Worksheet 11: 16.1, 16.2
MATH 23:
Fall Semester 2014
1. Sketch the vector elds in the xy-plane.
(i) F (x, y) = 2i + 3j
(ii) F (r) = r/ r
(iii) F (x, y) = y i + xj
(iv) F (x, y) = (x + y)i + (x y)j
2.
Worksheet 15: 16.7
MATH 23:
Spring Semester 2015
1. Consider the part of the surface z = 4 x2 y 2 (in meters) above the circle in the xy
plane of radius 1m centered at the origin, oriented with its no
Worksheet 13: 16.4, 16.5
MATH 23:
Spring Semester 2015
1. Use Greens theorem to calculate the integral of F around the curve, oriented counterclockwise. You might want to check your answer by parametr
Worksheet 12: 16.3
MATH 23:
Fall Semester 2014
1. Explain why the following is true: Whenever the line integral of a vector eld around every
closed curve is zero, the line integral along a curve with
Worksheet 14: 16.6
MATH 23:
Spring Semester 2015
1. Find a parametrisation representing a bagel if the bagel is obtained by rotating around the
z-axis a small circle of radius 1 in the xz-plane so tha
CSE 20
Intro to Computing I
General Course Information
What is Computing?
The discipline of computing is the systematic study of
algorithmic processes that describe and transform
information: their t
CSE 20
Intro to Computing I
Data Types
System Objects
System'
out'
print
'
in'
println'
System.out.println("World");
Scanner input = new Scanner(System.in);
Input - Scanner (Chapter 1.7)
Scanner'
next
MOTION OF A PROJECTILE
Objectives:
1. Analyze the free-flight
motion of a projectile.
In-Class Activities:
Kinematic Equations for
Projectile Motion
Group Problem Solving
APPLICATIONS
A good kicker
MASS MOMENT OF INERTIA
Objectives:
1. Determine the mass moment
of inertia of a rigid body or a
system of rigid bodies.
In-Class Activities:
Applications
Mass Moment of Inertia
Parallel-Axis Theore
Worksheet 7: 15.1,15.2
MATH 23:
Spring Semester 2015
1. Sketch the region of integration and evaluate the iterated integrals
3
4
(i)
3
(4x + 3y) dx dy
0
2
(ii)
0
6xy dy dx
0
0
2. Find the volume of th
Worksheet 10: 15.7, 15.8, 15.9
MATH 23:
1. Sketch the region of integration.
1
1
(i)
0
1
1x2
1
1x2
f (x, y, z) dz dx dy
(ii)
0
1z 2
1z 2
Spring Semester 2015
1y 2 z 2
f (x, y, z) dx dy dz
1y 2 z 2
2
Worksheet 8: 15.2, 15.3, 15.4
MATH 23
Spring Semester 2015
1. Sketch the region of integration and evaluate the iterated integrals
3
4
(i)
3
(4x + 3y) dx dy
0
2
(ii)
0
6xy dy dx
0
0
2. Find the volume
MATH 23: Multi-variable Calculus
Worksheet 2: 12.34
Spring Semester 2014
1. Write = 3 i + 2 j 6 k as the sum of two vectors, one parallel, and one perpendicular,
a
to d = 2 i 4 j + k
2. Consider a
MATH 23: Vector Calculus
Worksheet 3: 12.5, 12.6
Spring Semester 2015
1. Find an equation of the plane through (2, 3, 2) and parallel to the plane 3x + y + z = 4.
2. Find the points where the plane z
MATH 23: Vector Calculus
Worksheet 1: 12.12
Fall Semester 2014
1. Which two of the three points P1 (1, 2, 3), P2 (3, 2, 1) and P3 (1, 1, 0) are closest to each other?
2. Describe the set of points who
Worksheet 4: 13.1, 13.2, 13.3, 13.4
MATH 23:
Fall Semester 2014
1. Parameterize the following curves:
(i) y = esin(x) in the xy-plane.
(ii) z = y 3 + y + 1 in the yz-plane.
(iii) x =
1
z 2 +1
in the x
Worksheet 6: 14.4, 14.5, 14.6
MATH 23:
Spring Semester 2015
1. For the following functions, nd an equation of the tangent plane at the given point.
(i) f (x, y) = 1 (x3 + 8y 3 ) at the point (2, 1, 8)
Worksheet 5: 14.1, 14.3
MATH 23:
Spring Semester 2015
2
1. Plot vertical traces of the function z = ex sin y by setting:
(i) x = 0, x = 1, x = 1.
(ii) y = 0, y = /2, y = /2.
Sketch the graph of the fu
INTRODUCTION &
RECTILINEAR KINEMATICS: CONTINUOUS MOTION
Objectives:
1. Find the kinematic quantities
(position, displacement, velocity,
and acceleration) of a particle
traveling along a straight path