensory Cortex...
ASU >> BIO >> BIO 201 (Spring, 2009)
Identify the structure Frontal Lobe Identify the structure Parietal Lobe Identify the structure Temporal Lobe Identify the structure Occipital Lobe What composes the diencephalon? Thalamus Hypothalamus Infundibulum Mammillary body Pineal...
University of New England >> FIN >> Fin335 (Winter, 2003)
CHAPTER 1 AN OVERVIEW OF FINANCIAL MANAGEMENT (Difficulty Levels: Easy, Easy/Medium, Medium, Medium/Hard, and Hard) Note to Professors: We designated most of these questions as being MEDIUM. However, their difficulty as seen by students will depend ...
University of New England >> FIN >> Fin335 (Winter, 2003)
CHAPTER 2 TIME VALUE OF MONEY (Difficulty Levels: Easy, Easy/Medium, Medium, Medium/Hard, and Hard) PART I New and Revised Carryover Problems and Questions Multiple Choice: Problems FV of a lump sum 1 Answer: a EASY . What would the future valu...
University of New England >> FIN >> Fin335 (Winter, 2003)
CHAPTER 3 FINANCIAL STATEMENTS, CASH FLOW, AND TAXES (Difficulty Levels: Easy, Easy/Medium, Medium, Medium/Hard, and Hard) PART I New and Revised Carryover Problems and Questions Multiple Choice: Problems Notes to Professors: A good bit of relative...
University of New England >> FIN >> Fin335 (Winter, 2003)
CHAPTER 4 ANALYSIS OF FINANCIAL STATEMENTS (Difficulty Levels: Easy, Easy/Medium, Medium, Medium/Hard, and Hard) PART I New and Revised Carryover Problems and Questions Multiple Choice: Problems Notes to Professors: A good bit of relatively simple ...
University of New England >> FIN >> Fin335 (Winter, 2003)
CHAPTER 5 FINANCIAL MARKETS AND INSTITUTIONS (Difficulty Levels: Easy, Easy/Medium, Medium, Medium/Hard, and Hard) Multiple Choice: Conceptual Note to Professors: We designated most of these questions as being MEDIUM. However, their difficulty as se...
University of New England >> FIN >> Fin335 (Winter, 2003)
CHAPTER 7 BONDS AND THEIR VALUATION (Difficulty Levels: Easy, Easy/Medium, Medium, Medium/Hard, and Hard) PART I New and Revised Carryover Problems and Questions Multiple Choice: Problems Bond valuation 1 Answer: a EASY . The Carter Company\'s b...
University of New England >> FIN >> Fin335 (Winter, 2003)
CHAPTER 8 RISK AND RATES OF RETURN (Difficulty Levels: Easy, Easy/Medium, Medium, Medium/Hard, and Hard) PART I New and Revised Carryover Problems and Questions Multiple Choice: Problems Expected returns 1 Answer: a EASY . T. Martell Inc.\'s sto...
University of New England >> FIN >> Fin335 (Winter, 2003)
CHAPTER 9 STOCKS AND THEIR VALUATION (Difficulty Levels: Easy, Easy/Medium, Medium, Medium/Hard, and Hard) PART I New and Revised Carryover Problems and Questions Multiple Choice: Problems Expected dividend yield 1 Answer: a EASY . If D1 = $2.0...
University of New England >> FIN >> Fin335 (Winter, 2003)
CHAPTER 10 THE COST OF CAPITAL (Difficulty Levels: Easy, Easy/Medium, Medium, Medium/Hard, and Hard) PART I New and Revised Carryover Problems and Questions Multiple Choice: Problems Component cost of preferred stock 1 Answer: e EASY . Klieman ...
University of New England >> FIN >> Fin335 (Winter, 2003)
CHAPTER 11 THE BASICS OF CAPITAL BUDGETING (Difficulty Levels: Easy, Easy/Medium, Medium, Medium/Hard, and Hard) PART I New and Revised Carryover Problems and Questions Multiple Choice: Problems NPV (constant cash flows; 3 years) 1 Answer: a EASY...
