Academic Calendar - 2024
Western University Academic Calendar. - 2024
Applied Mathematics
Applications of integration, integration using mathematical software packages. Scaling and allometry. Basic probability theory. Fundamentals of linear algebra: vectors, matrices, matrix algebra. Difference and differential equations. Each topic will be illustrated by examples and applications from the biological sciences, such as population growth, predator-prey dynamics, age-structured populations.
Prerequisite(s): One or more of Calculus 1000A/B, Calculus 1500A/B, Mathematics 1225A/B, Numerical and Mathematical Methods 1412A/B, or the former Applied Mathematics 1412A/B.
Extra Information: 4 lecture hours.
Course Weight: 0.50
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Introduction to first order differential equations, linear second and higher order differential equations with applications, complex numbers including Euler's formula, series solutions, Bessel and Legendre equations, existence and uniqueness, introduction to systems of linear differential equations.
Prerequisite(s): A minimum mark of 60% in Calculus 1301A/B, or a minimum mark of 55% in Calculus 1501A/B or Numerical and Mathematical Methods 1414A/B or the former Applied Mathematics 1414A/B or the former Applied Mathematics 1413. Integrated Science 1001X with a minimum mark of 60% can be used in place of Calculus 1301A/B.
Pre-or Corequisite(s): Mathematics 1600A/B.
Extra Information: 3 lecture hours, 1 laboratory hour.
Course Weight: 0.50
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Vector space examples. Inner products, orthogonal sets including Legendre polynomials, trigonometric functions, wavelets. Projections, least squares, normal equations, Fourier approximations. Eigenvalue problems, diagonalization, defective matrices. Coupled difference and differential equations; applications such as predator-prey, business competition, coupled oscillators. Singular value decomposition, image approximations. Linear transformations, graphics.
Prerequisite(s): (Numerical and Mathematical Methods 1411A/B or the former Applied Mathematics 1411A/B, or Mathematics 1600A/B) and (Numerical and Mathematical Methods 1414A/B or Calculus 1301A/B or Calculus 1501A/B, or the former Applied Mathematics 1413 or the former Applied Mathematics 1414A/B). Integrated Science 1001X with a minimum mark of 60% can be used in place of Calculus 1301A/B.
Extra Information: 3 lecture hours.
Course Weight: 0.50
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Introduction to numerical analysis; polynomial interpolation, numerical integration, matrix computations, linear systems, nonlinear equations and optimization, the initial value problem. Assignments using a computer and the software package, Matlab, are an important component of this course.
Prerequisite(s): A minimum mark of 55% in Mathematics 1600A/B.
Pre-or Corequisite(s): Calculus 2302A/B, Calculus 2402A/B or Calculus 2502A/B.
Extra Information:3 lecture hours, 1 laboratory hour.
Course Weight: 0.50
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An introduction to mathematical biology. Case studies from neuroscience,immunology, medical imaging, cell biology, molecular evolution and ecology will give an overview of this diverse field, illustrating standard mathematical approaches such as compartmental analysis and evolutionary game theory.
Prerequisite(s): One of Calculus 2302A/B, Calculus 2402A/B, Calculus 2502A/B; plus one of Mathematics 1600A/B or the former Linear Algebra 1600A/B, or Applied Mathematics 1411A/B.
Extra Information: 3 lecture hours.
Course Weight: 0.50
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Functions of a complex variable, analytic functions, integration in the complex plane, Taylor and Laurent series, analytic continuation, Cauchy's theorem, evaluation of integrals using residue theory, applications to Laplace transforms, conformal mapping and its applications.
Prerequisite(s): Calculus 2303A/B or Calculus 2503A/B.
Extra Information: 3 lecture hours.
Course Weight: 0.50
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Existence and uniqueness of solutions, phase space, singular points, stability, periodic attractors, Poincaré-Bendixson theorem, examples from physics, biology and engineering, frequency (phase) locking, parametric resonance, Floquet theory, stability of periodic solutions, strange attractors and chaos, Lyapunov exponents, chaos in nature, fractals.
Prerequisite(s): Applied Mathematics 2402A/B or the former Differential Equations 2402A; Calculus 2303A/B or Calculus 2503A/B and Mathematics 1600A/B or the former Linear Algebra 1600A/B.
Extra Information: 3 lecture hours.
Course Weight: 0.50
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Boundary value problems for Laplace, heat, and wave equations; derivation of equations; separation of variables; Fourier series; Sturm-Liouville Theory; eigenfunction expansions; cylindrical and spherical problems; Legendre and Bessel functions; spherical harmonics; Fourier and Laplace transforms.
Prerequisite(s): (i) Mathematics 1600A/B; Applied Mathematics 2402A/B; Calculus 2303A/B or Calculus 2503A/B; or (ii) Calculus 2402A/B and Statistical Sciences 2503A/B. In each course a minimum mark of 60% is required.
