MATH 148, Calculus II for Biological Sciences

Transcription

1 Math 148 Syllabus Curse number and title MATH 148, Calculus II fr Bilgical Sciences Term Spring 2019 Lecture (Sectins ): MWF 10:20am-11:10am in RICH 114 Lecture (Sectins ): MWF 11:30am-12:20pm in RICH 114 Class times and lcatin Recitatin fr Sectin 501: Tues & Thurs 2:20pm-3:10pm in BLOC 120 Recitatin fr Sectin 502: Tues & Thurs 3:55pm-4:45pm in BLOC 121 Recitatin fr Sectin 503: Tues & Thurs 5:30pm-6:20pm in BLOC 164 Recitatin fr Sectin 504: Tues & Thurs 2:20pm-3:10pm in HRBB 224 Recitatin fr Sectin 505: Tues & Thurs 3:55pm-4:45pm in CHEM 2121 Recitatin fr Sectin 506: Tues & Thurs 5:30pm-6:20pm in BLOC 161 INSTRUCTOR INFORMATION Name address Office hurs Help Sessins Heather Ramsey Tues 10am-11am in BLOC 241B Wed 2pm-3pm in BLOC 241B Thurs 11am-12pm in BLOC 241B Day Time in Rm TBD Day Time in Rm TBD COURSE DESCRIPTION AND PREREQUISITES Title and Descriptin: Math 148 Calculus II fr Bilgical Sciences (4 credit hurs). Intrductin t integral calculus in a cntext that emphasizes applicatins in the bilgical sciences; rdinary differential equatins and analytical gemetry. Credit will nt be given fr mre than ne f MATH 148, MATH 152 and MATH 172. Prerequisite: MATH 147 r apprval f instructr. LEARNING OBJECTIVES This curse is fcused n quantitative literacy in mathematics with an emphasis n real wrld applicatins, especially t the bilgical sciences. Upn successful cmpletin f this curse, students will be able t: apply techniques fr integratin, including integratin by parts and partial fractin decmpsitin. identify and cmpute imprper integrals using limits. justify why an imprper integral cnverges r diverges by applying the cmparisn therem. apprximate functins with Taylr plynmials and evaluate the errr in the apprximatin by using the Taylr inequality. slve separable rdinary differential equatins. understand hw expnential ppulatin grwth is mdeled by a cnstant per capita grwth rate while lgistic ppulatin grwth incrprates density dependence. find equilibria f differential equatins and analyze their stability bth graphically and by apply varius techniques fr slving systems f equatins, including Gaussian eliminatin. apply basic matrix algebra skills including additin, subtractin, scalar multiplicatin, and multiplicatin f matrices and find the inverse f a matrix and be able t use matrix algebra t slve prblems. cmpute and interpret eigenvalues and eigenvectrs fr 2 2 matrices.

2 use matrices in bilgical applicatins, including the study f age-structured ppulatins. interpret 2 2 linear maps applied t 2 1 vectrs. add, subtract, and scale vectrs and cmpute dt prducts. use vectrs in applicatins, including finding equatins f lines and planes. understand cncepts f limits and cntinuity fr multivariable functins. use partial derivatives and linear apprximatins fr slving real-wrld prblems. understand and explain the cncepts f equilibria and stability fr bilgical systems f difference equatins. crrectly slve applied prblems and write the slutins in a cherent fashin. cnstruct and analyze linear and nnlinear systems f differential equatins applied in bilgy and medicine. Cre Objectives Critical Thinking The fllwing critical thinking skills will be assessed n exams and ther assignments. Students will: Analyze integrals and determine the prper technique fr integratin, including the integratin by parts and partial fractin decmpsitin methds. Identify and cmpute imprper integrals using limits. Apprximate functins with Taylr plynmials and evaluate the errr in the apprximatin by using the Taylr inequality. Slve separable rdinary differential equatins. Find equilibria f differential equatins and analyze their stability bth graphically and by Apply techniques fr slving systems f equatins, including Gaussian eliminatin. Learn basic matrix algebra skills including additin, subtractin, scalar multiplicatin, and multiplicatin f matrices and be able t find the inverse f a matrix. Creatively apply matrix algebra t slve systems f equatins. Cmpute and interpret eigenvalues and eigenvectrs fr 2 2 matrices. Understand and apply cncepts f limits and cntinuity fr multivariable functins. Cmpute partial derivatives and linear apprximatins t slve real-wrld prblems. Cmpute equilibria and analyze their stability fr bilgical systems f difference equatins. Slve applied prblems and write the slutins in a cherent fashin. Analyze and cnstruct linear and nnlinear systems f differential equatins applied in bilgy and medicine. Cmmunicatin Skills The fllwing cmmunicatin skills will be assessed n exams, during lecture, and n ther assignments. Students will: Justify why an imprper integral cnverges r diverges by applying the cmparisn therem. Understand hw expnential ppulatin grwth is mdeled by a cnstant per capita grwth rate while lgistic ppulatin grwth incrprates density dependence. Find equilibria f differential equatins and analyze their stability bth graphically and by Apply basic matrix algebra skills including additin, subtractin, scalar multiplicatin, and multiplicatin f matrices and finding the inverse f a matrix t slving prblems. Interpret the actin f 2 2 linear maps applied t 2 1 vectrs bth graphically and numerically. Add, subtract, and scale vectrs and cmpute dt prducts. Use vectrs in applicatins, including finding equatins f lines and planes. Slve applied prblems and write the slutins in a cherent fashin. Cnstruct and analyze linear and nnlinear systems f differential equatins applied in bilgy and medicine. Empirical and Quantitative Skills The fllwing empirical and quantitative skills will be assessed n exams and ther assignments. Students will: Apply techniques fr integratin, including integratin by parts and partial fractin decmpsitin. Slve separable rdinary differential equatins. Find equilibria f differential equatins and analyze their stability bth graphically and by

