Book:
Teacher: Andrea Valente (aaue.dk/~av)
Calculus 7 e, Edwards & Penny, Prentice Hall 2007
Software: matlab (ask IT-support) or Octave (free matlab alternative).
Course plan:
| Lecture nr | Date | Topic | Comments |
|---|---|---|---|
| 1 | 3 Sept - 12:30 - B205 | Intro: why Math??? (here,
here and
here)
Trigonometry and trigonometric identities Ch. Ap. C |
cos(a + b) = ? / tan(a + b) = ? / drawing
Ch. Appendix C: 15, 17, 19, 25, 27, 29, 31 |
| 2 | date - time - room | Chapter 1, 1.1 and 1.2. Real number. What is a function. How to draw it. Cartesian coordinate systems. | Try to tabulate a function with this javascript program
(download and edit it to change the function and the interval)
Chpt. 1.2, ex: 1,2,3,4, 11,12, 27,31,32,33,38,50, 82 |
| 3 | date - time - room | Chapter 1.2, 1.3, 1.4: graphs of parabolas and other functions. | Chpt. 1.4: 1, 31,32, 43,48 |
| 4 | date - time - room | Chapter 2.1: slope predictors. Intro to derivative. | Chpt. 2, page 62 1,2,3,5,10, 26,27,28,32
Visualize slopes and tangent lines: here and here. General applets to draw functons: here |
| 5 | date - time - room | Chapter 2.2, 2.3, 2.4: Limits and continuity. Special limits. | No exercises. Finish old ones. |
| 6 | date - time - room | Chapter 3.1, 3.2: Basic differentiation rules. | Chapter 3.1: 1,2,3,9, 13,20, 30,31,32, 56, (51 difficult). Page 116.
Chapter 3.2: 1,2,11, 31,40, 41,42, 55,60,66. Exercises / Solutions (a+b)^n = ? [see here] |
| 7 | date - time - room | Chapter 3.2, 3.4: ...
READ: chapter 3.5: max and min on closed intervals. Chapter 3.7, 3.8: Derivation of tri, log and exp functions. |
Chapter 3.7 (page 177): 1,5,7,19, 21,22,45, 61,62.
Chapter 3.7 (page 178): 73 (use section 3.5 to maximize), 75,76 (use example 12, page 174). Chapter 3.8 problems: 1,4,6, 15,29,37. Find the derivative in exercieses: 50,57. Solve exercise 73. |
| 8 | date - time - room | Chapter 5.3: Areas and summation.
READ: chapter 5.4, 5.5: integral, fundamental theorem of calculus. |
Chapter 5.3 (page 339): 1,3,6, 11,14,16,18, 20, 23.
(page 340): 33,35, 36 (difficult). Read introduction of this article, to see the problem definition. |
| 9 | date - time - room | Introduction to article
Particle system without interaction between particles: here and here (require javascript and canvas support). Height-fields (here). Navier-Stokes equations (here). |
Use matlab, octave
(here) or excell
(here).
Also try out this excel spread-sheet
(here) to play with the model in the article
Take a look at the great and inspirational pictures in "On Growth and form" (D'Arcy Thompson 1917)
(now out of copyright, so free: here)
|
| 10 | date - time - room | Algebras. Vectors in the plane Ch. 11.1. | Ch. 11.1 page 823, exercises: 1, 3, 7, 9, 13, 15, 25, 27, 29. And more difficult: 36, 51.
Problem: How to select a line in a 2D painter program? I.e.: given a segment, detect when a point is on it (or close ENOUGH to it). |
| 11 | date - time - room | Vectors in 3 dimensions Ch.: 11.2 | Ch. 11.2 Ex.: 2,5, 7(only for 2 and 5), 19, 26, 31,33,38. More difficult: 58,61, 69,70. Page 833-834.
Collision detection via Bounding Spheres at google books pages 62 (end of page)-67, example 2.13. . |
| 12 | date - time - room | Vectors in 3 dimensions. The cross product of vectors Ch. 11.3. | Ch. 11.3 Ex.: 1, 3, 7, 13, 15, 17, 19, 35
Resources: adding 2D vectors, dot and cross product of vectors, 3D cross product |
| 13 | date - time - room | Lines and plans in space, Ch. 11.4 | Ch. 11.4 Ex.: 1, 5, 9, 15, 17, 21, 35, 41
Skew lines |
| 14 | date - time - room | Computer graphics exercises. | Bird flocking simulator. |
| 15 | date - time - room | Ch. 11.5 (first part). A simulator of vector functions.
The 4th dimension. |
Ch. 11.5 Ex.: 1,2,3,4; 5,6,7,8; 11,12,13.
The Fourth Dimension: A Guided Tour of the Higher Universes By Rudy Rucker, David Povilaitis (book preview) Slides on the 4th dimension. |
| 16 | date - time - room | Introduction to multivariable calculus Ch. 12.1, 12.2 | Ch. 12.2: 1,2,3,4,6; 21,22,25,28,30; 32,33,35, 40 [difficult]; 47,48,49,50,51,52. |
| 17 | date - time - room | Introduction to partial derivatives Ch. 12.4.
Draw 2D and 3D graphs with Octave (link). |
Ch. 12.4: ... |
| 18 | date - time - room | Exam practice. | EXAM QUESTIONS |
| 19 | date - time - room | Exam simulation 2 | |
| 20 | date - time - room | On-demand exercises. And: ex. 48 page 850, ex 60,66 page 129. | |
| 21 | date - time - room | More on-demand exercises and review of topics.
Solving systems of linear equations: substitution, a problem that can be solved with a system of equations, system of linear equations in general on Wikipedia. Video: how to solve systems of equations by elimination. |
take a look at this: Efficient 2-D Geometric Operations. |
| 22 | date - time - room | On demand exercises: vectors in 2D and 3D, lines in 3D. | |
| 23 | date - time - room | Exam simulation 3: here. | Trigonometry explained here :)
Derivative Rules: table. |
| 24 | date - time - room | "Standard" way to find intersection of 2 lines in 3D: here.
Alternative way to find intersection of 2 lines in 3D: here. |
A collection of trigonometry applets. |
| 25 | date - time - room | Final summary of semester | ... |
table of derivatives taken from the book (more or less)
