2008-2009 Catalog - United States Air Force Academy

Math 152. Advanced Placed Calculus II. A more rigorous study of integral calculus for advanced-placed fourth-class cadets.
Content is similar to Math 142, but with more in-depth treatment. Additional emphasis is placed on the mathematical and
physical applications in preparation for students interested in pursuing a technical major.
Math 243. Calculus III. Multivariate calculus, including vector functions, partial differentiation, directional derivatives, line
integrals, and multiple integration. Maxima and minima in multiple dimensions and the method of Lagrange Multipliers. Solid
analytical geometry to include lines, planes, and surfaces in 3-space. Designed for cadets who indicate an interest in a technical
major.
Math 245. Differential Equations. Modeling with and analysis of linear ordinary differential equations. Includes matrix
algebra and matrix inverses, first-order ordinary differential equations (numerical methods, separation of variables, integrating
factors, and method of undetermined coefficients), and second-order linear differential equations/first-order linear systems
(Laplace transforms, determinants, eigenvalues, eigenvectors, and stability). Applications may include population growth,
predator/prey, and mass-spring system modeling.
Math 253. Advanced Placed Calculus III. A more intense study of multivariate calculus for advanced-placed fourth-class
cadets. Content is similar to Math 243. Additional emphasis is placed on mathematical and physical applications in preparation
for students interested in pursuing a technical major.
Math 300. Introduction to Statistics. Descriptive statistics emphasizing graphical displays; basic probability and probability
distributions; sampling distribution of the mean and the Central Limit Theorem; statistical inference including confidence
intervals and hypothesis testing correlation; and regression.. Math 300 is designed primarily for social science and humanities
majors. It emphasizes the elements of statistical thinking, focuses on concepts, automates most computations, and has less
mathematical rigor than Math 356.
Math 310. Mathematical Modeling. Introductory course in mathematical modeling. Students model various aspects of
real-world situations chosen from Air Force applications and from across academic disciplines, including military sciences,
operations research, economics, management, and life sciences. Topics include: the modeling process, graphical models,
proportionality, model fitting, optimization, and dynamical systems. Several class periods are devoted to in-class work on small
projects.
Math 320. Foundations of Mathematics. Emphasizes exploration, conjecture, methods of proof, ability to read, write, speak,
and think in mathematical terms. Includes an introduction to the theory of sets, relations, and functions. Topics from algebra,
analysis, or discrete mathematics may be introduced.
Math 340. Discrete Mathematics. Useful for students interested in applications of mathematics to computer science and
electrical engineering. Propositions and logic; sets and operations on sets; functions, recursion, and induction; graphs, trees,
and their applications; discrete counting and combinatorics.
Math 342. Numerical Analysis with Differential Equations. Introductory numerical analysis course. Specific topics
include round off, truncation, and propagated error; root finding; fixed-point iteration; interpolating polynomials, and numerical
differentiation and integration. The approach is a balance between the theoretical and applied perspectives with some computer
programming required.
Math 344. Matrices and Differential Equations. Properties, types, and operations of matrices; solutions of linear systems;
Euclidean vector spaces, linear independence, and bases; eigenvalues and eigenvectors. Computational aspects. Applications
to differential equations. First- and second-order differential equations and systems. Models may include population growth,
warfare, and economic growth.
Math 346. Engineering Math. Provides advanced mathematical concepts and skills necessary for technical disciplines.
Topics include differential and integral vector calculus (gradient, directional derivative, divergence, curl, Divergence Theorem,
Stokes’ Theorem), Fourier series, orthogonal functions, and partial differential equations (separation of variables, transform
methods, numerical techniques).
122 United States Air Force Academy Catalog