m201

Marywood University Department of Mathematics

Course Information for Math 202

Dr. Craig M. Johnson

Isaac Newton (1642-1727)

Math 202 Calculus II

This is the second course in the 12-credit calculus sequence: Math 201-204. The textbook is "Thomas' Calculus: Alternate Edition" by Thomas/Finney and published by Addison-Wesley. The course grade is based upon three tests, weekly homework sets, two Maple labs, and a final examination. Prerequisite: Successful completion of Calculus I. Useful websites for the course are listed at the end of this page.

Course Outline

Section

Main Topic

Section

Main Topic

Section

Main Topic

4.1
Indefinite Integrals

5.1

Area between curves

6.1

Inverse functions

4.2
Diff. Eqns ; Modeling

5.2

Volumes by slicing

6.2

Natural logs

4.3
Integration by Sub

5.3

Volumes of solids of revolution

6.3

Exponential function

4.5
Riemann sums

5.4

Cylindrical shells

6.4

a^x and log_ax

4.6
Properties, Area, MVT

5.5

Lengths of plane curves

6.5

Growth and decay

4.7
Fundamental Thm.

5.6

Areas of surfaces of revolution

6.6

L'Hopital's rule

4.8
Substitution

5.7

Moments, centers of mass

6.8

Inverse trig functions

4.9
Numerical Integration

5.8

Work

6.9

Deriv. of inverse trig fns

Test #1

5.10

Modeling applications

6.10

Hyperbolic functions

Test #2

Test #3

Test #1 Sample Problems

Assume f and g are two functions continuous over [ 1, 7 ] for which Int(3,7) f(x) dx = 14 , Int(1,3) g(x) dx = -3 , and Int(3,7) g(x) dx = 24. Use the properties of integrals to find:
- Int(1,7) 2g(x) dx
- Int(1,7) [3g(x) + 4] dx
- Int(3,7) [f(x) - g(x)] dx
Solve the IVP: dy/dx = x^(1/3) + x , y(1) = 3.
Evaluate the following definite and indefinite integrals. Note: Int = integral sign. Int(a,b) = definite integral from a to b.
- Int [ 4 sin x)^2 ] dx
- Int(4,9) [ x^(1/2) + 1] dx
- Int [sinq / cos³q] dq
- Int(pi/3, pi/2) [q - cscq cotq ] dq
- Int [x/(1+x²)² ] dx
- Int [sin(1/t)/t²] dt
- Int [z²(z³/18 -1)^5 ] dz
A projectile is fired vertically upward with an initial velocity of 49 m/sec from a tower 150 meters high.
- Find the expression for position as a function of time.
- How long does it take the projectile to reach its maximum height?
- What is the maximum height?
- How long will it take for the projectile to hit the ground?
Find the average value of f(x) = x² - 1 on the interval [0, sqrt(3)].
Find the area of the region between the graph of y = x² - 6x + 8 on the interval [0, 3].
Find the derivative of the integral: d/dx [Int (0, sqrt(x)) [ sec²t ] dt
Use both the Trapezoidal rule and Simpson's rule (n = 4) to evaluate Int(1,2) [sqrt(5+x²)] dx.

Test #2 Sample Problems

Sketch the region enclosed by the curves y = x² and y = 8 - x² and find the total area.
Use the method of washers to find the volume of the solid that results when the area of the region enclosed by y² = 4x, y = 2, and x = 4 is revolved about the x-axis.
Sketch the region enclosed by the curves x = y³ - y and x = 0 and find the total area of the region.
Find the surface area generated by rotating about the y-axis the arc of the curve y = x² between (0, 0) and (2, 4).
Find the arc length of the curve y = 1/3*(x² + 2)^3/2 , for 0 <= x <= 3.
A round hole of radius 3 is drilled through the center of a solid sphere of radius 5. Use the method of cylindrical shells to find the volume of the removed portion by revolving the curve y = sqrt(25 - x²) around the y-axis.
A particle having initial velocity v_o = -2 is moving with acceleration a(t) = 2t + 1 for 0 <= t <= 2. Find the displacement and total distance traveled by the particle.
Find the displacement and the distance traveled over the time interval 1 <= t <= 5 by a particle having velocity v(t) = 2t - 6.
A spring has a natural length of 12 m. What is the spring constant if 45 joules of work is required to stretch the spring from a length of 14m to a length of 20m? (Be sure to include the correct units with the constant.)
If the velocity of a fallen body is k*sqrt(s) at the instant when the body has fallen a distance s, find its acceleration. (k constant)

Test #3 Sample Problems

Useful Websites

http://www.math.psu.edu/dna/graphics.html (Great graphics for learning Calculus from Penn State)

http://www.ping.be/math (Tutorials about most of the main topics in Calculus and Linear Algebra)

http://www.calculus.net (Very interesting practice problems and projects in Calculus and Diff. Equations)

http://www.math.duke.edu/modules/materials/index.html (Modules and projects created by Duke University for enhancing the learning of Calculus, Diff. Equations, Linear Algebra, and Engineering Mathematics)

http://www.maplesoft.com/apps/powertools/ (Maple 6 Resource Center)

http://www.maa.org (Mathematical Association of America)

http://archives.math.utk.edu (Math Archives)

http://forum.swarthmore.edu (Math Forum)

Marywood University <|> Undergraduate School <|> Undergraduate Admissions

Comments to Dr. Craig M. Johnson, Chair, Dept. of Mathematics: johnsonc@marywood.edu

Last update: March 23, 2004

Section	Main Topic	Section	Main Topic	Section	Main Topic
4.1	Indefinite Integrals	5.1	Area between curves	6.1	Inverse functions
4.2	Diff. Eqns ; Modeling	5.2	Volumes by slicing	6.2	Natural logs
4.3	Integration by Sub	5.3	Volumes of solids of revolution	6.3	Exponential function
4.5	Riemann sums	5.4	Cylindrical shells	6.4	a^x and log_ax
4.6	Properties, Area, MVT	5.5	Lengths of plane curves	6.5	Growth and decay
4.7	Fundamental Thm.	5.6	Areas of surfaces of revolution	6.6	L'Hopital's rule
4.8	Substitution	5.7	Moments, centers of mass	6.8	Inverse trig functions
4.9	Numerical Integration	5.8	Work	6.9	Deriv. of inverse trig fns
	Test #1	5.10	Modeling applications	6.10	Hyperbolic functions
			Test #2		Test #3