University of New England >> FIN >> Fin335 (Winter, 2003)
CASH FLOW ESTIMATION AND RISK ANALYSIS CHAPTER 12 (Difficulty Levels: Easy, Easy/Medium, Medium, Medium/Hard, and Hard) PART I New and Revised Carryover Problems and Questions Multiple Choice: Problems Note to Professors: We designated many of thes...
Penn State >> CMLIT >> 108 (Spring, 2009)
Inanna and the mes According to one story, Inanna tricked the god of culture, Enki, who was worshipped in the city of Eridu, into giving her the \'Mes\'. The \'Mes\' (\"maes\") represented everything from truth to weaving to prostitution. Inanna traveled t...
Penn State >> CMPSC >> 473 (Fall, 2008)
1. Compare the pros and cons of hardware-managed and software-managed TLBs. Keep your answer to 2-3 sentences at the most. 2 What might happen if there were no Translation Lookaside Buffer? . A. Potent ially one extra memo ry access for every memo ...
Penn State >> CMPSC >> 473 (Fall, 2008)
1. Question 6.1 from your textbook. 2. Question 6.2 from your textbook. 3. Question 6.3 from your textbook. 4. Question 5.7 from your textbook. 5. In the busy waiting based definition of wait(), why is it enough to just ensure that the S- operation i...
Penn State >> CMPSC >> 473 (Fall, 2008)
What is an operating system? Piece of software that runs on a computer. Runs in privileged mode Helps user apps run and achieve goals Resource allocation Efficiency Fairness Contention Protection and Isolation System calls interface that OS provides...
Penn State >> CMPSC >> 473 (Fall, 2008)
QUIZ 1 Solution Set Q5. Compare the pros and cons of hardware-managed and software-managed TLBs. Keep your answer to 2-3 sentences at the most. A. Hardware-managed are faster than software-managed TLBs (this is essentially true when there are lots o...
hw1
Penn State >> STAT >> 319 (Fall, 2008)
Homework 1 Solutions 6.2. a. The values T0 can have are 0, 1, 2, 3, and 4. t 0 1 2 3 4 P (T0 = t) P (X1 = 0, X2 = 0) = .22 = .04 P (X1 = 0, X2 = 1) + P (X1 = 1, X2 = 0) = 2(.2)(.5) = .2 .37 .3 .09 b. By a proposal, E(T0 ) = E(X1 ) + E(X2 ) = 2 = 2.2...
hw2
Penn State >> STAT >> 319 (Fall, 2008)
Homework 2 Solutions 6.50. We know that if U = (n 1)S 2 / 2 2 , then E(U ) = n 1 and V (U ) = 2(n 1). Using n1 Equation (6.12) with X = U , k = 1/2, and = n 1 we get E( U ) = 2(n/2)/[(n 1)/2]. a. E(S 2 ) = E[ 2 U/(n 1)] = 2 E(U )/(n 1) = ...
hw3
Penn State >> STAT >> 319 (Fall, 2008)
Homework 3 Solutions 7.4. a. X Y is an unbiased estimator for 1 2 since E(X Y ) = 1 2 . To see this, E(X Y ) = E(X) E(Y ) = 1 m m E(Xi ) i=1 1 n n E(Yi ) = 1 2 i=1 For the observed data, the estimate of 1 2 is x y = 121.44 113.80 = 7....
Penn State >> STAT >> 319 (Fall, 2008)
Section 6.1 6. (a) X1 29.7(employee 1) 29.7(employee 1) 29.7(employee 1) 29.7(employee 1) 29.7(employee 1) 33.6(employee 2) 33.6(employee 2) 33.6(employee 2) 33.6(employee 2) 30.2(employee 3) 30.2(employee 3) 30.2(employee 3) 33.6(employee 4) 33.6(em...
Penn State >> STAT >> 319 (Fall, 2008)
In an experiment, with n=13 observations, the estimated regression line is y=0.365+ 0.967x. I am giving you the following MSE=0.0373 and MSR=1.0427. a) Calculate SSE. b) Calculate the estimated variance of the regression c) Calculate the Coefficient ...
