AS/SC/MATH 2015 3.0 F Applied
Multivariate and Vector Calculus
2001/2002 Calendar copy:
Topics covered
include partial derivatives; grad, div, curl and Laplacian
operators; line
and surface integrals; theorems of Gauss and Stokes; double and triple
integrals in various
coordinate systems; extrema and Taylor series for multivariate
functions. Prerequisite: One of AS/SC/ MATH 1010
3.0, AS/SC/ MATH 1014 3.0, AS/SC/AK/MATH
1310 3.0, or: AS/SC/
MATH 1505 6.0 plus permission of the Course
Coordinator.
2001/2002 Calendar copy:
Designed for students
in Applied Mathematics to complement and enrich material
in AS/SC/MATH 2015 3.0. The
module treats the theory in greater depth,
and explores extended applications and modeling. One lecture
hour per week. One term. One credit. Prerequisites: AS/SC/MATH 1014 3.0;
AS/SC/MATH 1017 1.0.
2001/2002 Calendar copy: Inner product spaces, linear transformations, eigenvalues, diagonalization, least squares, quadratic forms and Markov chains. Similiar to AS/SC/AK/MATH 2222 3.0 but at a more advanced level. Required in Specialized Honours Statistics and all Applied Mathematics, Mathematics, and Mathematics for Commerce programs except the BA Program in Mathematics for Commerce.
For a general
description of the subject "linear algebra'' see the minicalendar
entry for MATH 1021 3.0. Additional
topics: General linear transformations, matrix of a linear
transformation from
2001/2002 Calendar copy:
Introduction to
the theory of probability as preparation for further study
in either mathematical or
applied probability and statistics. Topics include probability
spaces, conditional probability, independence, random variables,
distribution functions,
expectation, Chebyshev's inequality, common distributions,
moment-generating functions and limit theorems.
2001/2002 Calendar copy:
An introduction
to symbolic computing in the Maple environment. Topics from
single-variable
differential and integral calculus, including simple ordinary
differential equations, are covered. Both mathematical understanding
and applications are emphasized.
2001/2002 Calendar copy:
Advanced symbolic
computing with Maple. Topics from linear algebra, differential
equations, multivariate calculus, integral theorems, are
covered. Both mathematical
understanding and applications are emphasized. Prerequisites: AS/SC/MATH 2041 3.0;
one of AS/SC/MATH 2010 3.0,
AS/SC/MATH 2015 3.0, AS/SC/AK/MATH 2310 3.0; one of AS/SC/AK/MATH 1021
3.0, AS/SC/MATH
1025 3.0, AS/SC/MATH
2021 3.0, AS/SC/AK/MATH 2221 3.0.
2001/2002 Calendar copy:
A continuation of AS/SC/AK/MATH 1090 3.0, this course uses
formal logic to study topics in discrete mathematics, including
sets, relations, functions, induction, the integers. Optional
topics include program specification, sequences, recurrence
relations.
2001/2002 Calendar copy:
This course is
a continuation of AS/SC/AK/MATH 2030 3.0. It provides students
with an introduction to
statistical methods with an
emphasis on applications using continuous
probability models. Note: Computer/Internet use
may be required to facilitate course work. Prerequisites: AS/SC/AK/MATH 2030 3.0;
one of AS/SC/ MATH
2010 3.0, AS/SC/MATH 2015 3.0, AS/SC/AK/MATH 2310 3.0.
2001/2002 Calendar copy:
Systems of
linear equations, linear and affine subspaces of Euclidean
Linear algebra
is a branch of mathematics which is particularly useful in
other fields and in other
branches of mathematics. Its frequent application in the
engineering and physical sciences rivals that of calculus. Computer
scientists and economists
have long recognized its relevance to their discipline.
Moreover, linear algebra is fundamental in the rapidly increasing
quantification that is
taking place in the management and social sciences. Finally,
ideas of linear algebra are essential to the development of algebra,
analysis, probability and
statistics, and geometry. Prerequisite: OAC algebra or any
university mathematics course.
2001/2002 Calendar copy:
Linear transformations
and their representation by matrices, change of basis and
similarity, eigenvalues and eigenvectors, diagonalization, inner
product spaces,
orthogonality, the Gram-Schmidt algorithm, least squares
approximations, abstract
vector spaces, various applications. This course is
a continuation of either MATH 1025 3.0W or MATH 2221
3.0, and requires knowledge of the topics discussed in those
courses. Prerequisite: AS/SC/AK/MATH 1021 3.0 or
AS/SC/MATH 1025 3.0 or
AS/SC/AK/MATH 2221 3.0.
2001/2002 Calendar copy:
Introduction to differential equations, including a discussion
of the formation of
mathematical models for real phenomena; solution by
special techniques; applications; linear equations; solutions in
series; other topics if
time permits. Prerequisites: One of
AS/SC/MATH 2010 3.0, AS/SC/MATH
2015 3.0, or AS/SC/AK/MATH 2310 3.0; one
of AS/SC/AK/MATH 1021 3.0, AS/SC/MATH 1025 3.0, AS/SC/MATH
2021 3.0, or AS/SC/AK/MATH 2221 3.0.
2001/2002 Calendar copy:
Topics include
measurement of interest, annuities, amortization of loans,
bonds, sinking funds and
depreciation. The course is at a level which will prepare
students for the interest theory portion of the Society of Actuaries
examinations. Prerequisite: AS/SC/MATH 1010 3.0 or
AS/SC/MATH 1014 3.0 or AS/SC/AK/MATH
1310 3.0.
2001/2002 Calendar copy:
Vector functions,
partial derivatives, gradient, multiple integrals, line integrals,
optimization, applications. Offered in both terms. Prerequisite: AS/SC/MATH 1010 3.0 or
AS/SC/MATH 1014 3.0 or AS/SC/AK/MATH
1310 3.0. Students should have a knowledge of vector
algebra in two and three dimensions.
2001/2002 Calendar copy:
Algebraic and combinatorial structures required in Computer
Science and other
disciplines. Review of sets; induction; combinatorics;
graph theory, trees; big Oh-notation, complexity of
algorithms; recursive definitions, recurrence relations;
posets; congruence
relations. This course emphasizes analysis, problem
solving and proofs.
2001/2002 Calendar copy:
This course provides an introduction to the concepts of
statistics with an emphasis on developing a critical attitude
towards the use and misuse
of statistics in business, health sciences
and other areas. Note:
Computer/Internet use may be required to facilitate course work.
2001/2002 Calendar copy:
Displaying and
describing distributions, normal distibution. Relationships
between variables,
regression and correlation. The need for design, experimental
design and sampling design. Sampling distributions, bias,
variability. Probability
models, random variables, probability laws. Prerequisite: Ontario Grade 12 Advanced
Mathematics.
2001/2002 Calendar copy:
Binomial distribution,
sampling distribution of sample proportions and means,
central limit theorem. Confidence intervals, tests and decisions,
abuse of tests. Inference
for a single mean, comparing two means, and for spread.
Contingency tables. Simple regression and basic analysis of
variance.
2001/2002 Calendar copy:
Theory of
interest; annuities certain; amortization and sinking funds;
evaluation of bonds and
other investments; depreciation, depletion and capital
cost; insurance, including mortality tables, principles of life
annuities, premiums and
reserves.
2001/2002 Calendar copy:
Spreadsheets and their application to business mathematics;
deepening of topics in Business Mathematics I, including
continuous compound interest, perpetuities, annuities where payments
vary, callable bonds, bond yield rate, capital budgeting;
mortality tables, life annuities, life insurance. |
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