Overview
Course Website
Syllabus
| Office Hours: | Tuesday 2-3 | Mathlab |
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| | Wednesday 4-5 | EH 1860 |
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| | Thursday 4-5 | EH 1860 |
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Daily Summary
9/4: 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
9/5: Sections 5.4, 6.1, 6.2
Quiz
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
9/9: Sections 6.1, 6.2, 6.4
Finished sections 6.1, 6.2, started section 6.4. Statement of the second fundamental theorom of calculus, why it's different from the 1st fundamental theorem of calculus.
6.4 #6, 9, 15, 17
9/11: Section 6.4 Continued
Gave intuition for why the second fundamental theorem is true.
6.4 #30-33, 37-39
Fall 2018 Exam 1 Problem 4
9/12: Section 7.1 and 7.2
Quiz
u-substitution and integration by parts.
7.1 #40, 70, 84
7.1 Extra practice #7, 28, 31, 41, 89-93 odd, 100, 129
7.2 #9, 20, 55, 74
7.2 Extra practice #21, 59, 75, 76
9/16: Section 7.4
Winter 2015 Exam 1 Problem 3
Using partial fractions to integrate.
7.2 #45, 46, 69
Integrate y/(25+y^4)
Winter 2018 Exam 1 Problem 6
9/18: Section 7.5
Left, Right, Midpoint and Trapezoid rule for estimating integrals. When each is an under or overestimate in terms of the slope and concavity of a function.
7.5 #16, 17, 22
Winter 2018 Exam 1 Problem 8
9/19: Section 4.7
Quiz
Discussed which functions dominate which, and how to use this to evaluate limits. Discussion of indeterminate forms, and when to apply L'Hopital's rule.
4.7 #29, 34, 78
9/23: Section 7.6
Improper integrals when the domain is unbounded, or the function is unbounded. How to split up improper integrals, and when they converge or diverge.
7.6 #27, 29, 38, 53
Fall 2018 Exam 2 Problem 1
9/25: Section 7.7
Direct comparison test, p-test and exponential decay test.
Guide for Convergence Arguments
7.7 #2, 6, 24, 28
9/26: Section 8.1
Quiz
How to find volume and area by slicing. How to write expressions for Riemann sums using sigma notation.
8.1 #3, 8, 17, 20
9/30: Section 8.2
Shell and washer method for finding volumes of solids of revolution.
8.2 #33, 34, 38
10/2: Section 8.4 (No Center of Mass)
How to compute mass of an object by slicing into constant density peices and integrating.
8.4 #3, 14, 32
10/3: Review
Quiz
Fall 2018 Exam 1 Problem 3
Winter 2019 Exam 1 Problem 1
10/6: Sunday Review Session
Gamma Function
Fall 2018 Exam 1 Problem 7
Winter 2019 Exam 1 Problem 2
10/7: Review
Test for divergence. Discussed the convergence of the integral from 0 to infinity of x^2e^(-x)
Winter 2019 Exam 1 Problems 3-5
Fall 2018 Exam 1 Problem 9
10/9: Section 8.5
Two kinds of work problems involving variable force and constant force.
8.5 #3, 11, 12, 25
10/10: Section 8.7
Defined the pdf and cdf of a random event, and how they are related.
8.7 #1, 12, 13, 15
Winter 2018 Exam 2 Problem 5
10/16: Section 8.8
Defined the mean of a probability distribution, gave some intuition for why it's defined that way. Defined the median of a probability distribution. Defined the normal distribution with mean μ and standard deviation σ.
8.8 #13, 17, 22
Winter 2018 Exam 2 Problem 10
Challenge Problem
10/17: Section 9.1
Quiz
Review of sequences. How to express them with a formula and recursively. When they converge and diverge. Definition of bounded and monotone sequences. Bounded monotone sequences converge.
9.1 #19, 28, 58
Winter 2018 Exam 2 Problems 1,2
10/21: Section 9.2
Finite and infinite geometric series. Closed forms for each, derivation of the closed form.
9.2 #33, 42, 46
10/23: Section 9.3
Winter 2018 Exam 2 Problem 9
Defined a series, partial sums. Convergence of a series is defined as the convergence of the sequence of partial sums. The integral test, pseries test, and nth term test for divergence.
9.3 #14, 19, 27, 37
10/24: Section 9.4
Quiz
Gave some intuition for why series are analogous to improper integrals. The direct comparison test, limit comparison test, nth term test for divergence, absolute convergence test.
10/28: Section 9.4 cont'd
Reviewed important examples to keep in mind when using series test, including alternating harmonic series, harmonic series, alternating p-series and p-series.
Alternating series test, absolute and conditional convergence. Ratio test.
Fall 2018 Exam 2 Problem 4
Winter 2019 Exam 2 Problem 4
10/30: Section 9.5
Power series. How to find the radius of convergence using the ratio test. How to find the interval of convergence by testing the endpoints.
9.5 #30, 32, 48
Winter 2018 Exam 2, Problems 3 and 4
10/31: (Spooky) Review
Quiz
Math 116 Winter 2019 Exam 2 Problem 9
Preparation for next time: If I know the value of a function, its slope and concavity at 0, how can I create a degree 2 polynomial with the same value, slope, and concavity at 0?
11/4: Section 10.1
Taylor polynomials. The basic idea is if you have some function f, and you know its derivatives up to nth order at a point, you can create a polynomial of degree n with the same derivatives at that point. This polynomial will approximate your function f, at least near that point. This is the Taylor polynomial, and it has a precise formula that you should know.
10.1 #18, 27, 29, 37, 47
Fall 2018 Exam 2, Problems 7 and 10
11/6: Section 10.2
Taylor series. We take the Taylor polynomials from last time and let n go to infinity. For "nice" functions, the Taylor series will converge on some radius, and the function will be actually equal to its Taylor series within that radius. As a warning, this is not always true, even if the function is infinitely differentiable.
10.2 #31, 44, 53, 58
11/7: Section 10.2 Cont'd
Quiz
Finish problems from last time. Preview of manipulations of known Taylor series to produce new Taylor series.
11/11: Review
11/13: Section 10.3
How to manipulate power series. How to find new power series using known power series.
10.3 #8, 26, 36, 40, 46
11/14: Section 4.8
Quiz
Beginning of 4.8, parametric equations.
11/18: Section 4.8 Cont'd
Parametric equations. How to find slope, concavity and arc length.
4.8 #41, 50
8.2 #82
Fall 2017 Final Problem 7
11/20: Section 8.3
Polar coordinates. Graphing, area and arc length formulas.
8.3 #21, 37, 42
11/21: Section 11.1
Differential equations. What they are, some examples of how they arise from physical problems.
11.1 #8, 13, 14, 29
11/25: Section 11.2
Slope fields. How to draw them. How to use them to extract qualitative information from a differential equation.
11.2 #2, 4, 17, 20
Winter 2019 Final Problem 6
12/2: Section 11.4
Separation of variables as a method to solve differential equations in closed form.
11.4 #15, 30, 35, 56
Fall 2018 Final Problem 4
12/4: Section 11.5
Differential equations governing growth and decay. How to set up a differential equation. Defined equilibrium solutions, stable and unstable. Gave an example of an inseparable differential equation.
11.5 #2, 3, 32, 33
12/5: Section 11.6
Quiz
More practice modeling physical situations with differential equations.
11.6 #7, 22, 25, 30