UCLA >> CEE >> 147 (Winter, 2009)
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UCLA >> CEE >> 101 (Winter, 2009)
Exercise 1.4.1 (p. 11) Statics by Sheri D. Sheppard and Benson H. Tongue Copyright 2005 by John Wiley Sons...
UCLA >> CEE >> 101 (Winter, 2009)
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UCLA >> CEE >> 101 (Winter, 2009)
PROBLEM 4.6.9 GOAL : To determine (a) the resultant force in vector notation in the xy coordinates, (b) the resultant force in vector notation in the x y coordinates, (c) that |TR | = |TR | GIVEN : Figure E.4.6.9. ASSUME : Planar. DRAW : FORMULATE ...
hw3
UCLA >> CEE >> 101 (Winter, 2009)
C&EE 121 Foundations and Earth Structures Assignment 3 DUE JANUARY 27, 2009 Design of Prefabricated Vertical Drains Prof. J.P. Stewart Winter, 2009 The results for Assignment No. 1 (now posted on the web site) are that 15 feet of fill is required t...
UCLA >> CEE >> 101 (Winter, 2009)
Exercise 5.2.9 (p. 174) Statics by Sheri D. Sheppard and Benson H. Tongue Copyright 2005 by John Wiley Sons...
UCLA >> CEE >> 101 (Winter, 2009)
...
UCLA >> CEE >> 147 (Winter, 2009)
Tall Building Team Project. Tall Building Team Project Work Product. PART I: Preliminary Site Assessment Your design team is required to conduct a preliminary site analysis to understand the site, the proposed program, and the surrounding environmen...
UCLA >> CEE >> 147 (Winter, 2009)
Tall Building Team Project. Part III Site Plan Based on the tall building project description, the site assessment, and the zoning analysis prepare a site plan that places the key architectural elements on the project site. To help prepare for the ...
Minnesota Colleges >> MRKT >> 317 (Spring, 2009)
Chapter 1 Tuesday, January 13, 2009 2:22 PM Product Manager is responsible for: 1. 2. 3. 4. 5. 6. 7. Name Package Customer Channel Promotion Development Advertising Product manager will NOT decide dropping or adding products Product manager deals mo...
Michigan >> PHYSICS >> 240 (Spring, 2009)
F= Forces add like vectors Potential Engergy: U = Potential Energy in Capacitor: forces are always equal E = U = = = = = ...
Michigan >> PHYSICS >> 240 (Spring, 2009)
V=IR Resistors in Series: Req = R1 + R2+ Current is constant, Voltage Changes Resistors in Parallel: 1 = + + Re q Moving charge or current creates magnetic field that exerts a force on any other moving charge or current. its proportional to ma...
Michigan >> PHYSICS >> 240 (Spring, 2009)
Mutual Inductance: units = di di Henry 2 = - M 1 ; 1 = - M 2 dt dt M= = L-R-C Circuits: \' = 1 R2 LC 4L2 Waves: E = ; B = Emax = ; v = Self Inductance: Vab = ; L= AC: I rav = ; I rms = ; Vrms = i = ; v = + Resist or ...
Michigan >> PHYSICS >> 240 (Spring, 2009)
Constructive: same freq, constant phase relationship, r2 = , amplitudes add Destructive: amplitudes subtract, r2 = + 2 slit interference: Constructive: d sin = Destructive: d sin = + Distance from center to mth brightest: ym = (sm...
Michigan >> MATH >> 216 (Spring, 2009)
Math 216 Study Group 9/18/08 1. Solve the following equations: a. y = 4x3 y; y(1) = -3 b. 3xy + y = 12x 2. The rate of change of the alligator population P(t) is proportional to the square of its size. If there are a dozen gators in 1988 and 2 doze...
Michigan >> MATH >> 216 (Spring, 2009)
Math 216 Study Group 9/25/08 1. 2. Given dx/dy=-2xy and y0=2 approximate the solution on the interval [0, 1/2] and compare with the actual value at x=1/2. h=0.1. Find the general solutions to the following: a. y + y + y = 0 b. y(3) 2y + 9y 18 = 0 3...
