# Calculus II - Summer I 2013

## Instructor Information

• Instructor: William Gunther
• Email: wgunther@math.cmu.edu
• Office: Wean 6211
• Office Hours:
• To Be Announced
• By Appointment

## Course Information

• Course Title: Integration, Differential Equations, and Approximation
• Course Number: 21-122
• Lecture Room: Wean 6423
• Lecture Time: 9:00-10:20am every weekday
• Syllabus: PDF
• Text: Essential Calculus 2nd Edition by James Stewart.

## Announcements

• Tuesday 4/30/13: Making website.

## Course Summary

This course is entitled "Integration, Differential Equations, and Approximation." At other schools it is generally called ``Calculus II.'' Going into the course, the assumption is that you have an advanced grasp of:

• Real valued functions, their graphs, and examples of standard functions (polynomials, rational, root, trigonometric, arctrigonometric, exponential, and logarithmic).
• Algebraic manipulation of real valued variables
• The derivative, the geometric interpretation of the derivative, and applications of the derivative in optimization, related rates, and curve sketching
• The intergral, the geometric interpretation of the integral, its relation to the derivative via the fundamental theorem of calculus, and applications of the integral in finding the area between two curves, or the volume of an three dimensional object which has uniform cross sections or is constructed from revolving a curve around a line.
• What a limit of a function is, how the derivaive is defined as the limit of average rate of change around the point, how the integral is defined as the limit of the area by rectangles.

This course will be divided into several parts.

• Advanced Intergration Techniques: We learn how to integrate a broader set of functions using the integration by parts, trigonometric substituion, partial fractions.
• Approimating Integrals: We learn a few techniques for approximating the value of an integral, such as partial Riemann sums, the midpoint rule, the trapizodial rule, and Simpson's rule
• Differential Equations: We learn how to solve a set of differential equations, called seperable differential equations.
• Sequences and Series: We look at sequences of real numbers, define the notion of convergence. Then we look at sequences of sums of real numbers (series), and look at when those converge.
• Parametization, Polar Coodinates, and Vectors
• We look at some other ways to represent functions and numbers, and then go from 2 dimensions to three dimensions.

## Course Calendar

Monday Tuesday Wednesday Thursday Friday
20
Integration Review
Notes: PDF
21
Trig Integrals
Notes: PDF
22
Trig Substituion
Notes: PDF
23
Partial Fractions
Notes: PDF
24
Approximations
Notes: PDF
HW1: HTML
27
Memorial Day
28
Quiz 1
Improper Integrals
Notes: PDF/LaTeX
29
Improper Integrals
Notes: PDF/LaTeX
30
Work
Notes: PDF/LaTeX
31
Center of Mass
Notes: PDF/LaTeX
HW2: HTML
3
Diff Eqs
Notes: PDF/LaTeX
4
Quiz 2
Diff Eqs
Notes: PDF
5
Diff Eqs
Notes: PDF/LaTeX
6
Euler's and Newton's Method
Notes: PDF/LaTeX
7
Sequences
Notes: PDF/LaTeX
HW3: HTML
10
Series
Notes: PDF/LaTeX
11
Quiz 3
Convergence Tests
Notes: PDF/LaTeX
12
Convergence Tests
Notes: PDF/LaTeX
13
Convergence Tests
Notes: PDF/LaTeX
14
Series Approximations
Notes: PDF/LaTeX
HW4: HTML
17
Power Series
Notes: PDF/LaTeX
18
Quiz 4
Power Series
Notes: PDF/LaTeX
19
Taylor Series
Notes: PDF/LaTeX
20
Taylor Series
Notes: PDF/LaTeX
21
Taylor Applications
Notes: PDF/LaTeX
HW5: HTML
24
Parameterization
Notes: PDF/LaTeX
25
Quiz 5
Parameterization
Notes: PDF/LaTeX
26
Polar Coordinates
Notes: PDF/LaTeX
27
Vector Geometry
Notes: PDF/LaTeX
28
Final Exam

Note: to use any of the LaTeX, you will need the preamble I import: preamble.tex