Difference between revisions of "Math 251-102 Fall 2022"

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=Course info=
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'''Description.''' Vectors and three-dimensional analytic geometry; curves and surfaces; functions of several variables, calculus of several variables; partial derivatives; gradient and linearization; multiple integrals; volume and surface area.
  
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'''Thursdays, 5-6:15pm EDT'''<br />
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'''Instructor.''' Casian Pantea https://math.wvu.edu/∼capantea/
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[https://wvu.zoom.us/j/96317244165?pwd=YVJGWHdxb2lGUHlkZEdRT1NPRFFsUT09 zoom link] (password ''euclid2022'')
 
  
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'''Schedule.''' Mondays, Wednesdays, Fridays 9:50-11AM, Hodges 338
  
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The 2022 WVU Junior Math Club is a mathematical enrichment program open to middle school and high school students in West Virginia and Southeast Pennsylvania. We meet on Zoom every Tuesday in Spring 2022 and we discuss various mathematical topics with special emphasis on competition-type problems. The club is supported by an [https://www.maa.org/programs-and-communities/outreach-initiatives/dolciani-mathematics-enrichment-grants MAA Dolciani grant] and the West Virginia University [https://mathanddata.wvu.edu School of Mathematical and Data Sciences]. If you would like to participate, or for additional info please contact Casian Pantea at [mailto:cpantea@math.wvu.edu cpantea@math.wvu.edu].  
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'''Office hours.''' Mondays 11:10AM-12:10PM and 5PM-6PM, Wednesdays 2:30-3:30 PM in Armstrong Hall 305B; and by appointment on zoom: https://wvu.zoom.us/j/92855687691
  
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= Schedule (updated as we go)=
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'''Textbook.''' Calculus: Early Transcendentals, 8th Edition, by James Stewart; we cover Chapters 12-16.
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{| cellpadding="8"
 
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!align="left" | date 
 
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!align="left" | topic
 
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!align="left" | instructor
 
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!align="left" | materials
 
  
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'''Prerequisite.''' C or better in Math 156 is required;
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=Evaluation=
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'''Grading scheme'''
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*30% Final Exam
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*2x20% Midterms
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*20% Quizzes
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*10% Homework
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Letter grades will be assigned as follows
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{|
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|-
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|'''A'''
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|>=90%
 
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|-
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| February 3
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|'''B'''
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| Geometry 1
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|80-90%
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| Pantea
 
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|[[#February 3  | Congruences, similarity and other interesting triangle-related stuff]]
 
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|
 
 
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|-
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| February 7
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|'''C'''
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| Algebra 1
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|70-80%
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| Voitiuk
 
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|[[#February 10  | Algebraic inequalities]]
 
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|
 
 
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|-
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| February 3
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|'''D'''
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| Combinatorics 1
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|60-70%
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| Goldwasser
 
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|[[#February 17  | Counting, Pascal triangle and other combinatorial identities ]]
 
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|
 
 
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|-
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| February 24
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|'''F'''
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| Probability 1
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|<60%
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| TBD
 
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|[[#February 24  | Expected values, or how to win big at the lottery]]
 
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|
 
 
|}
 
|}
  
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=Description and notes=
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=Schedule of topics=
  
