Math 213 - Calculus II - Winter 2025
Class Information
Instructor: Tuan Pham
Class meetings: M, T, W, Th, F: 8 - 8:50 AM at SCB 303
[Syllabus]
[Class schedule]
[Canvas]
[WebAssign]
Office Hours
Monday, Wednesday, Friday: 11:00 AM - 12:30 PM at SCB 316, or by appointment
Assignments
Homework problems are to be done in WebAssign.
Mathematica labs are to be submitted on Canvas as a pdf file and source file (nb or ipynb).
Get access to Mathematica
Quizzes are given in class. See the class schedule above.
Lecture notes
Review for Final Exam (Apr 11)
Lecture 51 (Apr 10): Taylor's series
Mathematica Lab day (Apr 9)
Lecture 50 (Apr 8): power series representation of rational functions
Lecture 49 (Apr 7): power series representation; solve differential equations using power series
Lecture 48 (Apr 4): radius of convergence
Lecture 47 (Apr 2): power series, interval of convergence
Lecture 46 (Apr 1): Ratio Test and Root Test
Lecture 45 (Mar 31): error estimation (cont.), absolute and conditional convergence
Lecture 44 (Mar 28): Alternating Series Test and error estimation
Lecture 43 (Mar 27): alternating series
Lecture 42 (Mar 25): Comparison Test (cont.)
Lecture 41 (Mar 24): interpretation of Integral Test; Comparison Test
Lecture 40 (Mar 21): Integral Test and p-series
Lecture 39 (Mar 20): Divergence Test
Lecture 38 (Mar 19): compute geometric series and telescoping series
Lecture 37 (Mar 18): series; number \(\pi\) and \(e\)
Lecture 36 (Mar 17): L'Hospital rule
Lecture 35 (Mar 14): limit of a sequence; Worksheet
Lecture 34 (Mar 13): monotonicity and boundedness of a sequence
Lecture 33 (Mar 12): sequence - general formula and recursive formula; Worksheet
Review for Midterm II (Mar 10)
Mathematica Lab day (Mar 7)
Lecture 32 (Mar 6): area swept by a polar curve, length of a polar curve
Lecture 31 (Mar 5): find intersection of polar curves
Lecture 30 (Mar 4): graph polar curves
Lecture 29 (Mar 3): area enclosed by simple closed curve; polar coordinates
Lecture 28 (Feb 28): tangent lines to a parametric curve
Lecture 27 (Feb 27): parametric curves, arclength formula
Lecture 26 (Feb 26): practice on logistic model
Lecture 25 (Feb 25): Verhulst's population model (logistic model); Worksheet
Lecture 24 (Feb 24): Malthus' population model
Mathematica Lab day (Feb 21)
Lecture 23 (Feb 20): Euler's method (cont.) and direction fields; Worksheet
Lecture 22 (Feb 19): Euler's method
Lecture 21 (Feb 18): practice on integrating factor; Worksheet
Lecture 20 (Feb 14): integrating factor
Lecture 19 (Feb 13): separation of variables (cont.)
Lecture 18 (Feb 12): separation of variables; Worksheet
Lecture 17 (Feb 10): introduction to differential equations; Worksheet
Review for Midterm I (Feb 7)
Lecture 16 (Feb 6): compute length of a curve (continued)
Lecture 15 (Feb 5): compute length of a curve
Mathematica Lab day (Feb 4)
Lecture 14 (Feb 3): Comparison Principle
Lecture 13 (Jan 31): improper integrals
Lecture 12 (Jan 30): error analysis of Riemann sums
Lecture 11 (Jan 29): numerical integration using Riemann sums
Lecture 10 (Jan 28): partial fraction decomposition in the case deg\(P\ge\) deg\(Q\)
Mathematica Lab day (Jan 27)
Lecture 9 (Jan 24): the case \(Q(x)\) cannot be factored
Lecture 8 (Jan 23): partial fraction decomposition when \(Q(x)\) only has simple real roots; Worksheet
Lecture 7 (Jan 22): integrals of rational function \(\frac{P(x)}{Q(x)}\) where deg\(P<\) deg\(Q\); Worksheet
Lecture 6 (Jan 21): trigonometric substitution involving \(\sqrt{x^2+a^2}\), \(\sqrt{x^2-a^2}\), \(\sqrt{a^2-x^2}\); Worksheet
Lecture 5 (Jan 17): integrals of the form \(\int\tan^mx\sec^nxdx\)
Lecture 4 (Jan 16): practice on integrals of the form \(\int\sin^mx\cos^nxdx\)
Lecture 3 (Jan 15): integrals of the form \(\int\sin^mx\cos^nxdx\)
Lecture 2 (Jan 14): practice on integration by parts; Worksheet
Lecture 1 (Jan 13): integration by parts
Mathematica Lab day (Jan 10)
Review worksheet (Jan 9)
Supplement materials
A simple method to find out when an ordinary differential equation is separable
Extra credit: find the length of the oscilating curve \(y=x\sin(1/x)\) where \(x\in(0,1]\)
Linear algebra method to find integrals of \(e^{ax}\sin(bx),\ e^{ax}\cos(bx),\ xe^{ax}\sin(bx),\ xe^{ax}\cos(bx)\)
Trigonometric identities printable table
Mathematica instruction from the Wolfram company:
- 15-minute video: Hands-on start to Mathematica
- Fast introduction for math students
- Mathematica as a programming tool: An elementary introduction
Use Mathematica on JupyterLab:
- Installation guide
- Video instruction, sample lab report:
pdf,
ipynb
Links
Joseph F. Smith Library,
Math Lab
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This page was last modified on Thursday, Apr 10, 2025.
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