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 1000 | Preparation for Engineering Mathematics (2.00) |

Covers the fundamental concepts necessary for success in engineering courses and Applied Mathemtics courses. Course was offered Fall 2009 | |

APMA 1090 | Single Variable Calculus I (4.00) |

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. Course was offered Fall 2017, Fall 2016, Fall 2015, Fall 2014, Fall 2013, Fall 2012, Summer 2012, Fall 2011, Summer 2011, Fall 2010, Summer 2010, Spring 2010, Fall 2009 | |

APMA 1110 | Single Variable Calculus II (4.00) |

Offered Spring 2018 | Includes the concepts of differential and integral calculus and applications to problems in geometry and elementary physics, including inverse functions, indeterminate forms, techniques of integration, parametric equations, polar coordinates, infinite series, including Taylor and Maclaurin series. Applications. Prerequisite: APMA 1090 or equivalent. Course was offered Fall 2017, Spring 2017, Fall 2016, Spring 2016, Fall 2015, Spring 2015, Fall 2014, Spring 2014, Fall 2013, Spring 2013, Fall 2012, Summer 2012, Spring 2012, Fall 2011, Summer 2011, Spring 2011, Fall 2010, Spring 2010, Fall 2009 |

APMA 1501 | Special Topics in Applied Mathematics (1.00) |

Student-led special topic courses which vary by semester. Course was offered Spring 2016, Spring 2014 | |

APMA 2102 | Discrete Mathematics I (3.00) |

Introduces discrete mathematics and proof techniques involving first order predicate logic and induction. Application areas include sets (finite and infinite, such as sets of strings over a finite alphabet), elementary combinatorial problems, and finite state automata. Develops tools and mechanisms for reasoning about discrete problems. Cross-listed as CS 2102. Prerequisite: APMA 1110 and CS 1110, or equivalent. | |

APMA 2120 | Multivariable Calculus (4.00) |

Offered Spring 2018 | 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. Course was offered Fall 2017, Summer 2017, Spring 2017, Fall 2016, Summer 2016, Spring 2016, Fall 2015, Summer 2015, Spring 2015, Fall 2014, Summer 2014, Spring 2014, Fall 2013, Summer 2013, Spring 2013, Fall 2012, Summer 2012, Spring 2012, Fall 2011, Summer 2011, Spring 2011, Fall 2010, Summer 2010, Spring 2010, Fall 2009 |

APMA 2130 | Ordinary Differential Equations (4.00) |

Offered Spring 2018 | First order differential equations, second order and higher order linear differential equations, reduction of order, undetermined coefficients, variation of parameters, series solutions, Laplace transforms, linear systems of first order differential equations and the associated matrix theory, numerical methods. Applications. Prerequisite: APMA 2120 or equivalent. Course was offered Fall 2017, Summer 2017, Spring 2017, Fall 2016, Summer 2016, Spring 2016, Fall 2015, Summer 2015, Spring 2015, Fall 2014, Summer 2014, Spring 2014, Fall 2013, Summer 2013, Spring 2013, Fall 2012, Summer 2012, Spring 2012, Fall 2011, Summer 2011, Spring 2011, Fall 2010, Summer 2010, Spring 2010, Fall 2009 |

APMA 2131 | Systems of Ordinary Differential Equations (1.00) |

Offered Spring 2018 | The focus will be on solving systems of ordinary differential equations using basic linear algebra. Techniques for both homogeneous and nonhomogenous systems will be introduced. Time permitting, solving differential equations with the unit step and unit impulse functions will also be covered. Prerequisite: Differential Equations from Virginia Community College or equivalent Course was offered Fall 2017 |

APMA 2501 | Special Topics in Applied Mathematics (1.00 - 4.00) |

Special topics in applied mathematics | |

APMA 2502 | Special Topics in Applied Mathematics (4.00) |

Offered Spring 2018 | Special topics in applied mathematics. Course was offered Spring 2017 |

