UVa Course Catalog (Unofficial, Lou's List)
Complete Catalog for the Applied Mathematics Department    
Class Schedules Index Course Catalogs Index Class Search Page
These pages present data mined from the University of Virginia's student information system (SIS). I hope that you will find them useful. — Lou Bloomfield, Department of Physics
Applied Mathematics
APMA 1000Preparation for Engineering Mathematics (1 - 3)
Covers the fundamental concepts necessary for success in engineering courses and Applied Mathemtics courses.
Course was offered Summer 2022, Spring 2022, Fall 2009
APMA 1001Calculus Placeholder (4)
This course will be used as an enrollment placeholder during summer orientation for incoming 1st year engineering students prior to receiving calculus placement results, AP scores, dual enrollment credit, etc. This course will be replaced with APMA 1090, APMA 1110, or APMA 2120 prior to the fall term based on the student's final calculus placement result.
APMA 1090Single Variable Calculus I (4)
Offered
Spring 2024
The concepts of differential and integral calculus are developed and applied to the elementary functions of a single variable. Limits, rates of change, derivatives, and integrals. Applications are made to problems in analytic geometry and elementary physics. For students with no exposure to high school calculus.
APMA 1110Single Variable Calculus II (4)
Offered
Spring 2024
Advanced techniques of integration are introduced, and integration is used in physics applications like fluid force, work, and center of mass. Improper integrals and approximate integration using Simpson's Rule are also studied. Infinite series including Taylor series are studied and numerical methods involving Taylor polynomials are studied. Parametric equations and polar coordinates are introduced and applied. Complex numbers are introduced.
APMA 1501Special Topics in Applied Mathematics (1)
Student-led special topic courses which vary by semester.
Course was offered Spring 2016, Spring 2014
APMA 2120Multivariable Calculus (4)
Offered
Spring 2024
Topics include vectors in three-space and vector valued functions. The multivariate calculus, including partial differentiation, multiple integrals, line and surface integrals, and the vector calculus, including Green's theorem, the divergence theorem, and Stokes's theorem. Applications. Prerequisite: APMA 1110 or MATH 1320.
APMA 2130Ordinary Differential Equations (4)
Offered
Spring 2024
First order differential equations, second order and higher order linear differential equations, undetermined coefficients, variation of parameters, Laplace transforms, linear systems of first order differential equations and the associated matrix theory, numerical methods. Applications. Prerequisite: APMA 2120 or equivalent.
APMA 2501Special Topics in Applied Mathematics (1 - 4)
Special topics in applied mathematics
APMA 3080Linear Algebra (3)
Offered
Spring 2024
Analyze and apply systems of linear equations; vector spaces; linear transformations; matrices; determinants; eigenvalues; eigenvectors; coordinates; diagonalization; orthogonality; projections; inner product spaces; quadratic forms; The course is both computational and applicable. MATLAB is frequently used and prior experience in MATLAB (loops, functions, arrays, conditional statements) is helpful. Prerequisite: APMA 2120 or equivalent.
APMA 3100Probability (3)
Offered
Spring 2024
A calculus-based introduction to probability theory and its applications in engineering and applied science. Includes counting techniques, conditional probability, independence, discrete and continuous random variables, probability distribution functions, expected value and variance, joint distributions, covariance, correlation, the Central Limit theorem, the Poisson process, an introduction to statistical inference. Students must have completed APMA 2120 or APMA 2512 Topic #1 Honors Engineering Math II and CS 1110 or CS 1111 or CS 1112
APMA 3110Applied Statistics and Probability (3)
Offered
Spring 2024
Introduces basic concepts of probability such as random variables, single and joint probability distributions, and the central limit theorem. The course then emphasizes applied statistics, including descriptive statistics, statistical inference, confidence intervals, hypothesis testing, correlation, linear regression, and ANOVA. Students cannot receive credit for both this course and APMA 3120. Prerequisite: APMA 2120 or equivalent.
