## Math 151, 152, 153, & 254 - Calculus I, II, III, & IV

**Resources Available: **Textbooks(2), Student
Solution Manuals (2), Student Study Guide Manuals (2), Video
Skillbuilder CD-ROM (2), TEC (Tools for Enriching Calculus)
Software on Computer, Video Tapes. and Printed Practice problems
(in binder) (from old text), Video Tapes on Basics of the TI 83
graphing calculator.

Online videos for
Calculus I, II, and III, and for
Calculus III and IV

**Resource Details**

**The CD-Rom**(Video Skillbuild CD) has on it selected examples from each section (2-3 typically) worked out live with explanations.**TEC Software**This software (Tools for Enriching Calculus) came on a disk with each new copy of the (5th edition ) textbook, and is available on the web for the 6th edition. It is loaded on the MRC computers from the 5th edition. Students can access it just by clicking an icon on the desktop. They should then select single or multi-variable Calc, click on the Main Menu button, and then choose Modules (to explore the ideas of Calculus graphically) or Homework Hints (for selelcted problems), or some of the other options, as desired. The advantage of the modules is that it generally uses graphing in a fairly nice way to reinforce the ideas of calculus, and it is quite interactive—students get to make lots of choices, answer questions, etc, and then see the results. It takes a little bit of work to get familiar with what’s available here, and to figure out how to use it, but the results are nice.**Video Tapes**(from 5th edition of text). These are video versions of the examples worked on the CD rom.**Practice Problems.**There are 50-100 multiple choice practice problems with answers for each chapter of the old text. Still useful, even if Chapter and section numbers are different from new text.**Graphing Calculator Video Tapes**. About an hour-long video on using the TI 83 graphing calculator. (We also have one for the TI 89). We also have a written instructional manual, and many copies of the manuals that come with the TI 83 (which the students can have for free).

**Videos for Calculus I, II, and III**

Videos provided thru Princeton University Press (here) are based on the text The Calculus Lifesaver: All the Tools You Need to Excel at Calculus by Adrian Banner.

Chapters / Sections |
Contents |
Streaming(RealPlayer) |
Download(Vodcast) |
Download(WMV) |

Chapters 1 & 2 | Functions, trig | Video 1 | File 1 | File 1 |

Chapters 3 & 4 | Limits: theory and polynomial examples | Video 2 | File 2 | File 2 |

Chapter 5 & Sections 7.1.1 & 7.1.2 |
Continuity, differentiability, trig limits | Video 3 | File 3 | File 3 |

Sections 7.1.3 & 7.1.4 Chapter 6 (except 6.6 & 6.7) Section 7.2, excluding 7.2.3 |
Trig limits (continued), how to solve differentiation problems, trig derivatives, simple harmonic motion | Video 4 | File 4 | File 4 |

Chapter 8 | Implicit differentiation, related rates | Video 5 | File 5 | File 5 |

Chapter 9 (except 9.6 & 9.7) Section 14.2 |
Exponentials, review of topics so far | Video 6 | File 6 | File 6 |

Sections 10.1, 10.2 & 13.2 (except 13.2.4) |
Inverse functions, inverse trig functions, linearization | Video 7 | File 7 | File 7 |

Section 13.2.2 Chapter 11 |
More on the differential, extrema, Rolle/Mean Value Theorem, critical points and the second derivatives (Note: The lecture stops suddenly but is made up at the beginning of the next video.) | Video 8 | File 8 | File 8 |

Section 11.5 Chapter 12 |
Classifying critical points, sketching graphs | Video 9 | File 9 | File 9 |

Sections 13.1 & 14.1 | Optimization, L’Hôpital's Rule | Video 10 | File 10 | File 10 |

Chapter 15 (except 15.1.2) Chapter 16 (except 16.7) Sections 17.1, 17.2, & 17.3 |
Sigma notation, Riemann sums, integration, introduction to the Fundamental Theorems | Video 11 | File 11 | File 11 |

Chapter 17 Section 18.1 |
Fundamental Theorems, integration by substitution | Video 12 | File 12 | File 12 |

Sections 18.1, 18.2, & 19.1 | Substitution revisited, integration by parts, integrals involving trig limits | Video 13 | File 13 | File 13 |

Section 18.3 | Partial fractions | Video 14 | File 14 | File 14 |

Sections 19.2, 19.3 & 19.4 | Trig integrals, trig substitutions, and summary of integration techniques | Video 15 | File 15 | File 15 |

Chapter 29 (except 29.2) | Volumes of revolution, arc lengths, and surface areas | Video 16 | File 16 | File 16 |

Chapter 20, Sections 21.1 & 21.3.1 | Improper integrals, part 1 | Video 17 | File 17 | File 17 |

Sections 21.3, 21.4, & 21.5 | Improper integrals, part 2 | Video 18 | File 18 | File 18 |

Sections 22.1, 22.2, 22.5.1, 22.5.2, 23.1, 23.2, 23.3, & 23.4 | Sequences and series, part 1 | Video 19 | File 19 | File 19 |

Sections 22.5.3, 22.5.4, 23.5, 23.6, 23.7 & 24.1 | Sequences and series, part 2, introduction to power | Video 20 | File 20 | File 20 |

Section 24.2, Chapter 25, Section 26.1 |
Estimation using Taylor series, the remainder/error term, radius of convergence of power series | Video 21 | File 21 | File 21 |

Chapter 26, Section 28.1 | More about power and Taylor series, introduction to complex numbers | Video 22 | File 22 | File 22 |

Sections 28.1.1, 28.2, 28.3, 28.4, 30.1 & 30.2 | Complex numbers, separable first-order differential equations | Video 23 | File 23 | File 23 |

Sections 30.3 & 30.4 | First order linear differential equations, first/second order constant coefficient linear differential equations | Video 24 | File 24 | File 24 |

**Videos for Calculus III and IV**

Videos provided thru MIT Open Courseware (here).

**Lecture number and topic**

**I. Vectors and matrices**

0: Vectors (Note: Video is not
available for this topic.)

1:
Dot product

2:
Determinants; cross product

3:
Matrices; inverse matrices

4:
Square systems; equations of planes

5:
Parametric equations for lines and curves

6:
Velocity: acceleration - Kepler's second law

7:
Review**II. Partial derivatives**

8:
Level curves; partial derivatives; tangent plane approximation

9:
Max-min problems; least squares

10:
Second derivative test; boundaries and infinity

11:
Differentials; chain rule

12:
Gradient; directional derivative; tangent plane

13:
Lagrange multipliers

14:
Non-independent variables

15:
PPartial differential equations; review**III.
Double integrals and line integrals in the plane**

16:
Double integrals

17:
Double integrals in polar coordinates; applications

18:
Change of variables

19:
Vector fields and line integrals in the plane

20:
Path independence and conservative fields

21:
Gradient fields and potential functions

22:
Green's theorem

23:
Flux; normal form of Green's theorem

24:
SSimply connected regions; review**IV. Triple
integrals and surface integrals in 3-space**

25:
Triple integrals in rectangular and cylindrical coordinates

26:
Spherical coordinates; surface area

27:
Vector fields in 3D; surface integrals and flux

28:
Divergence theorem

29:
Divergence theorem (cont.): applications and proof

30:
Line integrals in space: curl: exactness and potentials

31:
Stokes' theorem

32:
Stokes' theorem (cont.); review

33:
Topological considerations - Maxwell's equations

34:
Final review

35:
Final review (cont.)

Last updated:
March 29, 2010