APMA 2511 | Advanced Topics in Applied Mathematics (4.00) |

Advanced Special topics in Applied Mathematics Course was offered Fall 2017 | |

APMA 2512 | Advanced Topics in Applied Mathematics (4.00) |

Offered Spring 2018 | Advanced special topics in Applied Mathematics |

APMA 3080 | Linear Algebra (3.00) |

Offered Spring 2018 | Analyzes the systems of linear equations; vector spaces; linear dependence; bases; dimension; linear mappings; matrices; determinants; quadratic forms; eigenvalues; eigenvectors; orthogonal reduction to diagonal form; inner product spaces; numerical methods; geometric applications. Prerequisite: APMA 2120 or equivalent. Course was offered Fall 2017, Summer 2017, Spring 2017, Fall 2016, Summer 2016, Spring 2016, Fall 2015, Summer 2015, Spring 2015, Fall 2014, Summer 2014, Spring 2014, Fall 2013, Summer 2013, Spring 2013, Fall 2012, Summer 2012, Spring 2012, Fall 2011, Summer 2011, Spring 2011, Fall 2010, Summer 2010, Spring 2010, Fall 2009 |

APMA 3081 | Linear Algebra for General Vector Spaces (1.00) |

Offered Spring 2018 | Analyze systems of equations, finding the best approximation to a solution; vector space of matrices and polynomials; coordinate vectors, change of coordinate system; inner product space; linear transformations between general vector spaces; approximating a trigonometric function by a polynomial. Course was offered Fall 2017 |

APMA 3100 | Probability (3.00) |

Offered Spring 2018 | 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. Prerequisite: APMA 2120 or equivalent. |

APMA 3102 | Theory of Computation (3.00) |

Introduces computation theory including grammars, finite state machines and Turing machines; and graph theory. Prerequisite: APMA 2102 and either CS 2110 or 2220 all with grades of 'C' or better. | |

APMA 3110 | Applied Statistics and Probability (3.00) |

Offered Spring 2018 | Examines variability and its impact on decision-making. Introduces students to basic concepts of probability, such as random variables, probability distribution functions, and the central limit theorem. Based on this foundation, the course then emphasizes applied statistics covering topics such as descriptive statistics, statistical inference, confidence intervals, hypothesis testing, correlation, regression modeling, statistical quality control. Students cannot receive credit for both this course and APMA 3120. Prerequisite: APMA 2120 or equivalent. |

APMA 3120 | Statistics (3.00) |

Offered Spring 2018 | Includes confidence interval and point estimation methods, hypothesis testing for single samples, inference procedures for single-sample and two-sample studies, single and multifactor analysis of variance techniques, linear and non-linear regression and correlation, and using Minitab for large data sets. Students cannot receive credit for both this course and APMA 3110. Prerequisite: APMA 3100. |

APMA 3140 | Applied Partial Differential Equations (3.00) |

Offered Spring 2018 | 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 and 2130 or equivalents. |

APMA 3150 | From Data to Knowledge (3.00) |

This course uses a Case-Study approach to teach statistics with R. Basic statistical techniques covered include: correlation, confidence interval and point estimation methods, hypothesis testing for single samples, inference procedures for single-sample and two-sample studies, single and multifactor analysis of variance techniques, linear and non-linear regression, Monte-Carlo simulation techniques and bootstrap sampling. | |

APMA 3340 | Complex Variables with Applications (3.00) |

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 equivalent. | |

APMA 3501 | Special Topics in Applied Mathematics (1.00 - 4.00) |

Offered Spring 2018 | Applies mathematical techniques to special problems of current interest. Topic for each semester are announced at the time of course enrollment. |

APMA 4501 | Special Topics in Applied Mathematics (3.00) |

Offered Spring 2018 | 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 2017 |

APMA 4993 | Independent Reading and Research (1.00 - 3.00) |

Reading and research under the direction of a faculty member. Prerequisite: Fourth-year standing. | |

APMA 4995 | Independent Reading and Research (3.00) |

Reading and research under the direction of a faculty member. Prerequisite: Fourth-year standing. Course was offered Spring 2010 | |

