Lectures

These are the lectures which were used in Spring 2016.

Solutions and solution videos are posted here

Mathematica Files

You can download zipped Mathematica Files with Firefox, to use Mathematica files, you will need to download the student version of Mathematica from the OIT website (under downloads). Make sure you evaluate the notebook before viewing, (under Evaluation in the drop down menu).

Preview Lecture 1

1. Inverse Functions

Inverse Functions Mathematica

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Preview Lecture 2

Natural Logarithm Mathematica

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Preview Lecture 3

3. The natural Exponential Function

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Preview Lecture 4

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Preview Lecture 5

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Preview Lecture 6

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Preview Lecture 7

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Preview Lecture 8

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Preview Lecture 9

Trigonometric Integrals Essential Background and low powers

Trigonometric Integrals Extra Examples

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Preview Lecture 10

10. Trigonometric Substitution

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Preview Lectures 11/12

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Previrew Lecture 13

13. Strategy For Integration

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Preview Lecture 14

14. Approximating Integrals

Numerical Integration Mathematica File

From The Web

Video Explanation

Video Example

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Preview Lecture 15

15. Improper Integrals

Improper Integrals Mathematica File

From The Web

Video: Example1

Video: Example 2

Video: Example 3

Video: Example 4

Video: Example 5

Video: Example 6

Video: Example 7

Video: Example 8

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Preview lecture 16

16. Arclength

From The Web

Video Arc Length Formula

Video Arc Length Example

Video Arc Length More Examples

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Preview Lecture 17

Euler's Method Mathematica

From The Web

Video: Direction Fields

Video: Euler's Method Example

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18. Separable Equations

From The Web

Video Example

Video: Seperable EquationExample 1

Video: Seperable Equation Example 2

Video: Orthogonal Trajectories 1

Video: Orthogonal Trajectories 2

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Preview Lecture 19

19.First order Linear Differential Equations

From The Web

Video: Examples

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Preview Lecture 20

From the web

Video: Sequences

Video: Sequences 1: Definition

Video: Sequence 2 Convergence and Divergence

Video: Sequence 3, corresponding Function

Video: Sequences 4, Alternating Sequences

Video: Sequences 5, Squeeze Theorem for sequences

Video, Sequences 6, exponentials

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From The Web

Video: Series

Video: Geometric series and divergence test Part 1

Video: Geometric Series and divergence test Part 2

Video: Test for divergence

Video: Telescoping series

Video: Summation

Video: Partial sums

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22/23. Integral Test for p-series and Comparison Test

From The Web

Video: Integral Test Basic Idea

Video: Integral test, why it works

Video Direct Comaprison Test/Limit comparison test basic Info.

Video Direct Comparison Test Example 1

Video Direct Comparison Test Example 2

Video Direct Comparison Test Example 3

Video Direct Comparison Test Example 4

Video Direct Comparison Test Example 5

Video Limit Comparison Test Example 1

Video Limit Comparison Test Example 2

Video Limit Comparison Test Example 3

Video Limit Comparison Test Example 4

Video Limit Comparison Test Example 5

Video Limit Comparison Test Example 6

Video Limit Comparison Test Example 7

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24. Alternating Series

From the Web

Video Alternating Series

Video Alternating Series Estimation Theorem

Video Alternating Series Example 1

Video Alternating series Example 2

Video Alternating Series Example 3

Video Alternating series Example 4

Video Alternating series Estimating error 1

Video Alternating Series Estimating Error 2

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Video Preview 1 Lecture 25 Absolute Convergence

Video Preview 2 Lecture 26 Ratio Test

26. Ratio and Root test

Video Ratio Test Example 2

Video Ratio Test Example 3

Video Ratio Test Example 4

nth Root Test Example 2

nth Root Test Example 3

Old Exam Question 1

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Video Example 1 (old exam question)

Video Example 2 (old exam question)

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27. Power Series

Mathematica Worksheet Lecture 27

From The Web

Interval of Convergence

Interval and Radius of Convergence Example

Interval and Radius of Convergence Example

Interval and Radius of Convergence Example

Interval and Radius of Convergence Example

Interval and Radius of Convergence Example

Interval and Radius of Convergence Example

Interval and Radius of Convergence Example

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28. Representing Functions as Power Series

Mathematica Worksheet Lecture 28

From The Web

Substitution

Differentiating and Integrating Power Series

Integrating a Power Series

Finding Power series by differentiating(Examples)

Finding Power Series by Integration(Example)

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29. Taylor and McLaurin Series

From The Web

Taylor Series Expansion

McLaurin Series for Sin(x)

Taylor and McLaurin Series Example

Example: Taylor series for Ln(x) at a = 2

Estimating an integral with a Taylor Series

More Power Series From Known Power Series

Using Integration, substitution with the exponential power series

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30. Applications of Taylor series

Mathematica Worksheet Lecture 30

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31. Parametric Curves

Mathematica Worksheet Lecture 31

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33. Polar CoOrdinates

Mathematica Worksheet Polar Curves

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