Math 16A - UC Berkeley Department of Mathematics

Course Format: Two hours of lecture and one hour of discussion/workshop per week; at the discretion of the instructor, an additional hour of lecture or discussion/workshop per week.

Prerequisites: Three years of high school math, including trigonometry, plus a satisfactory grade in one of the following: CEEB MAT test, an AP test, the UC/CSU math diagnostic exam, or 32. Consult the mathematics department for details.

Credit Option: Students will receive no credit for 16A after taking 1A.

Description: This sequence is intended for majors in the life and social sciences. Calculus of one variable; derivatives, definite integrals and applications, maxima and minima, and applications of the exponential and logarithmic functions. (F,SP)

Textbook: Goldstein, Lay, Schneider, and Asmar, Calculus and Its Applications, Custom Edition for Math 16A, Volume I, University of California, Berkeley.

Outline of the Course:

Chapter 0	3 hours
Linear and quadratic functions, the quadratic formula, exponents and power functions, interest
Chapter 1: The Derivatives	8 hours
Slopes of lines and curves, limits and derivatives, differentiability and continuity, rules of differentiation, rate of change
Chapter 2: Applications	8 hours
Increasing and decreasing functions, maximum, minimum, curve sketching, optimization, application to business
Chapter 3: Differentiation	3 hours
Product and quotient rules, the chain rule, implicit differentiation, related rates
Chapter 4	5 hours
Exponential and logarithmic functions
Chapter 5: Applications	5 hours
Exponential growth, compound interest
Chapter 6: The Definite Integral	7 hours
Antidifferentiation, Riemann sums, the Fundamental Theorem, areas in the x,y-plane
Total	39 hours
Midterms	2 hours
Holidays & Reviews	4 hours
	45 hours

This course has 3 lectures and 1 discussion hour per week. The lecture should therefore include a large number of applications and examples so the students will not miss a second discussion hour.

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