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===February 3===
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{| class="wikitable" style="margin:auto"
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|-
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We'll talk about some geometry gems in a triangle (e.g. Ceva's Theorem), and about some other less known things. For example, did you know that all triangles are equilateral? That's a joke, of course; or is it? Come and find out.
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! Date !! Topic !! Section !! Other
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|-
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| Wed Aug 17 || 3D coordinate system, vectors || 12.1 ||
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|-
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| Fri Aug 19 || Vectors || 12.2 ||
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|-
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| Mon Aug 22 || Dot product || 12.3 ||
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|-
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| Wed Aug 24 || Cross product || 12.4 ||
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|-
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| Fri Aug 26 || Lines and planes || 12.5 ||
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|-
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| Mon Aug 29 || Problem session || 12.1-12.5 ||
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|-
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| Wed Aug 31 || Quadric surfaces || 12.6 ||
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|-
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| Fri Sep 2 ||Quadric surfaces || 12.6 || [[Media:25122Q1Soln.png|'''Quiz 1''']]
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|-
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| Wed Sep 7 || Review || 12.1-12.6 ||
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|-
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| Fri Sep 9 || Vector functions and curves || 13.1 || [[Media:25122HW1.png|'''HW 1 due''']]
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|-
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| Mon Sep 12 || Derivatives and integrals || 13.2 ||
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|-
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| Wed Sep 14 || Arc length and curvature || 13.3 ||
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|-
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| Fri Sep 16 || Motion in space || 13.4 || [[Media:25122Q2Soln.png|'''Quiz 2''']]
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|-
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| Mon Sep 19 ||  ||  ||
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|-
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| Wed Sep 21 || Problem session  ||  ||
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|-
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| Fri Sep 23 || Functions of multiple variables  || 14.1  ||[[Media:25122HW2.png|'''HW 2 due''']]
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|-
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| Mon Sep 26 || Review ||  ||
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|-
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| Wed Sep 28 ||'''Midterm 1''' ||  ||[[Media:25122MT1Soln.png|'''Midterm 1''']]
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|-
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| Fri Sep 30 || Functions of multiple variables  || 14.1  ||
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|-
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| Mon Oct 3 || Limits and continuity || 14.2 ||
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|-
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| Wed Oct 5 || Partial derivatives || 14.3 ||
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|-
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| Mon Oct 10 || Tangent planes || 14.4 ||
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|-
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| Wed Oct 12 || Chain rule || 14.5 || [[Media:25122Q3Soln.png|'''Quiz 3''']]
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|-
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| Fri Oct 14 || Directional derivatives and gradients || 14.6 || [[Media:25122HW3.png|'''HW 3 due''']]
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|-
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| Mon Oct 17 || Directional derivatives and gradients || 14.6 ||
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|-
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| Wed Oct 19 || Maxima and minima || 14.7 ||
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|-
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| Fri Oct 21 || Lagrange multipliers ||14.8  || [[Media:25122Q4Soln.png|'''Quiz 4''']]
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|-
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| Mon Oct 24 || Problem session ||  ||
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|-
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| Wed Oct 26 || Double integrals over rectangles || 15.1 ||
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|-
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| Fri Oct 28 || Double integrals over general domains || 15.2 || [[Media:25122HW4.png|'''HW 4 due''']]
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|-
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| Mon Oct 31 || Polar coordinates || 15.3 ||
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|-
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| Wed Nov 2 || Polar coordinates || 15.3 ||
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|-
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| Fri Nov 4 || Surface area || 15.5 || [[Media:25122Q5Soln.png|'''Quiz 5''']]
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|-
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| Mon Nov 7 || Review ||  ||
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|-
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| Wed Nov 9 ||'''Midterm 2'''||  ||[[Media:25122MT2Soln_part1.png|'''Midterm 2 (file 1)''']]<br> [[Media:25122MT2Soln_part2.png|'''Midterm 2 (file 2)''']]
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|-
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| Fri Nov 11 || Triple integrals || 15.6 || [[Media:25122HW5.png|'''HW 5 due''']]
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|-
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| Mon Nov 14 || Cylindrical coordinates || 15.7 ||
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|-
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| Wed Nov 16 || Spherical coordinates || 15.8 ||
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|-
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| Fri Nov 18 || Vector fields || 16.1 || [[Media:25122Q6Soln.png|'''Quiz 6''']]
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|-
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| Mon Nov 28 || Line integrals || 16.2 ||
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|-
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| Wed Nov 30 || Fundamental theorem for line integrals || 16.3 ||
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|-
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| Fri Dec 2 || Green's theorem || 16.4 || [[Media:25122HW6.png|'''HW 6 due''']]
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|-
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| Mon Dec 5 || Review ||  ||
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|-
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| Wed Dec 7 || Review ||  ||
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|-
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| Mon Dec 12 ||'''Final Exam'''  ||  || 8-10pm<br /> Hodges 338
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|}

Latest revision as of 13:24, 10 December 2022

Course info

Description. Vectors and three-dimensional analytic geometry; curves and surfaces; functions of several variables, calculus of several variables; partial derivatives; gradient and linearization; multiple integrals; volume and surface area.

