|Calculus I Laboratory, MAT 155, 1 credit
Sections 81 and 82: 6-7:40pm T Th
Prerequisite: MAT 172
Corequisite: MAT 175
Text: Larson, Hostetler and Evans, Calculus Early Transcendentals, Houghton Mifflin, second edition.
Course Webpage: select
Calculus I Lab from my webpage.
|Professor C. Sormani
Office Hours: 5:30-6:00pm TuTh
Office: Gillet Hall 200B
Projects and an explanation about how to download them can be found at http://comet.lehman.cuny.edu/calculus/maple.html
Students with very little computer experience should sit next to students who have used windows in the past.
Week 1 (Th 8/31 or Tu 9/5):
Project I: Intro to Maple
calculations, order of operations, evalf, sqrt, sine, cosine, defining functions, evaluating functions, saving files
Read P1-P3 for homework before week 2.
Week 2 (Th 9/7 or Tu 9/12):
Project II: Functions
defining functions, graphing functions with given intervals, graphing lines using the point slope formula, odd and even functions, graphing sine,cosine, radians, cut and paste
Bring a copy of page 19 of the text.
Read Appendix A1, P6 Example 3, and 1.2 An Intro to Limits, Example 1 for homework.
Week 3 (Th 9/14 or Tu 9/19):
Project III: Examining Graphs
creating a file from scratch, factor, solve, fsolve, the number e and (1+x)^(1/x) near x = 0
Read A3, P5 and P6 for homework.
Week 4 (Th 9/21 or Tu 9/26):
Project IV: Inverses and Exponentials
bring page 44 of the text
review and sin(x)/x behavior near 0, using solve to find inverse functions, graphing functions and inverses, exp and ln, arcsin and arccos, using the command index.
Read 1.3 and 1.5 for homework.
Week 5 (Th 9/28 or Tu 10/3):
Project V: Limits and Vertical Asymptotes
limit command, the simplify command, vertical asymptotes, graphing with y bounds, graphing tan(x), x/(x+1),
Be sure to review all old labs and commands for homework.
Week 6 (Th 10/5 or Tu 10/17): Exam I
On defining functions, graphing a line using point slope formula, graphing functions, solving equations and finding limits. Writing a Maple file from scratch, using the command index.
Read 2.1 pages 109-112 before Week 7.
Week 7 (Th 10/12 or Tu 10/24):
Project VI: Finding Tangent Lines
Graphing pairs of functions, plotting curves with secant and tangent lines, verifying slopes of sin(x) and exp(x) at x=0, for loops
Read 2.1 pages 112-114 for homework.
Week 8 (Th 10/19 or Tu 10/31):
Project VII: Derivatives
Taking derivatives using limits and using D(f), the expand command, and graphing tangent lines and examining them as a linear approximation of functions. Using variables which are words.
Week 9 (Th 10/26 or Tu 11/7*): Free Lab
Catch up lesson where students can finish projects who need to and others can do extra exploration.
(* Tu 11/7 is election day, so take the time to vote! If necessary come to lab Th 11/2 instead.)
Homework before next week: 1.4: The Intermediate Value Theorem and Example 8, and in 2.8: Newton's Method, Example 1, Example 2 and Example 3.
Week 10 (Th 11/2 or Tu 11/14):
Project VIII: Newton's Method
Method of Tabulation, review of for loops,
clear x, define a
review of tan line, while loops
Week 11 (Th 11/9 or Tu 11/21): Exam II
includes all old topics including loops but not while loops
Read 3.1 and 3.3 before Week 12.
Week 12 (Th 11/16 or Tu 11/28):
Project IX: Increasing and Decreasing
Graph f(x) with D(f)(x) and write comments regarding inc and dec. Find critical points using solve and fsolve. plotting parabolas
read 3.4 before Week 13.
Week 13 (Th 11/30 or Tu 12/5):
Project X: Concavity and Inflection
Review of increasing/decreasing, concavity, inflection points, graphing f D(f) D(D(f))
read 3.6 and 3.7 before week 14.
Week 14 (Th 12/7 or Tu 12/12)
Project XI: Graphing and Optimization
Find inflection and critical points, then graph and find absolute max and min
Short final during finals week.