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Course Criteria
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3.00 Credits
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 312.
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3.00 Credits
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 311.
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3.00 Credits
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 212 and 213 or equivalents.
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3.00 Credits
Topics include analytic functions, Cauchy Theorems and formulas, power series, Taylor and Laurent series, complex integration, residue theorem, conformal mapping, and Laplace transforms.
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3.00 Credits
Reading and research under the direction of a faculty member.
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3.00 Credits
Reading and research under the direction of a faculty member.
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3.00 Credits
Introduces techniques used in obtaining numerical solutions, emphasizing error estimation. Includes approximation and integration of functions, and solution of algebraic and differential equations.
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3.00 Credits
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 602, CE 602, and MAE 602.
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3.00 Credits
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 613.
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3.00 Credits
Analyzes systems of linear equations; least squares procedures for solving over 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.
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