# Multivariable Calculus With Analytic Geometry, ... UPD

MATH 120 Precalculus (5) NSc, RSNBasic properties of functions, graphs; with emphasis on linear, quadratic, trigonometric, exponential functions and their inverses. Emphasis on multi-step problem solving. Recommended: completion of Department of Mathematics' Guided Self-Placement. Offered: AWSpS.View course details in MyPlan: MATH 120

## Multivariable Calculus with Analytic Geometry, ...

MATH 124 Calculus with Analytic Geometry I (5) NSc, RSNFirst quarter in calculus of functions of a single variable. Emphasizes differential calculus. Emphasizes applications and problem solving using the tools of calculus. Recommended: completion of Department of Mathematics' Guided Self-Placement. Offered: AWSpS.View course details in MyPlan: MATH 124

MATH 125 Calculus with Analytic Geometry II (5) NScSecond quarter in the calculus of functions of a single variable. Emphasizes integral calculus. Emphasizes applications and problem solving using the tools of calculus. Prerequisite: either minimum grade of 2.0 in MATH 124, score of 3 on AB advanced placement test, or score of 3 on BC advanced placement test. Offered: AWSpS.View course details in MyPlan: MATH 125

MATH 126 Calculus with Analytic Geometry III (5) NScThird quarter in calculus sequence. Introduction to Taylor polynomials and Taylor series, vector geometry in three dimensions, introduction to multivariable differential calculus, double integrals in Cartesian and polar coordinates. Prerequisite: either a minimum grade of 2.0 in MATH 125, or a score of 4 on BC advanced placement test. Offered: AWSpS.View course details in MyPlan: MATH 126

MATH 342 Art of Problem Solving (3) NScExplores the artful side of problem-solving, with examples from various fields across mathematics, including combinatorics, number theory, algebra, geometry, probability, and analysis. Offered: A.View course details in MyPlan: MATH 342

MATH 425 Fundamental Concepts of Analysis (3) NScIntroduction to metric spaces and multivariable differential calculus: Euclidean spaces, abstract metric spaces, compactness, Bolzano-Weierstrass property, sequences and their limits, Cauchy sequences and completeness, Heine-Borel Theorem, continuity, uniform continuity, connected sets and the intermediate value theorem. Derivatives of functions of several variables, chain rule, mean value theorem, inverse and implicit function theorems. Prerequisite: a minimum grade of 2.0 in either MATH 136 or MATH 208; and a minimum grade of 2.0 in either MATH 335 or MATH 424. Offered: WSp.View course details in MyPlan: MATH 425

MATH 493 Stochastic Calculus for Option Pricing (3) NScIntroductory stochastic calculus mathematical foundation for pricing options and derivatives. Basic stochastic analysis tools, including stochastic integrals, stochastic differential equations, Ito's formula, theorems of Girsanov and Feynman-Kac, Black-Scholes option pricing, American and exotic options, bond options. Prerequisite: minimum grade of 2.0 in either STAT 395/MATH 395, or a minimum grade of 2.0 in STAT 340 and STAT 341. Offered: jointly with STAT 493.View course details in MyPlan: MATH 493

MATH 515 Optimization: Fundamentals and Applications (5)Maximization and minimization of functions of finitely many variables subject to constraints. Basic problem types and examples of applications; linear, convex, smooth, and nonsmooth programming. Optimality conditions. Saddlepoints and dual problems. Penalties, decomposition. Overview of computational approaches. Prerequisite: Proficiency in linear algebra and advanced calculus/analysis; recommended: Strongly recommended: probability and statistics. Desirable: optimization, e.g. Math 408, and scientific programming experience in Matlab, Julia or Python. Offered: jointly with AMATH 515/IND E 515.View course details in MyPlan: MATH 515

MATH 574 Fundamental Concepts of Analysis (3)Sets, real numbers, topology of metric spaces, normed linear spaces, multivariable calculus from an advanced viewpoint. Introduction to Lebesque measure and integration. Intended for students in biostatistics and related fields; does not fulfill requirements for degrees in mathematics.View course details in MyPlan: MATH 574

MATH 575 Fundamental Concepts of Analysis (3)Sets, real numbers, topology of metric spaces, normed linear spaces, multivariable calculus from an advanced viewpoint. Introduction to Lebesque measure and integration. Intended for students in biostatistics and related fields; does not fulfill requirements for degrees in mathematics.View course details in MyPlan: MATH 575

