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MATH 4740: Advanced Applied Mathematics I
3.00 Credits
University of Toledo
Series and numerical solutions to ordinary differential equations, special functions, orthogonal functions, Sturm-Liouville problems, self-adjointness, vector analysis.
Prerequisite:
MATH 2860 FOR LEVEL UG WITH MIN. GRADE OF C-
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MATH 4740 - Advanced Applied Mathematics I
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MATH 4750: Advanced Applied Mathematics II
3.00 Credits
University of Toledo
Continuation of vector analysis, introduction to complex analysis, partial differential equations, Fourier series and integrals.
Prerequisite:
MATH 4740 FOR LEVEL UG WITH MIN. GRADE OF C-
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MATH 4750 - Advanced Applied Mathematics II
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MATH 4760: Actuarial Mathematics I
3.00 Credits
University of Toledo
Survival distributions and life tables, life insurance, life annuities, benefit premiums and reserves and multiple life functions are some topics covered in this course.
Prerequisite:
MATH 4680 FOR LEVEL UG WITH MIN. GRADE OF C-
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MATH 4760 - Actuarial Mathematics I
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MATH 4770: Actuarial Mathematics II
3.00 Credits
University of Toledo
Continuation of Actuarial Mathematics I. Multiple decrement models, collective risk models and applications of risk theory.
Prerequisite:
MATH 4760 FOR LEVEL UG WITH MIN. GRADE OF C-
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MATH 4770 - Actuarial Mathematics II
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MATH 4780: Advanced Calculus
3.00 Credits
University of Toledo
Extrema for functions of one or more variables, Lagrange multipliers, indeterminate forms, inverse and implicit function theorems, uniform convergences, power series, transformations, Jacobians, multiple integrals.
Prerequisite:
MATH 2850 FOR LEVEL UG WITH MIN. GRADE OF C-
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MATH 4780 - Advanced Calculus
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MATH 4800: Ordinary Differential Equations
3.00 Credits
University of Toledo
Modern theory of differential equations; transforms and matrix methods; existence theorems and series solutions; and other selected topics.
Prerequisite:
MATH 2860 FOR LEVEL UG WITH MIN. GRADE OF C-
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MATH 4800 - Ordinary Differential Equations
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MATH 4810: Partial Differential Equations
3.00 Credits
University of Toledo
First and second order equations; numerical methods; separation of variables; solutions of heat and wave equations using eigenfunction techniques; and other selected topics.
Prerequisite:
MATH 2860 FOR LEVEL UG WITH MIN. GRADE OF C-
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MATH 4810 - Partial Differential Equations
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MATH 4820: Introduction To Real Analysis I
3.00 Credits
University of Toledo
The real number system; continuity and differentiability of functions; convergence of sequences and series; applications.
Prerequisite:
MATH 2190 FOR LEVEL UG WITH MIN. GRADE OF C- OR MATH 3190 FOR LEVEL UG WITH MIN. GRADE OF C-
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MATH 4820 - Introduction To Real Analysis I
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MATH 4830: Introduction To Real Analysis II
3.00 Credits
University of Toledo
Riemann Integral; limits of functions; elementary metric space theory including compactness, connectedness and completeness. Optional topics include differentiable functions on Rn; the Implicit and Inverse Function Theorems.
Prerequisite:
MATH 4820 FOR LEVEL UG WITH MIN. GRADE OF C-
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MATH 4830 - Introduction To Real Analysis II
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MATH 4860: Calculus Of Variations And Optimal Control I
3.00 Credits
University of Toledo
Conditions for an extrema (Euler's equations, Erdman corner conditions, conditions of Legendre, Jacobi, and Weierstrass, fields of extremals, Hilbert's invariant integral); Raleigh-Ritz method; isoperimetric problems; Lagrange, Mayer-Bolza problems. Recommended: MATH 4820.
Prerequisite:
MATH 1890 FOR LEVEL UG WITH MIN. GRADE OF C- OR MATH 2890 FOR LEVEL UG WITH MIN. GRADE OF C-
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MATH 4860 - Calculus Of Variations And Optimal Control I
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