APMA 3120Statistics (3)
Offered
Spring 2024
Includes point estimation methods, confidence intervals, hypothesis testing for one population and two populations, categorical data tests, single and multi-factor analysis of variance (ANOVA) techniques, linear and non-linear regression and correlation analysis, and non-parametric tests. Students cannot receive credit for both this course and APMA 3110. Prerequisite: APMA 3100 or MATH 3100.
APMA 3140Applied Partial Differential Equations (3)
Offered
Spring 2024
Partial differential equations that govern physical phenomena in science and engineering. Separation of variables, superposition, Fourier series, Sturm-Liouville eigenvalue problems, eigenfunction expansion techniques. Particular focus on the heat, wave, and Laplace partial differential equations in rectangular, cylindrical, and spherical coordinates. Prerequisites: (APMA 2120 or MATH 2310 or MATH 2315) AND (APMA 2130 or MATH 3250 or APMA 2501 topic Diff Equations & Linear Algebra)
APMA 3150From Data to Knowledge (3)
Offered
Spring 2024
This course uses a Case-Study approach to teach statistical techniques with R: confidence intervals, hypotheses tests, regression, and anova. Also, it covers major statistical learning techniques for both supervised and unsupervised learning. Supervised learning topics cover regression and classification, and unsupervised learning topics cover clustering & principal component analysis. Prior basic statistic skills are needed.
APMA 3340Complex Variables with Applications (3)
Offered
Spring 2024
Topics include analytic functions, Cauchy Theorems and formulas, power series, Taylor and Laurent series, complex integration, residue theorem, conformal mapping, and Laplace transforms. Prerequisite: APMA 2120 or MATH 2310 or APMA 2512 - Honors Engineering Mathematics II.
APMA 3501Special Topics in Applied Mathematics (1 - 4)
Offered
Spring 2024
Applies mathematical techniques to special problems of current interest. Topic for each semester are announced at the time of course enrollment.
APMA 4501Special Topics in Applied Mathematics (3)
Applies mathematical techniques to special problems of current interest. Topic for each semester are announced at the time of course enrollment.
Course was offered Spring 2019, Spring 2018, Spring 2017
APMA 4993Independent Reading and Research (1 - 3)
Reading and research under the direction of a faculty member. Prerequisite: Fourth-year standing.
APMA 4995Independent Reading and Research (3)
Reading and research under the direction of a faculty member. Prerequisite: Fourth-year standing.
Course was offered Spring 2010
APMA 5070Numerical Methods (3)
Introduces techniques used in obtaining numerical solutions, emphasizing error estimation. Includes approximation and integration of functions, and solution of algebraic and differential equations. Prerequisite: Two years of college mathematics, including some linear algebra and differential equations, and the ability to write computer programs in any language.
APMA 6000TNon-UVa Transfer/Test Credit (3)
APMA 6020Continuum Mechanics with Applications (3)
Introduces continuum mechanics and mechanics of deformable solids. Vectors and cartesian tensors, stress, strain, deformation, equations of motion, constitutive laws, introduction to elasticity, thermal elasticity, viscoelasticity, plasticity, and fluids. Cross-listed as AM 6020, MAE 6020, CE 6720 Prerequisite: Instructor Permission
APMA 6130Mathematical Foundations of Continuum Mechanics (3)
Describes the mathematical foundations of continuum mechanics from a unified viewpoint. Review of relevant concepts from linear algebra, vector calculus, and Cartesian tensors; kinematics of finite deformations and motions; finite strain measures; linearization; concept of stress; conservation laws of mechanics and equations of motion and equilibrium; constitutive theory; constitutive laws for nonlinear elasticity; generalized Hooke's law for a linearly elastic solid; constitutive laws for Newtonian and non-Newtonian fluids; basic problems of continuum mechanics as boundary-value problems for partial differential equations. Cross-listed as AM 6130. Prerequisite: Linear Algebra, Vector Calculus, Elementary PDE (may be taken concurrently).
