MATH 138 Winter 2012 Assignment 1 Topics: Review the Fundamental Theorems of Calculus, Integration by substitution and by parts. Due: 11 am Friday, January 13.
Instructions: Print your name and I.D. number at the top of the first page of your solutions, a
CS 136 Assignment 2 Final 100114.2
Revision 1: score should be 'undefined if no games have been played Revision 2: added bonus question Due Thursday, January 21 at 22:00 sharp. No late marks will be awarded. All work must be submitted to the Marmoset subm
CS 136 Assignment 5 Draft 100205.5
Due Thursday, February 11 at 22:00 sharp. No late marks will be awarded. This assignment will use RunC tool v0.2 (updated since assignment 4) to evaluate your C and Scheme submissions. To upgrade to Runc v0.2, download t
Math 136
Assignment 3 Solutions
2 1 1 and v = -1. Calculate projv u and perpv u. 1. Let u = 3 1 Solution: We have 1 uv 4 projv u = v = -1 v 2 3 1 2 1 2/3 4 perpv u = u - projv u = 1 - -1 = 7/3 3 1 3 5/3
1 1 2. Let u = 2 and v = 0. Calculate projv u and
Math 136
Assignment 3
Due: Wednesday, Jan 25th
2 1 1 and v = -1. Calculate projv u and perpv u. 1. Let u = 3 1 1 1 2 and v = 0. Calculate projv u and perpv u. 2. Let u = -3 1 -2 1 1 1 onto the plane S = span -2 , 1 . 3. Find the projection of v = 1 -2 2
Math 136
Assignment 2 Solutions
1. Determine, with proof, which of the following are subspaces of R3 and which are not. x1 a) S1 = 0 R3 | x1 - x2 = 0 x2 0 3 0 S1 since 0 - 0 = 0. Thus, S1 is a Solution: By definition S1 is a subset of R . Also, 0 3 non-em
Math 136
Term Test 1 Information
Monday, Feb 6th, 7:00 - 8:30 pm
Material Covered: Chapters 1 and 2 (assignments 1 - 4). You need to know: - All definitions and statements of theorems. - How to perform operations on vectors (addition, scalar multiplicatio
Computer Science 136: Elementary Algorithm Design and Data Abstraction Winter 2012
David R. Cheriton School of Computer Science
Lecture 12 Memoization and Ordered Lists
We examine more closely the idea of accumulating multiple values and examine the costs
Computer Science 136: Elementary Algorithm Design and Data Abstraction Winter 2012
David R. Cheriton School of Computer Science
Lecture 11 - Destructive and Non-destructive List Processing
The list operations we have seen in Racket, and in C so far, have
Section 5.3 54) Evaluate the integral and interpret it as a difference of areas. Illustrate with a sketch.
2
cos x dx.
/6
Solution:
2
cos x dx = [sin x]2 = 0 - /6
/6
1 1 =- . 2 2
It is a sum of the two areas with + and subtracts the area with a - symbol.
MATH 138 Winter 2012 Assignment 2 Topics: Trigonometric Integrals, Trigonometric Substitutions Due: 11 am Friday, January 20.
Instructions: Print your name and I.D. number at the top of the first page of your solutions, and underline your last name. Submi
MATH 138 Winter 2012 Assignment 3 Topics: Integration by rational functions and Volumes of revolution Due: 11 am Friday, January 27.
Instructions: Print your name and I.D. number at the top of the first page of your solutions, and underline your last name
MATH 138 Winter 2012 Assignment 4 Topics: Volumes of revolution, Approximate Integration and Improper Integrals Due: 11 am Friday, February 3.
Instructions: Print your name and I.D. number at the top of the first page of your solutions, and underline your
MATH 138 Winter 2012 Assignment 5 Topics: Differential Equations (Chapter 9) Due: 11 am Friday, February 17th.
Instructions: Print your name and I.D. number at the top of the first page of your solutions, and underline your last name. Submit your solution
Computer Science 136: Elementary Algorithm Design and Data Abstraction Winter 2012
David R. Cheriton School of Computer Science
Lecture 10 Linked Structures, Racket
We look more deeply at pointers and linked structures in C. We also look at lists in Racke
Computer Science 136: Elementary Algorithm Design and Data Abstraction Winter 2012
David R. Cheriton School of Computer Science
Lecture 9 A Miscellany of C-isms
So far we have taken an idiomatic approach to learning C. Here we are a little more systematic
Computer Science 136: Elementary Algorithm Design and Data Abstraction Winter 2012
David R. Cheriton School of Computer Science
Lecture 9 Linked Data Structures
The C language does not provide the convenient "growing" data structures that are given by man
CS 136 Assignment 3 Final 100124.5
Due Thursday, January 28 at 22:00 sharp. No late marks will be awarded. All work must be submitted to the Marmoset submission system. See the preamble of assignment 1 for more information.
Assignment 3 Problem 1. 20 Mark
CS 136 Assignment 4 Final (revised 100131.7)
Note (January 31): float and double are prohibited.
Due Thursday, February 4 at 22:00 sharp. No late marks will be awarded. All work must be submitted to the Marmoset submission system. See the preamble of assi
Formula Sheet: MATH 138-W12-003 Trigonometric Identites: sin2 x + cos2 x = 1 tan2 x + 1 = sec2 x sin2 x = 1 (1 - cos 2x) , 2 cos2 x = 1 (1 + cos 2x) . 2
Midterm 2012
1 [sin(A - B) + sin(A + B)] , 2 1 sin A sin B = [cos(A - B) - cos(A + B)] , 2 1 cos A cos
MATH 138 Maple Lab 1 Assignment (for Assignment 4)
Integral Approximations in Maple
Due: Friday, February 3, 2012 by 11:00 a.m. in the MATH 138 dropboxes outside of MC 4066. Be sure to staple your Maple Lab 1 to your Assignment 4 and submit them together.
Section 7.2: 14) Evaluate the integral, cos cos5 (sin ) d. Solution: Substitute u = sin and du = cos d to obtain, cos cos5 (sin ) d = cos5 u du
Next, we separate one of the cosines and use the trigonometric identity that cos2 x = 1 - sin2 x, cos cos5 (sin
Assignment 3: Solutions MATH 138 2012 Section 7.4: 14) Evaluate the integral, 1 dx. (x + a)(x + b) Solution: If a = b then we have the following decomposition, 1 1 = (x + a)(x + b) b-a 1 1 - x+a x+b
With this it is easy to integrate the problem above, x+a
Computer Science 136: Elementary Algorithm Design and Data Abstraction Winter 2012
David R. Cheriton School of Computer Science
Lecture 1 Welcome to CS136
CS 136 builds on CS 135. Introduction of C (along with Scheme) Details of effective use of programmi
Computer Science 136: Elementary Algorithm Design and Data Abstraction Winter 2012
David R. Cheriton School of Computer Science
Lecture 2 I/O and a bit of mutation
Side-effects, Input/Output Formatted output Memory through mutation More Encapsulation Game
Computer Science 136: Elementary Algorithm Design and Data Abstraction Winter 2012
David R. Cheriton School of Computer Science
Lecture 3 Separation of Concerns
Separate code which implements functionality from code which uses functionality. How should th
Computer Science 136: Elementary Algorithm Design and Data Abstraction Winter 2012
David R. Cheriton School of Computer Science
Lecture 4 Abstract Data Types (ADTs)
An Abstract Data Type is a mathematical description of a collection of data. ADTs are an i