Math 16B - 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: 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 and Schneider, Calculus and Its Applications, 9th Edition, Prentice-Hall

Outline of the Course:

Chapter 7: Functions of Several Variables	9 hours
Partial derivatives, maxima, minima, Lagrange multipliers, least squares, double integrals
Chapter 8: The Trigonometric Functions	4 hours
Radian measure, differentiation and integration of sin, cos, tan
Chapter 9: Techniques of Integration	6 hours
Substitution, integration by parts, evaluation and approximation of definite integrals, applications, improper integrals
Chapter 10: Differential Equations	7 hours
Simple equations, separation of variables, numerical solutions, applications
Chapter 11: Taylor Polynomials and Infinite Series	7 hours
Taylor polynomials, Newton-Raphson, infinite series, convergence of series with positive terms, Taylor series
Chapter 12: Probability and Calculus	6 hours
Discrete and continuous random variables, expected value and variance, exponential, normal and Poisson distributions
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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