## 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