Math 10A

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 RestrictionsNone

Required TextbookBiocalculus: Calculus, Probability, and Statistics for the Life Sciences (custom UC Berkeley Edition).

Online Class NotesThe 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