3 Cmpute and interpret eigenvalues and eigenvectrs fr 2 2 matrices. Cmpute the Leslie matrix assciated with a given data set pertaining t an age-structured ppulatin and use it t make predictins f ppulatin sizes fr future generatins. Use partial derivatives and linear apprximatins fr slving real-wrld prblems. Cmpute equilibria and analyze their stability fr bilgical systems f difference equatins. Manipulate given infrmatin t cnstruct and analyze linear and nnlinear systems f differential equatins applied in bilgy and medicine. TEXTBOOK AND OTHER REQUIRED MATERIALS Calculus fr Bilgy and Medicine, Furth Editin, by Claudia Neuhauser and Marcus Rper, Pearsn 2017, ISBN-13: Fur gray TAMU Scantrns (8.5 in by 11 in) Printed cpy f each chapter f lecture ntes, available in ecampus, brught t all class meetings Optinal: A fur-functin calculatr, such as the Sharp EL233SB Pcket Calculatr Optinal: A flder t rganize yur lecture ntes and a ntebk in which t wrk the suggested hmewrk prblems CALCULATOR POLICY The nly calculatr that will be allwed in this curse is a fur-functin calculatr, such as the Sharp EL233SB Pcket Calculatr. Graphing calculatrs and scientific calculatrs will nt be allwed. A fur-functin calculatr may be used n all recitatin assignments, quizzes, and exams. GRADING POLICIES The curse grading will be based n the results f three midterm exams, weekly recitatin assignments and quizzes, and a cmprehensive final exam. Midterm Exams: Each midterm exam will cnsist f tw parts: multiple chice (n partial credit) and wrk ut (partial credit pssible). The multiple chice part f the exam will be administered during recitatin sessins, and 50 minutes will be given. The wrk ut part f the exam will be administered during lecture, and 50 minutes will be given. Bth parts f each exam are clsed bk. Students are nt allwed t use ntes, frmula sheets, bks, r electrnic devices, with ne exceptin an apprved 4-functin calculatr may be used fr all parts f all exams. The Sharp EL233SB Pcket Calculatr is an example f an apprved 4-functin calculatr that can be purchased fr less than $4 at Wal-Mart. Students need t bring a N. 2 pencil and their TAMU student ID t each part f each exam. Students will als be asked t prvide 4 gray TAMU Scantrns during the first week f classes. Recitatin Assignments: A set f prblems will be assigned during recitatin each Tuesday and will be due during that class perid. Students may wrk n these prblems in grups f up t three. These assignments will be graded n a 10-pint scale, and n make-up assignments will be given withut written verificatin f a University excused absence. Cntact yur TA with verificatin that yur absence is University excused and t schedule a make-up assignment. TA fr Sectins : Arpan Pal, arpantamu@tamu.edu TA fr Sectins : Vivian Deng, vivian.deng@math.tamu.edu Quizzes: Annunced and unannunced quizzes and will be given thrughut the semester during Thursday recitatins and pssibly during MWF lecture. Each quiz will be graded n a 10-pint scale, and n make-up quizzes will be given withut written verificatin f a University excused absence. One quiz grade will be drpped. Cntact yur TA with verificatin that yur absence is University excused and t schedule a make-up quiz (see abve fr addresses). Hmewrk Assignments: Hmewrk assignments will be psted n the curse website. These assignments will nt be cllected fr a grade, but cmpleting them is essential t ding well in the curse. I will assume that all students have wrked all prblems, s all material cvered in the hmewrk assignments is fair game fr all exams and quizzes.

