Math 10A - Methods of Mathematics: Calculus, Statistics and Combinatorics -- [4 units]
Course Format: Three hours of lecture and three hours of discussion per week.
Prerequisites: Three and one-half years of high school math, including trigonometry and analytic geometry. Consult the Mathematics Department for details. Students who have not had calculus in high school are strongly advised to take the Student Learning Center’s Math 98 adjunct course for Math 10A; contact the SLC for more information.
Description: The sequence Math 10A,B is intended for majors in the life sciences. Introduction to differential and integral calculus of functions of one variable, and matrix algebra and systems of linear equations. (F)
Credit Restrictions: None
Required Textbook: Biocalculus: Calculus, Probability, and Statistics for the Life Sciences (custom UC Berkeley Edition).
Online Class Notes: The Mathematics Department has created extensive online lecture notes for this class, and these will serve as the supplementary text.
Outline of the Course:
Week 1: Sets and basic function properties, familiar function families, inverse functions
Week 2: Limits and asymptotes
Week 3: Continuity and definition of derivative
Week 4: Derivative laws
Week 5: Chain rule, derivatives of inverse functions, implicit differentiation
Week 6: Graphing functions, optimization, linear approximation
Week 7: Antiderivatives, area under curves, Riemann sums, definite integrals
Week 8: Fundamental theorem of calculus, integration by substitution
Week 9: Integration by parts, improper integrals
Week 10: Vectors and matrices, determinants, inverses, solving linear systems
Week 11: Gaussian elimination, coordinate systems, dot products and projections
Week 12: Linear combinations, eigenvalues and eigenvectors
Week 13: Least squares