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This 11 page Class Notes was uploaded by Alex Medhurst on Sunday October 11, 2015. The Class Notes belongs to MAT 130 at Davidson College taught by Laurie Heyer in Fall. Since its upload, it has received 12 views. For similar materials see /class/221247/mat-130-davidson-college in Mathematics (M) at Davidson College.
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Date Created: 10/11/15
Calculus amp Modeling 939 ll 9 IV 3quot 13 a I x 1 1 O 1 1 Introduction Mathematics in Medicine and Biology Roadside Repair Wouldn t it be nice to know a little about what s under the hood Under the Life Science Hood Metabolism Ecology Neuroscience Immunology Genomics Cardiology Cancer Epidemiology Pharmacology Population biology Medical News Mathematical Model Clarifies Progression of HIV To AIDS Mathematical Model To Predict Spread And Continue Fight Against Flesh Eating Bacteria SugerBug Mathematical Tools For Predicting Facial Surgery Results Mathematical Analysis Could Aid In Predicting Cancer Cases New Research Proiect Curinq Cancer With Mathematics A New Mathematical Method Provides A Better Way To Analvze Noise Could Lead To Improved Cochlear lmglants Proteins Anchor Memories In Our Brain Increasing Adoption of Computational BIOIOQV TOOIS In Drug D39scoverv Indus try Mathematics Used To Discern Immune Resgonse To Infectious Diseases Tumour 39weather Forecast39 Gives New Insights In Cancer The Basics of MRI ChaQter 2 THE MATHEMATICS OF NMR Logarithms and Decibels Exponential Functions Trigonometric Functions Differentials and Integrals Vectors Matrices Rotation Matrices Coordinate Transformations Convolutions Joseph P Homak PhD Imaginary Numbers Copy grn 1m2007JPJhnnkA yns Reserved The Fourier Transform MATH AWARENESS WEEK APRIL 1994 MATHEMATICS AND MEDICINE At Los Alamos National Laboratory in New trying to explain why the virus that causes AIDS is so deadly The researchers do not study AIDS patients nor do they follow the effects ofthe virus human 39mmunode ciencyvirus or HIV in animals such as mice They use mathematics How Mathematics Coupled Experiment Revealed Nature of HIV Infection The mathematIcs ofthe models are sImIlar to those used in population dynamics and include ordinary differential equations Nevertheless t e mo els are coming up short of an accurate picture ofthe attack of HIV One reason is that HIV can hide in speci c locations ofthe body quotTo explain this requires another generation of modelsquot m Perelson notes He and colleagues are now WEI developing these improved mode 5 I H WWI MATH AWARENESS MONTH APRIL 1999 MATHEMATICS AND BIOLOGY During the course of a typical human life the VnAL BuyHMS heart beats about 2 billion times Yet in spite Mathematics in the Heart ofthe obvious reliability ofthe heart nearly half ofthe deaths in the United States are due to the failure ofthe heart to beat properly Mathematics is at the quotheartquot oftrying to understand how the heart beats and why it fails to beat properly To follow what individual cells do requires tracking how ions move and how voltages change To determine how cells communicate to each other requires a description of currents between cells To follow how a signal propagates requires a description of the geometry ofthe medium the orientation of bers the thickness of walls etc And all ofthese descriptions use the language of mathematics MATH AWARENESS MONTH APRIL 2002 MATHEMATICS AND THE GENOME The NIH can wage an effective war on disease only if we as a nation and a scienti c community not just as a single agency harness the energies of many disciplines not just biology and medicine These allied disciplines range from mathematics engineering and computer sciences to sociology anthropology and behavioral sciences as well as chemistry and physics Biology is rapidly becoming a science that demands more intense mathematical and physical analysis than biologists have been accustomed to using For example such analysis will be required to understand the workings of cell signaling systems In the last twenty years molecular and cell biologists have moved much closer to the quotradical physical explanationquot of cell behavior that the physicist Max Delbruck called for in 1949 I take this opportunity of Math Awareness Month 2002 to encourage young people with skills in these needed quantitative and physical elds tojoin us in working collaboratively towards Delbruck39s quotradical physical explanationquot for biological systems Dr Harold Varmus President Memorial Sloan Kettering Cancer Center former Director National Institutes of Health and Nobel Prize Winner Medicine 1989 MATH AWARENESS MONTH APRIL 2007 MATHEMATICS AND THE BRAIN One of the most exciting challenges in modern science is to fully understand the human brain and its mechanisms Mathematics plays a vital role in this research to understan e mechanisms and function of the human brain from its smallest components to the whole brain The 1963 Nobel Prize was awarded to Alan Lloyd Hodgkin and Andrew Huxley for a model that uses differential equations to ap rox39mate the electrical characteristics of excitable cells Their origina mo e escri e the ionic mec an39sms underlying the initiation and propagation of action potentials int e squi giant axon an ed to many later developments to model brain activity at the single neuron level VSTEM CHIS m HELP FEEDBACK SUBSCRIPTIONS ARCHIVE SEARCH TABLE OF CONTENTS First published online August 25 2005 Stem Cells Vol 24 No 2 February 2006 pp 368375 doi101634stemcels2005 0148 wwtemCellscom 2006 AlghaMed Press TISSUE SPECIFIC STEM CELLS Cell Size Correlates with Phenotvpe and Proliferative Capacity in Human Corneal Epithelial Cells A Mathematical Model of Cell Size httplsberkeleyedubiogallerymcbwoundhtml estimated scale bar added
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