4 Final Exam: The final will be a cmprehensive, all multiple chice exam. N partial credit will be given. Nte that the scre earned n the final exam can be used t replace the lwest f the first three midterm exam grades if the final exam scre is higher than this lwest scre. At mst ne grade replacement will be made, and the final exam grade cannt be drpped (meaning the final is required fr all students). Exam grades assciated with acts f academic dishnesty cannt be replaced by the final exam scre. Curse Timeline and Percentages Activity Date Weight Exam I Feb. 14 and 15 18% Exam II Mar. 21 and 22 18% Exam III * Apr. 17 and 18 18% Recitatin Assignments Weekly 10% Quizzes Weekly 13% Final Exam : May 6, 8-10am 23% : May 7, 10:30am-12:30pm TOTAL 100% *Due t the reading day n Friday, April 19, Exam 3 will be n a Wednesday and Thursday. Grading Scale Range Grade 90% Curse Average A 80% Curse Average < 90% B 70% Curse Average < 80% C 60% Curse Average < 70% D Curse Average < 60% F Excused absences: Attendance is mandatry and may affect yur grade. Fr excused absences we refer the student t Student Rule 7 at Excuses fr absences during an exam must be substantiated by apprpriate dcumentatin. N make-up recitatin assignments, quizzes, r exams will be given withut an fficial, written, University Excuse. Falsificatin f dcumentatin is a vilatin f the Aggie Hnr Cde. Yu must ntify me (ramsey@math.tamu.edu) fr exams r yur TA fr recitatin assignments and quizzes in advance t ensure the right t a make-up. If advance ntice is nt pssible (i.e. sudden illness), yu MUST cntact me r yur TA, as apprpriate, within TWO wrking days f the missed exam/assignment/quiz; therwise, yu frfeit the right t a make-up. An absence fr a nn-acute medical service r regular check-up des nt cnstitute an excused absence. Please nte that I will NOT accept the Explanatry Statement fr Absence frm Class frm as sufficient written dcumentatin f an excused absence. Missed Recitatin Assignments and Quizzes: Yur teaching assistant will crdinate with yu fr making up a recitatin assignment r quiz. TA fr Sectins : Arpan Pal, arpantamu@tamu.edu TA fr Sectins : Vivian Deng, vivian.deng@math.tamu.edu Missed Exams: If yu have a University apprved absence fr missing an exam, yu will be expected t make up yur exam accrding t the Math Department s Make-up Schedule that can be fund at

5 starting with the first ptin fr each exam. Only if yu have a University apprved absence fr the day f the exam and the previus makeup day will yu be allwed t use the later ptins r have ther arrangements made. Yu must discuss ( is fine) the need fr a make-up exam with me befre ging t a scheduled time. AMERICANS WITH DISABILITIES ACT (ADA) The Americans with Disabilities Act (ADA) is a federal anti-discriminatin statute that prvides cmprehensive civil rights prtectin fr persns with disabilities. Amng ther things, this legislatin requires that all students with disabilities be guaranteed a learning envirnment that prvides fr reasnable accmmdatin f their disabilities. If yu believe yu have a disability requiring an accmmdatin, please cntact Disability Services, currently lcated in the Disability Services building at the Student Services at White Creek cmplex n west campus r call Fr additinal infrmatin visit ACADEMIC INTEGRITY Fr additinal infrmatin please visit: An Aggie des nt lie, cheat, r steal, r tlerate thse wh d. In this curse students can discuss hmewrk assignments and slutins. Hwever, it is NOT permissible t cpy hmewrk slutins frm anther student. It is NOT permissible t discuss any aspect f any test r examinatin until ALL students have cmpleted the exam. The penalties fr vilating this plicy will range frm an F n an assignment r test, t failing in the curse. Yu are encuraged t wrk tgether n the hmewrk assignments, but d nt cpy anther student s wrk. Cpying wrk dne by thers, either in class r ut f class, is an act f schlastic dishnesty and will be prsecuted t the full extent allwed by University plicy. During recitatin, yu will be allwed t wrk in grups f up t three students. All grup members are expected t cntribute t the assignment. If the teaching assistant finds that ne r mre members f a grup are nt participating, and if this is a first ffence, then all members f the grup will be asked t wrk individually fr the rest f the perid and submit individual assignments. If this happens n a subsequent assignment, ALL members f the grup will be submitted t the Aggie Hnr Office fr schlastic dishnesty. Fr example, if the name f a student wh was absent appears n that day s recitatin assignment, ALL students in that grup will receive a 0 n the assignment and be reprted t the Aggie Hnr Office. Using an unauthrized calculatr during an exam r quiz will result in a zer n the assignment. Als, cell phne use during an exam, quiz, r recitatin assignment will result in a zer n the assignment. These vilatins f the Aggie Hnr Cde will be reprted. Always abide by the Aggie Cde f Hnr: An Aggie des nt lie, cheat, r steal r tlerate thse wh d. Please refer t Hnr Cuncil Rules and Prcedures at fr mre infrmatin n academic integrity and schlastic dishnesty. I have served as a member f the Aggie Hnr Cuncil, s I take these matters very seriusly. EXTRA HELP AND PREPARING FOR EXAMS Yur Instructr: I want each and every ne f my students t be successful in this class. Please feel free t ask questins in class. If yu need mre help, cme by my ffice during ffice hurs r make an appintment t see me. Remember, I am here t help, but I cannt d that if I dn t knw that there is a prblem. Recitatin and TA: Yu will attend recitatin with a teaching assistant twice per week. During these class perids, yu will be able t ask the TA t explain hmewrk prblems and review any tpics frm lecture, s be sure t take advantage f this class time. Yur Classmates: Get t knw yur classmates. Frm study grups and wrk n hmewrk prblems utside f class.

