Fall 2023 MATH UN1101 Section 11: Calculus I
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Basic info
- Lectures: Tuesday Thursday 6:10PM-7:25PM
- Location: 407 Mathematics Building
- Instructor: Sam DeHority (samdehority@math.columbia.edu)
- Office hours: Monday Wednesday 1:00PM - 2:00PM
- TA: TBA
Syllabus
The course syllabus has additional information about the course and a tentative calendar for the whole course.
Calendar
Listed below are the lecture dates, a list of key topics covered during the lecture.
| Date | Topics covered | Additional resources |
| Sep 5, 2023 | Functions Vertical line test Trigonometric functions |
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| Sep 7, 2023 | Exponential functions Transforming graphs Amplitude and period Function composition Inverse functions Logarithmic functions |
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| Sep 12, 2023 | Derivative as slope of tangent line Intuitive definitions of limits One-sided limits Infinite limits |
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| Sep 14, 2023 | Limit laws Calculating limits Formal definition of a limit |
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| Sep 19, 2023 | Squeeze theorem Continuity Classifying discontinuities Intermediate value theorem Asymptotics: limits at infinity |
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| Sep 21, 2023 | Limit definition of the derivative Infinitesimal rate of change Velocity and acceleration Second derivative |
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| Sep 26, 2023 | Derivative rules Definition of $e$ Derivative of $e^x$ Power rule and quotient rule |
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| Sep 28, 2023 | Midterm review | |
| Oct 5, 2023 | More on periodic functions Derivative of $\sin$, $\cos$ Intro to chain rule |
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| Oct 10, 2023 | Composition of functions Chain rule Derivative of exponentials Implicit differentiation Tangent line to implicit curve |
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| Oct 12, 2023 | Derivative of log Proof of power rule Derivative of inverse trig functions |
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| Oct 17, 2023 | Drawing pictures from word problems Related rates using implicit differentiation Tangent line as linear approximation Differentials as new independent coordinates |
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| Oct 19 | Critical points Extreme value theorem Fermat’s theorem (on extreme values) Rolle’s theorem Mean value theorem Finding minima and maxima |
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| Oct 24 | Concavity First derivative test L’hospital’s rule |
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| Oct 26 | Indeterminate forms Graph sketching |
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| Oct 31 | Graphs of $x^{a/b}$ Sign tests and graph sketching Beginning of optimization |
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| Nov 2 | More optimization examples Antiderivative General form of antiderivative Antiderivatives of $x^a, \log(x), b^x, \sin(x), \cos(x)$ One dimensional motion with constant acceleration |
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| Nov 9 | Midterm review | |
| Nov 16 | Introduction to integrals Area under a curve Integral as an antiderivative |
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| Nov 21 | Integral rules Riemann sums Area by approximation |
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| Nov 28 | Fundamental theorem of calculus Functions defined using an integral |
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| Nov 30 | Integration using substitution Net change theorem Integrals in the sciences |
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| Dec 5 | Volumes using integration Volumes of revolution using circles Volumes of revolution using annuli |
Homeworks
Homeworks are due Tuesday at 11:59pm, to be submitted on Courseworks.