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