6 Practice: Wrking ALL f the hmewrk prblems frm yur textbk is essential t ding well in this curse. If yu struggle with these prblems the first time yu wrk them, be sure t wrk them again AND wrk ther prblems frm the textbk that are similar. I strngly recmmend that yu practice prblems DAILY. Dr. Glenn Lahdny s Math 148 Web Page: Dr. Lahdny has very generusly ffered his curse materials fr ur use. He has practice prblems fr each exam, alng with blank cpies f his lecture ntes, psted at Free Tutring!!! (a.k.a. Help Sessins): Help sessins are an pprtunity fr yu t ask questins and get help with yur hmewrk. The schedule fr fall help sessins can be fund n my webpage. These sessins are cme-and-g, i.e., yu can cme at any pint during the help sessin and leave whenever yu want. OTHER CLASS POLICIES Plicy: Check yur TAMU accunt and ecampus EVERY day. Yu are respnsible fr any infrmatin I pst in ecampus and send thrugh . If yu send an t me, be sure t include yur full name, Math 148, and sectin number in the message. NOTE: Because f privacy rights, I cannt discuss grades via r ver the phne. Cell Phne/Laptp Cmputer Plicy: As a curtesy t me and yur classmates, and t imprve student participatin and reduce distractins, all cell phnes and laptp cmputers (unless they can be laid flat in tablet mde and are being used fr ntetaking) must be OFF and put away during lecture. If yu disrupt class r distract yur neighbr r distract me with yur cell phne r ther electrnic device, yu may be asked t leave class. COURSE TOPICS (Tentative weekly schedule) WEEK TOPIC REQUIRED READING 1 Integratin by Parts, Partial Fractins Sectins: 7.2, Partial Fractins, Imprper Integrals, Taylr Apprximatin Sectins: 7.3, 7.4, Taylr Apprximatin, Slving Differential Equatins Sectins: 7.6, Equilibria and Their Stability, Applicatins Sectins: 8.2, Linear Systems, Matrices Sectins: 9.1, 9.2 Exam 1 (Cvering , 7.6, ) 6 Linear Maps, Eigenvalues, Eigenvectrs, the Leslie Matrix Sectins: 9.3, Analytic Gemetry, Functins f Several Variables, Limits and Cntinuity Sectins: 9.5.1, 9.5.2, 10.1, Limits and Cntinuity fr Functins f Several Variables, Sectins: 10.2, 10.3 Partial Derivatives 9 Tangent Planes, Differentiability, Linearizatin Sectins: 10.4 Exam 2 (Cvering Sectins , ) 10 Chain Rule fr Functins f Tw Variables, Maxima and Sectins: , Minima 11 Maxima and Minima, the Hessian Matrix, Systems f Sectins: , 10.9 Recurrence Equatins 12 Hmgeneus Linear First-rder Systems f Differential Sectins: 11.1, 11.2 Equatins, Applicatins 13 Nnlinear Autnmus Systems Sectins: 11.3 Exam 3 (Cvering Sectins 10.4, 10.5, 10.7, 10.9, 11.1, 11.2) 14 Ltka-Vlterra Mdel fr Interspecific Interactins Sectins: Catch up and Review