• 1st week: Aug. 26, 28, 30
• Sec. 1.4-1.7
• 2nd week: Sept. 2, 4, 6
• Labor Day Holiday Monday Sept. 2
• Sec. 1.8-1.11
• Sec. 2.1-2.6.1
• 3rd week: Sept. 9, 11, 13
• Sec. 2.6.2-2.7.1
• Test! Wednesday Sept. 11 Solutions
• Sec. 3.1, 3.3 (skip 3.2)
• 4th week: Sept. 16, 18, 20
• Geogebra http://www.geogebra.org This is a wonderful free program that produces very nice graphs, computes derivatives and integrals, and all kinds of other things. It even includes a simple spreadsheet.
• Sec. 3.4-3.5.1
• Sec. 3.5.2-3.6.1, 3.8-3.9 (skip 3.7)
• 5th week: Sept. 23, 25, 27
• Sec. 4.1-4.1
• Test! Friday Sept. 27 Solutions
• 6th week: Sept. 30, Oct. 2, 4
• Sec. 4.5, 4.6
• 7th week: Oct. 7, 9, 11
• Sec. 5.1-5.3
• 8th week: Oct. 14, 16, 18
• Sec 5.4-5.5.5
• 9th week: Oct. 21, 23, 25
• Sec. 5.6
• Sec.6.1
• 10th week: Oct. 28, 30, Nov. 1
• Sec. 6.2-6.5
• 11th week: Nov. 4, 6, 8
• 12th week: Nov. 11, 13, 15
• Veterans' Day Holiday Monday Nov. 11
• Integration: solve the differential equation $$\frac{dg}{dx}=f(x)$$ where $$f$$ is a known function. A solution is a function $$g(x)$$ that satisfies the differential equation. Basic example: a car is driving down the $$x$$ axis. $$t$$ hours after it starts driving its position is $$x(t)$$ miles from the origin, and when $$t=0$$ its position is $$x(0)=0$$. Its velocity at time $$t$$ is $$\frac{dx}{dt} = t^2$$ miles per hour at every time $$t$$. Find $$x(t)$$ at every time $$t$$.
The text covers this in chapters 11 and 12 but we'll go through it quicker and in a different order. Chapter 11 talks about areas, sums, and applications. Chapter 12 has the Fundamental Theorem of Calculus which shows that the solution to the differential equation can be interpreted as an area.
• 13th week: Nov. 18, 20, 22
• Continue with integration. Notation for integration $$\int f(x) \,dx$$ and $$\int_a^b f(x) \,dx$$. Section 11.4
• Nice Geogebra Applet relating areas to sums http://webspace.ship.edu/msrenault/ggb/riemann_sum.html
• The fundamental theorem of calculus (Chapter 12.1 in the text) says that the area under the curve $$y=f(x)$$ solves the differential equation $$\frac{dy}{dx}=f(x)$$. Since the area is essentially the sum of the areas of a lot of little rectangles, it also solves many scientific problems that require calculating sums. Chapters 12 and 13 in the text have lots of examples.
• Data for Friday's lecture Nov22lectData.xls Nov22lectData.csv
• 14th week: Nov. 25, 27, 29
• Sec. 17.1-17.4
• Thanksgiving Holiday Friday Nov. 29
• 15th week: Dec. 2, 4, 6
• Final Exams week:
• Final Exam Monday Dec. 9 4-6pm