APMA 6150Linear Algebra (3)
Analyzes systems of linear equations; least squares procedures for solving overĀ­ determined systems; finite dimensional vector spaces; linear transformations and their representation by matrices; determinants; Jordan canonical form; unitary reduction of symmetric and Hermitian forms; eigenvalues; and invariant subspaces. Prerequisite: Three years of college mathematics or instructor permission.
APMA 6240Nonlinear Dynamics and Waves (3)
Introduces phase-space methods, elementary bifurcation theory and perturbation theory, and applies them to the study of stability in the contexts of nonlinear dynamical systems and nonlinear waves, including free and forces nonlinear vibrations and wave motions. Examples are drawn from mechanics and fluid dynamics, and include transitions to periodic oscillations and chaotic oscillations. Also cross-listed as MAE 6240. Prerequisite: Undergraduate ordinary differential equations or instructor permission.
APMA 6340Numerical Analysis (3)
Topics include the solution of systems of linear and nonlinear equations, calculations of matrix eigenvalues, least squares problems, and boundary value problems in ordinary and partial differential equations. Prerequisite: Two years of college mathematics, including some linear algebra, and the ability to write computer programs.
APMA 6370Singular Perturbation Theory (3)
Analyses of regular perturbations; roots of polynomials; singular perturbations in ODE's; periodic solutions of simple nonlinear differential equations; multiple-Scales method; WKBJ approximation; turning-point problems; Langer's method of uniform approximation; asymptotic behavior of integrals; Laplace Integrals; stationary phase; and steepest descents. Examples are drawn from physical systems. Cross-listed as MAE 6370. Prerequisite: Familiarity with complex analysis.
APMA 6410Engineering Mathematics I (3)
Review of ordinary differential equations. Initial value problems, boundary value problems, and various physical applications. Linear algebra, including systems of linear equations, matrices, eigenvalues, eigenvectors, diagonalization, and various applications. Scalar and vector field theory, including the divergence theorem, Green's theorem, Stokes theorem, and various applications. Partial differential equations that govern physical phenomena in science and engineering. Solution of partial differential equations by separation of variables, superposition, Fourier series, variation of parameters, d' Alembert's solution. Eigenfunction expansion techniques for nonhomogeneous initial-value, boundary-value problems. Particular focus on various physical applications of the heat equation, the potential (Laplace) equation, and the wave equation in rectangular, cylindrical, and spherical coordinates. Cross-listed as MAE 6410. Prerequisite: Graduate standing.
APMA 6420Engineering Mathematics II (3)
Further and deeper understanding of partial differential equations that govern physical phenomena in science and engineering. Solution of linear partial differential equations by eigenfunction expansion techniques. Green's functions for time-independent and time-dependent boundary value problems. Fourier transform methods, and Laplace transform methods. Solution of a variety of initial-value, boundary-value problems. Various physical applications. Study of complex variable theory. Functions of a complex variable, and complex integral calculus, Taylor series, Laurent series, and the residue theorem, and various applications. Serious work and efforts in the further development of analytical skills and expertise. Cross-listed as MAE 6420. Prerequisite: Graduate standing and APMA 6410 or equivalent.
APMA 6430Statistics for Engineers and Scientists (3)
Offered
Spring 2024
Analyzes the role of statistics in science; hypothesis tests of significance; confidence intervals; design of experiments; regression; correlation analysis; analysis of variance; and introduction to statistical computing with statistical software libraries. Prerequisite: Admission to graduate studies.
APMA 6440Applied Partial Differential Equations (3)
Includes first order partial differential equations (linear, quasilinear, nonlinear); classification of equations and characteristics; and well-posedness of initial and boundary value problems. Cross-listed as MAE 6440. Prerequisite: APMA 6420 or equivalent.
APMA 6548Special Topics in Applied Mathematics (1 - 3)
Offered
Spring 2024
Topics vary from year to year and are selected to fill special needs of graduate students.
