Video Lectures for Calculus with Analytic Geometry II, MATH 2414



These lectures cover the basic material for calculus II at an introductory level. Students study the lectures at home and do the homework assignments. Class time will be used for problem solving and presentation by students.
Last Update: January 2011

Announcements:

1: Information sheet for Calculus 2 Desciption of the basic format, policy, dates, and requirements for the course.

2: Tutoring Lab in LUCAS 209 will open soon.

3: Good handwriting, good exposition, and good mathematical grammar count heavily. Putting an equal sign between items that are obviously not equal is a big No-No. Not putting an equal sign between consecutive equal items is also unacceptable. Missing parantheses, mis-aligned equations, small handwriting, use of blunt pencils, missing equal signs, missing operaion or relational symbols (e.g. lim, d/dx, ' , ", =, >) are some of the items to be avoided in your presentation. Bring three already-sharpened pencils to tests. Show all work. All algebra and calculus related work must be exhibited. Utilize the space/white paper next to problem before parking solutions on scratch sheet. Scratch sheet is mainly for trial and error or a first draft. It is not intended as the final resting place for solutions.

4: Calculator Policy. Only basic scientific calculators are allowed on tests. These calculators cost about 20 dollars, have a one-line or two-line display, and do NOT have the following capabilities: Graphing, solving equations, programming, integrating, differentiating. You need to practice using the calculator early on and become confident about its operations. Do keep its mannual and record its web site.

Basics: Here you will find the daily lectures. Clicking on any video link opens up windows media player (WMP), or a designated compatible player, on your computer and starts the presentation. (On Mac use RealPlayer.) Maximize the window size for WMP and adjust the volume. You can scroll back and forth in the file (up to the point it has been downloaded). You can also use the fast forward. To save the file for viewing at a later time (for example in case you have a dial-up) "right click" and use "save target as".

Searching: To search this page press CTRL F and fill in the box. Search is exact.

Software Requirements: The following items will be needed. You may want to install all now or update these when you come across a web page that requires them.

1. WMV files (all video lectures) require Microsoft's Windows Media Player ,or a compatible player.

2. PDF files (class notes) require Adobe Acrobat Reader. Be aware: Adobe Yahoo! Toolbar and Adobe Photoshop or other software may be automatically included in the download as well. Uncheck the boxes for those options before downloading.

3. JAVA applets (extras) require Sun Microsystems Java Runtime Environment (JRE). Once you are in an applet page click somewhere on the demo and look for a slider or a point that you can grab by mouse and move it around. Or there may be an input box where you type in a formula and the page responds by analyzing your input.

4. FLASH files (extras) require Adobe/Macromedia Flash Player.

You may find the following viewerd useful if you browse Internet for course related material. In case of commercial products like Quicktime and RealPlayer you have be EXTRA careful in terms of the privilages that you give them.
Livemath
Geomview for UNIX and Mac OS X or Win/Cygwin
Quicktime



Online courses on trigonometry
You will need a review of trigonometry for 9.1, 9.2, especially the sections on inverse trig functions. Here are some resources:
a. D. E. Joyce Trig Course (interactive text)
b. Maesumi's lectures
c. Dawkins' Notes

Online Calculators
Wolfram Natural Language Calculator .
Function Analyzer. Comprehensive Calculus 1 and Taylor Series calculator. (Fractional powers of negative numbers should be handled carefully here.)
InstaCalc a calculator with spread sheet concept .
Calc98 a downloadable basic calculator.
Power Calculator a downloadable calculator from Microsoft with graphics.

Start of Calculus II
Chapter 9: Inverse Trig Functions:
Read Sections 9.1 and 9.2
Lecture 1: Inverse Trig Functions, derivative and related integral formula starts with a brief description of inverse functions.
Lecture 2: Examples related to Inverse Trig Functions, evaluation and differentiation
Lecture 3: explaining arccot(-2), examples related to Inverse Trig Functions, substitution
Lecture 4: several example of integrals with inverse trig functions in answer, completion of squares, range of inverse trig functions
We skipped 9.3 Hyperbolic Functions.
Chapter 10: Techniques of Integration
Read Section 10.1.
Lecture 5: Integration by Parts
Read Section 10.2.
Lecture 6: Integration of products of powers of trig functions, Sin^n Cos^m cases
Read Section 10.2.
Lecture 7: Integration of products of powers of trig functions, Tan^n Sec^m cases
Read Section 10.1
Lecture 8: Multiple Integration by Parts, Polynomial * (Sin, Cos, or Exp)
Read Section 10.1
Lecture 9: Reduction of Powers / Integration by Parts, Sin^n, Cos^n, Sec^n
Read Section 10.3
Lecture 10: Trigonometric Substitutions
Review of Sections 10.1, 10.2
Lecture 11: Examples from integration of powers of trigs and integration by parts
Read Section 10.4
Lecture 12: Integration using Partial Fraction Decomposition
Read Section 10.4
Lecture 13: Integration using Partial Fraction Decomposition
Read Section 10.4, 10.6
Lecture 14: Integration using Partial Fraction Decomposition, numerical integration
Read Section 10.6
Lecture 15: Numerical Integration, Left, Right, Trapezoid rule, error formula
Read Section 10.6
Lecture 16: Numerical Integration, Simpson Rule
Read Section 11.1
Lecture 17: L'Hopital Rule for Indeterminate forms 0/0, inf/inf, application to 0.inf, 1^inf
Read Section 11.1
Lecture 18: The 7 Indeterminate forms 0/0, inf/inf, 0.inf, inf-inf, 1^inf, inf^0, 0^0
Read Section 11.2, 11.3
Lecture 19: Imroper Integrals
Read Section 11.4
Lecture 20: Taylor Polynomials
Review of 10.3, 10.4
Lecture 21: Solution of 3 problems from integration
Review of 11.4
Lecture 22: Examples from Taylor Polynomials
Review of 11.4
Lecture 23: Examples from Taylor Polynomials and improper integrals
Read 12.1
Lecture 24: Sequences
Read 12.2
Lecture 25: Sequences and Series
Read 12.2
Lecture 26: Series by partial fraction decomposition,
Read 12.3
Lecture 27: Integral Test
Read 12.3
Lecture 28: Examples of Integral Test, estimating a sum
Read 12.3
Lecture 29: Comparison Test
Read 12.4
Lecture 30: Limit Comparison Test, examples
Read 12.5
Lecture 31: Alternating series
Read 12.6
Lecture 32: Ratio and Root tests
Read 13.1
Lecture 33: example sum of n^2/2^n, Power series
Read 13.1
Lecture 34: differentiation, integration, substitution of Power series
Review of 12.1, 12.2
Lecture 35: Review of sequences and Series
Review of 12.4, 12.5
Lecture 36: Review of sequences and Series
Read 13.2
Lecture 37: Taylor and MacLaurin Series
Read 14.1
Lecture 38: Polar Coordinates
Read 14.1
Lecture 39: Polar Coordinates, circle and rose
Read 14.1,14.2
Lecture 40: Examples from Polar Coordinates, Area and length of a slice of circle
Read 14.2
Lecture 41: Area and length in polar coordinates
Read 14.2
Lecture 42: Examples of Area and length in polar coordinates
Read 14.2
Lecture 43: Examples of Area in polar coordinates
Read 15.1
Lecture 44: Vectors,Law of Cosines
Read 15.2
Lecture 45: Vectors, dot product
Read 15.2
Lecture 46: Vectors, Velocity
Read 16.1
Lecture 47: 3 dimensiona space
Read 16.2
Lecture 48: Equations of lines and planes
Review
Lecture 49: Review of problems in series and polar functions