Math 1B - UC Berkeley Department of Mathematics

Course Format: Three hours of lecture and two hours of discussion/workshop per week; at the discretion of the instructor, an additional hour of discussion/workshop or computer laboratory per week.

Prerequisites: 1A or equivalent.

Credit Option: Students will receive 2 units of credit for 1B after taking 16B.

Description: Continuation of 1A. Techniques of integration; applications of integration. Infinite sequences and series. First-order ordinary differential equations. Second-order ordinary differential equations; oscillation and damping; series solutions of ordinary differential equations. (F,SP)

Textbook: Stewart, Single Variable Essential Calculus, Student Edition, University of California, Berkeley

Outline of the Course:

Chapter 6: Techniques of Integration	8 hours
All of the material in section 7.5 on Strategies on Integration from our previous book Stewart: Early Transcendentals, 5th edition can be found on the website stewartcalculus.com. Rational substitutions is not covered in the new edition.
Chapter 7: Applications of Integration	9 hours
Sections 7.1-7.3 are covered in Math 1A. In Math 1B cover section 7.4 and either section 7.5 or "Area of a Surface of Revolution". The last subject can be found on the website stewartcalculus.com, which also contains the full solutions to all the odd problems. Note that the section on Differential Equations (7.6) is fairly long, and that Exponential Groth/Decay and Newtons law of cooling is covered in Math 1A. The material on Linear Differential Equation is important, and can be found on the website, together with the soluions of all odd problems. The new edition does not cover Eulers method.
Chapter 8: Series	13 hours
This is a difficult topic for the students. Supply motivation for studying infinite series at the beginning, give lots of numerical examples of non-trivial divergent and convergent series, and mention sections 8.8 and 17.4 below as payoff.
Chapter 17: Second Order Differential Equations	10 hours
The students have trouble with this chapter. The exposition is very terse, so go slowly and supply lots of explanation.
Total	40 hours
Midterms	2 hours
Holidays & Reviews	3 hours
	45 hours

Suggestion: It is possible to teach the material in a different order, namely: first 6.1 and then chapter 8 followed by 6.2-6.6 and 7.4 and maybe 7.5 or surface area and finishing up with 17.1-17.4. This has the advantage of exposing the students to convergence proofs and concepts early on. Also it is something new for students coming directly from high school.

Warning: The student edition is missing the appendices with the detailed proofs, "the logarithm defined as an integral" and "general exponential functions". It has second order ODE (1B), but is missing linear equations (which however can be found on the website). Section 9.6 in the student edition contains the material from the solution manual for section 9.7 of Stewart: Calculus, Early Transcendentals, 5th edition, but the Lotka-Volterra theory is neither in the book, nor the website: stewartcalculus.com. Notice that population growth and Newtons law of cooling has moved from second semester to first.

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