Lower-Division

Introduces mathematical functions and their uses for modeling real-life problems in the social sciences. Includes inequalities, linear and quadratic equations, functions (linear, quadratic, polynomial, rational, power, exponential, logarithmic, trigonometric), inverses, and the composition of functions. Students cannot receive credit for both this course and MATH 3. MATH 3 can substitute for this course. (Formerly Applied Mathematics and Statistics 3.)

Reviews and introduces mathematical methods useful in the elementary study of statistics, including logic, real numbers, inequalities, linear and quadratic equations, functions, graphs, exponential and logarithmic functions, and summation notation. (Formerly AMS 6.)

Applications-oriented course on complex numbers and linear algebra integrating Matlab as a computational support tool. Introduction to complex algebra. Vectors, bases and transformations, matrix algebra, solutions of linear systems, inverses and determinants, eigenvalues and eigenvectors, and geometric transformations. Students cannot receive credit for this course and for AM 10A or MATH 21. (Formerly AMS 10.)

Introduction to mathematical tools and reasoning, with applications to economics. Topics are drawn from differential calculus in one variable and include limits, continuity, differentiation, elasticity, Taylor polynomials, and optimization. Students cannot receive credit for both this course and MATH 11A or MATH 19A or AM 15A. (AM 11A formerly AMS 11A.)

Mathematical tools and reasoning, with applications to economics. Topics are drawn from multivariable differential calculus and single variable integral calculus, and include partial derivatives, linear and quadratic approximation, optimization with and without constraints, Lagrange multipliers, definite and indefinite integrals, and elementary differential equations. Students cannot receive credit for both this course and MATH 11B or MATH 19B or AM 15B. (AM 11B formerly AMS 11B.)

Applications-oriented class on ordinary differential equations (ODEs) and systems of ODEs using Matlab as a computational support tool. Covers linear ODEs and systems of linear ODEs; nonlinear ODEs using substitution and Laplace transforms; phase-plane analysis; introduction to numerical methods. Students cannot receive credit for this course and for AM 20A or MATH 24. (Formerly AMS 20.)

Advanced multivariate calculus for engineering majors. Coordinate systems, parametric curves, and surfaces; partial derivatives, gradient, Taylor expansion, stationary points, constrained optimization; integrals in multiple dimensions; integrals over curves and surfaces. Applications to engineering form an integral part of the course.