Overview
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Syllabus
| Office Hours: | Monday | 2-3pm | Mathlab
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| | Wednesday | 3-4pm | East Hall Atrium
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| | Thursday | 1-2pm | East Hall Atrium
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Daily Summary
1/9: Sections 5.1-5.3
Defined the definite integral as signed area under the curve, how to approximate it with Riemann sums, estimate error, and how to compute and interpret it using the fundamental theorem of calculus.
5.1 and 5.2 Worksheet
5.3 Worksheet
1/10: Sections 5.4, 6.1, 6.2
Gave some more properties of definite integrals. Defined the average value of a function. Defined an anti-derivative, and discussed it's relation to the fundamental theorem of calculus. Listed some properties and formulas for anti-derivatives.
5.4 Worksheet 1
5.4 Worksheet 2
6.1 #3, 8, 15, 22
6.2 #1, 5, 15, 20, 57-61 odd, 82, 86
1/14: Section 6.4
Wrote down the second fundamental theorem of calculus. Gave some intuition for why it's definitely true.
6.4 #6, 9, 15, 17, 25, 30-33, 37-39
Winter '18 Exam 1 Problem 4
1/16: Section 7.1
u-substitutions
7.1 #7, 28, 31, 40, 41, 70
7.1 #84, 89-93 odd, 100, 129
1/17: Section 7.2
Gave a quiz.
Integration by parts.
7.2 #9, 20, 21
7.2 #55, 59, 74-76
1/23: Section 7.4
Integration using partial fractions.
7.4 #45, 46, 49
Winter '18 Exam 1 Problem 6
1/24: Section 7.5
Gave a quiz.
Reminder about left and right Riemann sums, introduced trapezoid sums and midpoint sums. Discussed when each is an over or under estimate based on the concavity of the function.
7.5 #16, 17, 22
1/28: Section 8.1
Method of finding volume by slicing.
8.1 #3, 8, 17, 20
8.1 #38, 45
Solutions
1/29-1/30: Winter Vortex
A higher power attempts to freeze us all to death.
8.2 #1, 3, 4, 7, 35, 50-54, 63
"Quiz"
"Solutions"
2/4: Section 8.2
Using the Shell and Washer methods to compute volumes of solids of revolution. Arc-length formula.
8.2 #33, 34, 42, 88
2/6: Section 8.4
Computing mass given a density function.
8.4 # 3, 12, 14, 32
Exam Problem
2/7: Section 8.5
Quiz
Computing total work given either varying force or varying distance.
Extra credit problem: The Lune of Hippocrates.
2/11: Review
Review for the midterm.
2/13: Section 4.7 and 7.6
L'Hospital's rule for evaluating limits of an indefinite form. Applying this to improper integrals with unbounded domains and also unbounded funtions.
4.7 #29, 34, 78
7.6 #27, 29, 38, 53
2/14: Section 7.7
Quiz
Using the comparison test to determine if an integral converges or diverges.
7.7 #2, 4, 6, 24, 28
2/18: Section 7.7 Cont'd
The Gamma Function
2/20: Section 8.7
Probability density functions, cumulative density functions and their properties.
8.7 #1, 12, 13, 15
Winter 2018 Exam 2 Problem 5
2/21: Section 8.8
Quiz
Review of pdf's and cdf's. Defined mean, median and mode in terms of the pdf's and cdf's. Defined the normal distribution with mean μ and standard deviation σ.
8.8 #13, 17, 22
2/25: Section 9.1
Sequences of real numbers, what it means to converge, not converge, or diverge. Convergent sequences are bounded, and bounded monotonic sequences converge.
9.1 #19, 28, 58
Winter 2018 Exam 2 Problems 1 and 2
Winter 2018 Exam 2 Problem 10
2/27: Section 9.2
Finite and infinite geometric series. Expressing them in a closed form and determining when they converge.
9.2 #9, 10, 31, 33, 42, 56
Winter 2018 Exam 2 Problem 9
The Limit Comparison test for improper integrals.
2/28: Section 9.3
Quiz
What it means for a series to converge. Properties of convergent series. Divergence of Harmonic series. The Integral test and p-Series test.
