Prerequisites: 16A
Credit Option: Students will receive no credit for 16B after 1B, 2 units after 1A.
Description: Continuation of 16A. Application of integration to economics and life sciences. Differential equations. Functions of many variables. Partial derivatives, constrained and unconstrained optimization. (F,SP)
Textbook: Goldstein, Lay, Schneider, and Asmar, Calculus and Its Applications, Custom Edition for Math 16B, Volume 2, University of California, Berkeley.
Outline of the Course:
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Chapter 7: Functions of Several Variables |
9 hours |
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Partial derivatives, maxima, minima, Lagrange multipliers, least squares, double integrals |
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Chapter 8: The Trigonometric Functions |
4 hours |
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Radian measure, differentiation and integration of sin, cos, tan |
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Chapter 9: Techniques of Integration |
6 hours |
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Substitution, integration by parts, evaluation and approximation of definite integrals, applications, improper integrals |
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Chapter 10: Differential Equations |
7 hours |
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Simple equations, separation of variables, numerical solutions, applications |
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Chapter 11: Taylor Polynomials and Infinite Series |
7 hours |
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Taylor polynomials, Newton-Raphson, infinite series, convergence of series with positive terms, Taylor series |
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Chapter 12: Probability and Calculus |
6 hours |
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Discrete and continuous random variables, expected value and variance, exponential, normal and Poisson distributions |
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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.