Extra Information: 3 lecture hours.
Course Weight: 0.50
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The course will provide an overview of the mathematical modelling of the spread of infectious disease within populations and equip students to use mathematical models to describe real-world disease incidence data. Topics include: ordinary differential equation models of endemic, epidemic and pandemic diseases; model selection, data fitting and parameter estimation.
Antirequisite(s): Applied Mathematics 3615A/B, if taken in the 2020-21 or 2021-22, and Mathematics 4958B, if taken in 2022-23 with the topic “Covid Modelling”.
Prerequisite(s): Applied Mathematics 2402A/B or Statistical Sciences 2503A/B or Numerical and Mathematical Methods 2270A/B. Recommended: Applied Mathematics 3615A/B and Applied Mathematics 2814A/B as pre- or co-requisites.
Extra Information: 3 lecture hours.
Course Weight: 0.50
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An introduction to neural networks, covering the fundamentals of neural computation and how networks of neurons support information processing in the brain. Coursework will introduce techniques in computational modeling, programming and data science, focusing on recent developments in deep learning as applied to the context of explaining the brain.
Prerequisite(s): Applied Mathematics 3813A/B and Applied Mathematics 3815A/B or with the permission of the Department of Mathematics.
Extra Information: 2 lecture hours, 2 computer lab hours.
Course Weight: 0.50
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Strengths and limitations of computer algebra systems (CAS); complexity of exact computations versus possible instability of numerical computations; selecta from Groebner bases, resultants, fractional derivatives, Risch integration algorithm, special functions including the Lambert W function. The emphasis is on preparing the student to use CAS in mathematics, science, and engineering.
Prerequisite(s): Applied Mathematics 2814F/G or the former Applied Mathematics 2413, the former Applied Mathematics 2415.
Extra Information: 3 lecture hours.
Course Weight: 0.50
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Boundary value problems for Laplace and Helmholtz equations, initial value problems for heat and wave equations, in one to three dimensions; Green's functions in bounded and unbounded domains; Method of Images.
Prerequisite(s): Applied Mathematics 3815A/B.
Extra Information: 3 lecture hours.May be offered in alternate years.
Course Weight: 0.50
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The student will work on a project under faculty supervision. The project may involve an extension, or more detailed coverage, of material presented in other courses. Credit for the course will involve a written as well as oral presentation.
Prerequisite(s): Registration in the fourth year of a program in Applied Mathematics.
Course Weight: 0.50
Return to top
Applied Mathematics
Applications of integration, integration using mathematical software packages. Scaling and allometry. Basic probability theory. Fundamentals of linear algebra: vectors, matrices, matrix algebra. Difference and differential equations. Each topic will be illustrated by examples and applications from the biological sciences, such as population growth, predator-prey dynamics, age-structured populations.
Prerequisite(s): One or more of Calculus 1000A/B, Calculus 1500A/B, Mathematics 1225A/B, Numerical and Mathematical Methods 1412A/B, or the former Applied Mathematics 1412A/B.
Extra Information: 4 lecture hours.
Course Weight: 0.50
Return to top
Introduction to first order differential equations, linear second and higher order differential equations with applications, complex numbers including Euler's formula, series solutions, Bessel and Legendre equations, existence and uniqueness, introduction to systems of linear differential equations.
Prerequisite(s): A minimum mark of 60% in Calculus 1301A/B, or a minimum mark of 55% in Calculus 1501A/B or Numerical and Mathematical Methods 1414A/B or the former Applied Mathematics 1414A/B or the former Applied Mathematics 1413. Integrated Science 1001X with a minimum mark of 60% can be used in place of Calculus 1301A/B.
Pre-or Corequisite(s): Mathematics 1600A/B.
Extra Information: 3 lecture hours, 1 laboratory hour.
Course Weight: 0.50
Return to top
Vector space examples. Inner products, orthogonal sets including Legendre polynomials, trigonometric functions, wavelets. Projections, least squares, normal equations, Fourier approximations. Eigenvalue problems, diagonalization, defective matrices. Coupled difference and differential equations; applications such as predator-prey, business competition, coupled oscillators. Singular value decomposition, image approximations. Linear transformations, graphics.
Prerequisite(s): (Numerical and Mathematical Methods 1411A/B or the former Applied Mathematics 1411A/B, or Mathematics 1600A/B) and (Numerical and Mathematical Methods 1414A/B or Calculus 1301A/B or Calculus 1501A/B, or the former Applied Mathematics 1413 or the former Applied Mathematics 1414A/B). Integrated Science 1001X with a minimum mark of 60% can be used in place of Calculus 1301A/B.
Extra Information: 3 lecture hours.
Course Weight: 0.50
Return to top
Introduction to numerical analysis; polynomial interpolation, numerical integration, matrix computations, linear systems, nonlinear equations and optimization, the initial value problem. Assignments using a computer and the software package, Matlab, are an important component of this course.