Uni. Helsinki >> THEORETICA >> 53704 (Fall, 2006)
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Uni. Helsinki >> THEORETICA >> 53704 (Fall, 2007)
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Uni. Helsinki >> THEORETICA >> 53705 (Winter, 2005)
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Uni. Helsinki >> THEORETICA >> 53705 (Winter, 2009)
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Uni. Helsinki >> THEORETICA >> 53704 (Fall, 2007)
Final exam answers, Fall 2007...
Uni. Helsinki >> THEORETICA >> 53704 (Spring, 2006)
Matemaattiset apuneuvot I, SL 2006 Kurssikoe 23.10.2006 Oikeat vastaukset 1. x lim ln e2x 3 = 3 e2x+3 + 7 2. Projisoimalla tai yritett kytten. wu = 4u Niinp w = 4u + (w 4u) = (4i 12j) + (6i + 2j + 10k). 3. Kytetn tunnettua binomisarjaa. ...
Uni. Helsinki >> THEORETICA >> 53704 (Fall, 2004)
Matemaattiset apuneuvot I, SL 2004 Kurssikoe 27.10.2004 Oikeat vastaukset 1. Mrit raja-arvot a) x lim 2x2 + 1 2 = 2 6 + x 3x 3 b) n0 lim 1 (1 xn ) = ln x. n Tarkkana l\'Hospitalissa, mink muuttujan suhteen derivoidaan! 2. Binomisarja E=...
Uni. Helsinki >> THEORETICA >> 53705 (Winter, 2008)
Matemaattiset apuneuvot II, SL 2008 Kurssikoe 16.12.2008, klo: 8.00-12.00 MALLIV ASTAUKSET Tee jokainen tehtv eri konseptille (a- ja b -kohdat samalle paperille). Laita jokaiseen paperiin nimi ja opiskelijanumero. Laskimia ja taulukoita ei saa kytt....
Uni. Helsinki >> THEORETICA >> FYMM Ib (Winter, 2008)
FYMM Ib Laskuharjoitus 1 syksy 2008 Palautetaan viimeistn ma 3.11. klo 12.00 1. Osoita, ett integraali 0 ezt dt mrittelee analyyttisen funktion alueessa Re z > 0. t2 + 1 2. Osoita, ett sarjana mritelty funktio F (z) = n=1 (1)n1 z 2n on in...
Uni. Helsinki >> THEORETICA >> FYMM 1B (Winter, 2008)
FYMM Ib Laskuharjoitus 2 syksy 2008 Palautetaan viimeistn ma 10.11. klo 12.00 1. Osoita, ett a) xa = o xb , x +, a < b; b) xa = o xb , x +0, a > b; c) ln x = o (xa ), x +, a > 0. 2. Osoita, ett x t2 + 1 dt = x2 1 + ln x + O(1) , x + . 2 2 ...
Uni. Helsinki >> THEORETICA >> FYMM IB (Winter, 2008)
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Stony Brook University >> BIO >> 203 (Spring, 2009)
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UCSD >> ECON >> 100B (Winter, 2009)
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UCSD >> ECON >> 100B (Winter, 2009)
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UCSD >> ECON >> 100B (Winter, 2009)
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UCSD >> ECON >> 100B (Winter, 2009)
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UCSD >> ECON >> 100B (Winter, 2009)
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UCSD >> ECON >> 100B (Winter, 2009)
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UCSD >> ECON >> 100B (Winter, 2009)
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UCSD >> ECON >> 100B (Winter, 2009)
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UCSD >> ECON >> 100B (Winter, 2009)
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UCSD >> ECON >> 100B (Winter, 2009)
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UCSD >> ECON >> 100B (Winter, 2009)
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UCSD >> ECON >> 100A (Fall, 2008)
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UCSD >> ECON >> 100A (Fall, 2008)
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UCSD >> ECON >> 100A (Fall, 2008)
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