APMA 6720Computational Fluid Dynamics I (3)
Topics include the solution of flow and heat transfer problems involving steady and transient convective and diffusive transport; superposition and panel methods for inviscid flow; finite-difference methods for elliptic, parabolic, and hyperbolic partial differential equations; elementary grid generation for odd geometries; and primitive variable and vorticity-steam function algorithms for incompressible, multidimensional flows. Extensive use of personal computers/workstations including graphics. Cross-listed as MAE 6720. Prerequisite: MAE 6310 or instructor permission.
Course was offered Spring 2010
APMA 6993Independent Study (1 - 12)
Detailed study of graduate-level material on an independent basis under the guidance of a faculty member.
APMA 6995Supervised Project Research (1 - 12)
Formal record of student commitment to project research under the guidance of a faculty advisor. May be repeated as necessary.
Course was offered Spring 2010
APMA 7080Inelastic Solid Mechanics (3)
Emphasizes the formulation of a variety of nonlinear models. Specific topics include nonlinear elasticity, creep, visco-elasticity, and elasto-plasticity. Solutions to boundary value problems of practical interest are presented in the context of these various theories in order to illustrate the differences in stress distributions caused by different types of material nonlinearities. Cross-listed as AM 7080. Prerequisite: AM 6020.
APMA 7140Nonlinear Elasticity Theory (3)
Describes the theory of finite (nonlinear) elasticity governing large deformations of highly deformable elastic solids. Both physical and mathematical implications considered. The results are applicable to rubber-like and biological materials and the theory serves as a prototype for more elaborate nonlinear theories of mechanics of continuous media. Cross-listed as AM 7140 Nonlinear Elasticity. Prerequisite: AM 6020 Continuum Mech. (or equiv)
Course was offered Spring 2013, Spring 2011
APMA 7340Numerical Solution of Partial Differential Equations (3)
Topics include the numerical solution of elliptic equations by finite element methods; solution of time dependent problems by finite element and finite difference methods; and stability and convergence results for the methods presented. Prerequisite: One or more graduate courses in mathematics or applied mathematics.
APMA 7548Selected Topics in Applied Mathematics (3)
Content varies annually; topics may include wave propagation theory, shell theory, control theory, or advanced numerical analysis. Prerequisite: Instructor permission.
APMA 7670Micromechanics of Heterogeneous Media (3)
Includes averaging principles; equivalent homogeneity; effective moduli; bounding principles; self-consistent schemes; composite spheres; concentric cylinders; three phase model; repeating cell models; inelastic and nonlinear effects; thermal effects; isotropic and anisotropic media; and strength and fracture. Cross-listed as AM 7670, and CE 7770. Prerequisite: APMA 6020.
APMA 7720Computational Fluid Dynamics II (3)
A continuation of APMA 6720. More advanced methods for grid generation, transformation of governing equations for odd geometries, methods for compressible flows, methods for parabolic flows, calculations using vector and parallel computers. Use of personal computers/workstations/supercomputer including graphics. Cross-listed as MAE 7720. Prerequisite: APMA 6720 or equivalent.
APMA 7993Independent Study (1 - 12)
Detailed study of advanced graduate-level material on an independent basis under the guidance of a faculty member.
APMA 8548Advanced Topics in Applied Mathematics (3)
Course content varies from year to year and depends on students' interests and needs. See APMA 7548 for possible topics. Prerequisite: Instructor permission.
APMA 8897Graduate Teaching Instruction (1 - 6)
For master's students.
APMA 8995Supervised Project Research (1 - 12)
Formal record of student commitment to project research for Master of Applied Mathematics degree under the guidance of a faculty advisor. Registration may be repeated as necessary.
Course was offered Spring 2010
APMA 8999Non-Topical Research, Master's Thesis (1 - 12)
Formal record of student commitment to master's thesis research under the guidance of a faculty advisor. Registration may be repeated as necessary.
Course was offered Spring 2010
APMA 9897Graduate Teaching Instruction (1 - 6)
For doctoral students.
APMA 9999Non-Topical Research, Doctoral Thesis (1 - 12)
Formal record of student commitment to doctoral research under the guidance of a faculty advisor. May be repeated as necessary.
Course was offered Spring 2010, Fall 2009