Prerequisite(s): A minimum mark of 55% in Mathematics 1600A/B.
Pre-or Corequisite(s): Calculus 2302A/B, Calculus 2402A/B or Calculus 2502A/B.
Extra Information:3 lecture hours, 1 laboratory hour.
Course Weight: 0.50
Return to top
An introduction to mathematical biology. Case studies from neuroscience,immunology, medical imaging, cell biology, molecular evolution and ecology will give an overview of this diverse field, illustrating standard mathematical approaches such as compartmental analysis and evolutionary game theory.
Prerequisite(s): One of Calculus 2302A/B, Calculus 2402A/B, Calculus 2502A/B; plus one of Mathematics 1600A/B or the former Linear Algebra 1600A/B, or Applied Mathematics 1411A/B.
Extra Information: 3 lecture hours.
Course Weight: 0.50
Return to top
Functions of a complex variable, analytic functions, integration in the complex plane, Taylor and Laurent series, analytic continuation, Cauchy's theorem, evaluation of integrals using residue theory, applications to Laplace transforms, conformal mapping and its applications.
Prerequisite(s): Calculus 2303A/B or Calculus 2503A/B.
Extra Information: 3 lecture hours.
Course Weight: 0.50
Return to top
Existence and uniqueness of solutions, phase space, singular points, stability, periodic attractors, Poincaré-Bendixson theorem, examples from physics, biology and engineering, frequency (phase) locking, parametric resonance, Floquet theory, stability of periodic solutions, strange attractors and chaos, Lyapunov exponents, chaos in nature, fractals.
Prerequisite(s): Applied Mathematics 2402A/B or the former Differential Equations 2402A; Calculus 2303A/B or Calculus 2503A/B and Mathematics 1600A/B or the former Linear Algebra 1600A/B.
Extra Information: 3 lecture hours.
Course Weight: 0.50
Return to top
Boundary value problems for Laplace, heat, and wave equations; derivation of equations; separation of variables; Fourier series; Sturm-Liouville Theory; eigenfunction expansions; cylindrical and spherical problems; Legendre and Bessel functions; spherical harmonics; Fourier and Laplace transforms.
Prerequisite(s): (i) Mathematics 1600A/B; Applied Mathematics 2402A/B; Calculus 2303A/B or Calculus 2503A/B; or (ii) Calculus 2402A/B and Statistical Sciences 2503A/B. In each course a minimum mark of 60% is required.
Extra Information: 3 lecture hours.
Course Weight: 0.50
Return to top
The course will provide an overview of the mathematical modelling of the spread of infectious disease within populations and equip students to use mathematical models to describe real-world disease incidence data. Topics include: ordinary differential equation models of endemic, epidemic and pandemic diseases; model selection, data fitting and parameter estimation.
Antirequisite(s): Applied Mathematics 3615A/B, if taken in the 2020-21 or 2021-22, and Mathematics 4958B, if taken in 2022-23 with the topic “Covid Modelling”.
Prerequisite(s): Applied Mathematics 2402A/B or Statistical Sciences 2503A/B or Numerical and Mathematical Methods 2270A/B. Recommended: Applied Mathematics 3615A/B and Applied Mathematics 2814A/B as pre- or co-requisites.
Extra Information: 3 lecture hours.
Course Weight: 0.50
Return to top
An introduction to neural networks, covering the fundamentals of neural computation and how networks of neurons support information processing in the brain. Coursework will introduce techniques in computational modeling, programming and data science, focusing on recent developments in deep learning as applied to the context of explaining the brain.
Prerequisite(s): Applied Mathematics 3813A/B and Applied Mathematics 3815A/B or with the permission of the Department of Mathematics.
Extra Information: 2 lecture hours, 2 computer lab hours.
Course Weight: 0.50
Return to top
Strengths and limitations of computer algebra systems (CAS); complexity of exact computations versus possible instability of numerical computations; selecta from Groebner bases, resultants, fractional derivatives, Risch integration algorithm, special functions including the Lambert W function. The emphasis is on preparing the student to use CAS in mathematics, science, and engineering.
Prerequisite(s): Applied Mathematics 2814F/G or the former Applied Mathematics 2413, the former Applied Mathematics 2415.
Extra Information: 3 lecture hours.
Course Weight: 0.50
Return to top
Boundary value problems for Laplace and Helmholtz equations, initial value problems for heat and wave equations, in one to three dimensions; Green's functions in bounded and unbounded domains; Method of Images.
Prerequisite(s): Applied Mathematics 3815A/B.
Extra Information: 3 lecture hours.May be offered in alternate years.
Course Weight: 0.50
Return to top
The student will work on a project under faculty supervision. The project may involve an extension, or more detailed coverage, of material presented in other courses. Credit for the course will involve a written as well as oral presentation.
Prerequisite(s): Registration in the fourth year of a program in Applied Mathematics.