9.3 #14, 19, 27, 37, 35, 45, 49, 50, 55
3/11: Section 9.4
Direct comparison test, limit comparison test, Absolute convergence test, Alternating series test, Ratio test. The Harmonic series diverges, but the Alternating Harmonic series converges.
Fall 2018 Exam 2 Problem 4
9.4 #73, 75, 77
3/13: Section 9.5
Power series. Finding the radius of convergence using the ratio test. Finding the interval of convergence by testing the endpoints.
9.5 #30, 32, 48
Winter 2018 Exam 2 Problems 3 and 6
3/14: Review Day
Quiz
Fall 2017 Exam 2 Problem 10
Does the integral from 0 to infinity of sin(x^2) converge or diverge, and why?
3/18: Section 10.1
Defined the degree n Taylor polynomial as the polynomial of degree <= n that matches the first n derivatives of our function. Gave a formula for the Taylor polynomial about 0 and the Taylor polynomial about x=a. Demonstrated via example why that Taylor polynomial gives better approximations near the center of expansion as n increases.
10.1 #18, 27, 29, 37, 47
Work Problem: You are given a sphere of sand, with center 10m above the ground, radius 4m, density 1.2 kg/m^3. The sand falls onto the ground forming a right cone. Compute the amount of energy released in the process.
3/20: Section 10.2
Defined the Taylor series of a function centered around 0 and centered around x=a. Showed by example that a function is not always equal to it's power series. Gave some examples of functions that are equal to their power series (when it converges) e.g. exponentials, log, rational functions, sin, cos.
Find the Taylor series for sin(x), e^x.
10.2 # 31, 44, 53, 58
3/21: Review Day
Quiz
Winter 2018 Exam 1 Problem 5
3/25: Exam Day
Common mistakes on this exam include not stating convergence/divergence tests used, checking they satisfy the hypothesis, comparing integrals instead of integrands, dropping limits mid-calculation, and not using limits with improper integrals.
Winter 2018 Exam 2 Problems 8-10
3/27: Section 10.3
Finding new Taylor series by manipulating known Taylor series. Tricks include multiplying known series, termwise integrating and differentiating known series, and 'plugging in' one series into another and expanding.
10.3 #8, 26, 36, 40, 46
3/28: Section 10.3 Cont'd
Quiz
10.3 #52
Find the degree 3 expansion of e^sin(x) using the Taylor series for sin, e.
4/1: Section 4.8 and 8.2
Parametric equations. How to find the speed, velocity, tangent line and arc length of a parametrized curve. How to find the slope of the tangent line, and the concavity.
Fall 2017 Final Problem 7
4/3: Section 4.8 and 8.2 cont'd
4.8 #41, 50
8.2 #82
Winter 2018 Final Problems 1, 5, 7, 8
4/4: Section 8.3
Quiz
Started discusion of polar coordinates. How to graph in polar coordinates.
4/8: Section 8.3 Cont'd
Area, slope and arc length in polar coordinates.
Find area of one "petal" of r = 3sin(2θ)
Find the area bounded by r = 3 + 2cos(θ)
8.3 #21, 37, 42
4/10: Section 11.1
Introduced differential equations, why they are useful. Differences between 1st and 2nd order equations in terms of number of derivatives, number of unknown constants, initial conditions needed. Summary of Euler's method.
11.1 #8, 13, 14, 29
Winter 2018 Final Problem 6
4/11: Section 11.2
Quiz
Slope fields, how to use them to guess solutions to differential equations and get qualitative information about solutions to differential equations.
11.2 #2, 4, 17, 20
Fall 2018 Final Problems 8, 10
4/15: Section 11.4
Separation of variables.
11.4 #15, 30, 35, 56
Fall 2018 Final Problems 5-7
4/17: Section 11.5
Differential equations governing growth and decay. Newtons law of cooling. Equilibrium solutions, stable and non-stable.
11.5 #2, 3, 32, 33
Fall 2017 Final Problems 1, 2
4/18: Section 11.6
Quiz
11.6 #7, 22, 25, 30
4/22: Review
Fall 2017 Final Problems 9-12