# Lower-Division

## AM3 Precalculus for the Social Sciences

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 Mathematics 3. Mathematics 3 can substitute for this course. (Formerly Applied Mathematics and Statistics 3.)

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## AM6 Precalculus for Statistics

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.)

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## AM10 Mathematical Methods for Engineers I

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 courses 10A or Mathematics 21. (Formerly AMS 10.)

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## AM11A Mathematical Methods for Economists I

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.)

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## AM11B Mathematical Methods for Economists II

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.)

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## AM15A Case-Study Calculus I

Case-study-based, first-quarter introduction to single-variable calculus, with computing labs/discussion sections featuring contemporary symbolic, numerical, and graphical computing tools. Case studies drawn from biology, environmental sciences, health sciences, and psychology. Includes functions, mathematical modeling, limits, continuity, tangents, velocity, derivatives, the chain rule, implicit differentiation, higher derivatives, exponential and logarithmic functions and their derivatives, differentiating inverse functions, the mean value theorem, concavity, inflection points, function optimization, and curve-sketching. Students cannot receive credit for this course and course 11A or Economics 11A or Mathematics 11A or 19A. (Formerly AMS 15A.)

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## AM15B Case-Study Calculus II

Case-study based, second-quarter introduction to single-variable calculus, with computing labs/discussion sections featuring symbolic numerical, and graphical computing tools. Case studies are drawn from biology, environmental science, health science, and psychology. Includes indefinite and definite integrals of functions of a single variable; the fundamental theorem of calculus; integration by parts and other techniques for evaluating integrals; infinite series; Taylor series, polynomial approximations. Students cannot receive credit for this course and course 11B or Economics 11B or Mathematics 11B or 19B. (Formerly AMS 15B.)

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## AM20 Mathematical Methods for Engineers II

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 courses 20A or Mathematics 24. (Formerly AMS 20.)

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## AM30 Multivariate Calculus for Engineers

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.

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