APMA 5070 | Numerical Methods (3.00) |

Offered Spring 2018 | 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. Course was offered Spring 2017, Spring 2016, Spring 2015, Spring 2014, Spring 2013, Spring 2012, Spring 2011, Spring 2010 |

APMA 6000T | Non-UVa Transfer/Test Credit (3.00) |

APMA 6020 | Continuum Mechanics with Applications (3.00) |

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 6130 | Mathematical Foundations of Continuum Mechanics (3.00) |

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 6150 | Linear Algebra (3.00) |

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 6240 | Nonlinear Dynamics and Waves (3.00) |

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 6340 | Numerical Analysis (3.00) |

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 6370 | Singular Perturbation Theory (3.00) |

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 6410 | Engineering Mathematics I (3.00) |

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 6420 | Engineering Mathematics II (3.00) |

Offered Spring 2018 | 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. Course was offered Spring 2017, Spring 2016, Spring 2015, Spring 2014, Spring 2013, Spring 2012, Spring 2011, Spring 2010 |

APMA 6430 | Statistics for Engineers and Scientists (3.00) |

Offered Spring 2018 | 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. Course was offered Fall 2017, Spring 2017, Spring 2015, Spring 2014, Spring 2013, Spring 2012, Spring 2011, Spring 2010 |

APMA 6440 | Applied Partial Differential Equations (3.00) |

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 6548 | Special Topics in Applied Mathematics (1.00 - 3.00) |

Offered Spring 2018 | Topics vary from year to year and are selected to fill special needs of graduate students. |

APMA 6720 | Computational Fluid Dynamics I (3.00) |

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 6993 | Independent Study (1.00 - 12.00) |

Offered Spring 2018 | Detailed study of graduate-level material on an independent basis under the guidance of a faculty member. Course was offered Spring 2017, Spring 2016, Spring 2015, Spring 2014, Spring 2013, Spring 2012, Spring 2011, Spring 2010, Fall 2009 |

APMA 6995 | Supervised Project Research (1.00 - 12.00) |

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 7080 | Inelastic Solid Mechanics (3.00) |

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 7140 | Nonlinear Elasticity Theory (3.00) |

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 7340 | Numerical Solution of Partial Differential Equations (3.00) |

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 7548 | Selected Topics in Applied Mathematics (3.00) |

Offered Spring 2018 | Content varies annually; topics may include wave propagation theory, shell theory, control theory, or advanced numerical analysis. Prerequisite: Instructor permission. Course was offered Spring 2017, Spring 2016, Spring 2015, Spring 2014, Spring 2012, Spring 2011, Spring 2010 |

APMA 7670 | Micromechanics of Heterogeneous Media (3.00) |

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 7720 | Computational Fluid Dynamics II (3.00) |

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 7993 | Independent Study (1.00 - 12.00) |

Detailed study of advanced graduate-level material on an independent basis under the guidance of a faculty member. | |

APMA 8548 | Advanced Topics in Applied Mathematics (3.00) |

Course content varies from year to year and depends on students' interests and needs. See APMA 7548 for possible topics. Prerequisite: Instructor permission. | |

APMA 8897 | Graduate Teaching Instruction (1.00 - 12.00) |

Offered Spring 2018 | For master's students. Course was offered Fall 2017, Spring 2017, Fall 2016, Spring 2016, Fall 2015, Spring 2015, Fall 2014, Spring 2014, Fall 2013, Spring 2013, Spring 2012, Spring 2011, Spring 2010 |

APMA 8995 | Supervised Project Research (1.00 - 12.00) |

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 8999 | Non-Topical Research, Master's Thesis (1.00 - 12.00) |

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 9897 | Graduate Teaching Instruction (1.00 - 12.00) |

Offered Spring 2018 | For doctoral students. Course was offered Fall 2017, Spring 2017, Fall 2016, Spring 2016, Fall 2015, Spring 2015, Fall 2014, Spring 2014, Fall 2013, Fall 2012, Fall 2011, Fall 2010, Spring 2010, Fall 2009 |

APMA 9999 | Non-Topical Research, Doctoral Thesis (1.00 - 12.00) |

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 |