MATH 576 Fundamental Concepts of Analysis (3)Sets, real numbers, topology of metric spaces, normed linear spaces, multivariable calculus from an advanced viewpoint. Introduction to Lebesque measure and integration. Intended for students in biostatistics and related fields; does not fulfill requirements for degrees in mathematics.View course details in MyPlan: MATH 576

This is an intensive course whose topics are traditionally found in the separate courses of precalculus algebra and trigonometry. This course is a preparation for calculus covering polynomial, absolute value, radical, rational, exponential, logarithmic, and trigonometric functions and their graphs as well as additional topics in analytic geometry. This course is designed for the student in mathematics who desires to fulfill the requirements of Math D and Math 1 in one semester.

This course presents a study of the techniques of calculus with emphasis placed on the application of these concepts to business and management related problems as well as applications for social and life science majors. The applications of derivatives and integrals of functions including polynomials, rational, exponential and logarithmic functions are studied. This course is not equivalent to Math 3A.

MATH 2030 - Calculus and Analytic Geometry III (3) Prerequisites: C or better in MATH 2020 . An introduction to Multivariable calculus, partial derivatives with applications to special partial differential equations, double and triple integrals with applications, and analytic geometry in space. Vectors and parametric equations in space, infinite sequences and series, including power series, Taylor series with remainder, and applications. Click here for the Spring 2022 Class Schedule

(I teach standard American third semester of calculus, 4 credit hours, covers from vectors and three dimensional coordinate geometry through the basic vector calculus including Stokes' Theorem, however, I'm generally interested in any geometric craft to help ingrain principles of analytic geometry.)

Here's a crafty but perhaps crazy way to convey some ideas to a class. Have all the students gather on the football field (or another field) in a grid on a mildly windy day. Each student carries a little stick with a strand of paper to measure the direction of the wind. Perhaps with some physics they can also estimate the speed of the wind. Have them make several measurements, compile the data and make a vector field of the wind pattern on the field at that point in time. Of course, for best effect, the students will be synchronized in their measurements to have more impact. You can use this exercises as a segue into many topics ranging from the difficulties of measurement in general, the imprecision of the real-world compared to the idealized calculus situations, and of course calculus ideas like vector fields. They'll now know from experience what a vector field is - they were part of one.

This course provides a study of advanced techniques of differential and integral calculus, including plane curves and polar coordinates, three-dimensional analytic geometry including vectors, differentiation and integration of multivariable functions and applications.

Basic techniques of differential and integral calculus of functions of one variable, including polynomial, rational, exponential, logarithmic and exponential functions. Selected topics from applications in analytic geometry, limits, differentiation, applications of the derivative, and applications of the integral.

The second half of a two-semester calculus sequence designed for business and applied science majors. Topics include the integral, techniques of integration, an introduction to trigonometry, multivariable calculus, and differential equations.

This course is a study of the numerical, analytical, and geometric properties of right and oblique triangles, of trigonometric and inverse trigonometric functions, and their applications. The course content includes right angle trigonometry, radian measure, circular functions, graphs of circular functions and their inverses, trigonometric identities, equations involving trigonometric and inverse trigonometric functions, an introduction of the complex plane, vectors and their operations, and the trigonometric form of complex numbers. This course is designed as a preparation for calculus and it is intended for the transfer student planning to major in mathematics, engineering, economics, or disciplines included in the physical or life sciences.

This course examines the study of calculus using numerical, graphical, and analytical methods to analyze calculus problems encountered in real-world applications in business, natural/life sciences, and social sciences. Topics include limits, derivatives, and integrals of algebraic, exponential, and logarithmic functions, curve sketching, optimization, and areas under and between curves and partial derivatives and optimization of multivariable functions. This is the first course in a sequence of mathematics courses for students intending to major in business, economics, or natural and social sciences.

This course is a study of numerical, analytical, and graphical properties of functions. The course content includes polynomial, rational, irrational, exponential, logarithmic, and trigonometric functions. Additional topics include: inverse functions, complex numbers, polar coordinates, matrices, conic sections, sequences, series and the binomial theorem. This course is designed as a preparation for calculus and is intended for the transfer student planning to major in mathematics, engineering, economics, or disciplines included in the physical or life sciences. 041b061a72