Instructor. Casian Pantea https://math.wvu.edu/∼capantea/

Schedule. Mondays, Wednesdays, Fridays 9:50-11AM, Hodges 338

Office hours. Mondays 11:10AM-12:10PM and 5PM-6PM, Wednesdays 2:30-3:30 PM in Armstrong Hall 305B; and by appointment on zoom: https://wvu.zoom.us/j/92855687691

Textbook. Calculus: Early Transcendentals, 8th Edition, by James Stewart; we cover Chapters 12-16.

Prerequisite. C or better in Math 156 is required;

Evaluation

Grading scheme

  • 30% Final Exam
  • 2x20% Midterms
  • 20% Quizzes
  • 10% Homework

Letter grades will be assigned as follows

A >=90%
B 80-90%
C 70-80%
D 60-70%
F <60%

Schedule of topics

Date Topic Section Other
Wed Aug 17 3D coordinate system, vectors 12.1
Fri Aug 19 Vectors 12.2
Mon Aug 22 Dot product 12.3
Wed Aug 24 Cross product 12.4
Fri Aug 26 Lines and planes 12.5
Mon Aug 29 Problem session 12.1-12.5
Wed Aug 31 Quadric surfaces 12.6
Fri Sep 2 Quadric surfaces 12.6 Quiz 1
Wed Sep 7 Review 12.1-12.6
Fri Sep 9 Vector functions and curves 13.1 HW 1 due
Mon Sep 12 Derivatives and integrals 13.2
Wed Sep 14 Arc length and curvature 13.3
Fri Sep 16 Motion in space 13.4 Quiz 2
Mon Sep 19
Wed Sep 21 Problem session
Fri Sep 23 Functions of multiple variables 14.1 HW 2 due
Mon Sep 26 Review
Wed Sep 28 Midterm 1 Midterm 1
Fri Sep 30 Functions of multiple variables 14.1
Mon Oct 3 Limits and continuity 14.2
Wed Oct 5 Partial derivatives 14.3
Mon Oct 10 Tangent planes 14.4
Wed Oct 12 Chain rule 14.5 Quiz 3
Fri Oct 14 Directional derivatives and gradients 14.6 HW 3 due
Mon Oct 17 Directional derivatives and gradients 14.6
Wed Oct 19 Maxima and minima 14.7
Fri Oct 21 Lagrange multipliers 14.8 Quiz 4
Mon Oct 24 Problem session
Wed Oct 26 Double integrals over rectangles 15.1
Fri Oct 28 Double integrals over general domains 15.2 HW 4 due
Mon Oct 31 Polar coordinates 15.3
Wed Nov 2 Polar coordinates 15.3
Fri Nov 4 Surface area 15.5 Quiz 5
Mon Nov 7 Review
Wed Nov 9 Midterm 2 Midterm 2 (file 1)
Midterm 2 (file 2)
Fri Nov 11 Triple integrals 15.6 HW 5 due
Mon Nov 14 Cylindrical coordinates 15.7
Wed Nov 16 Spherical coordinates 15.8
Fri Nov 18 Vector fields 16.1 Quiz 6
Mon Nov 28 Line integrals 16.2
Wed Nov 30 Fundamental theorem for line integrals 16.3
Fri Dec 2 Green's theorem 16.4 HW 6 due
Mon Dec 5 Review
Wed Dec 7 Review
Mon Dec 12 Final Exam 8-10pm
Hodges 338
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