Complementary Studies elective

Introduces the basic concepts, frameworks and methodologies useful to managers in crafting and executing entrepreneurial business strategies in technology-based and selected CPG companies. In the first part of the course, students gain an understanding of the external, internal, and dynamic environments of a business and the elements of a superior competitive position. In the second part, we focus on designing and delivering customer value, which involves strategic decisions about segmentation, targeting and positioning, and tactical decisions related to product introductions, marketing communications, distribution channels and pricing. In the third part of the course, we build on these fundamentals and examine considerations related to commercialization, modes to exploit technology/product, intellectual property, and approaches to business start-up.

Spans three inter-related topics within organizational behavior and human resources: individual behaviour, group behaviour, and leadership. It provides students with both the theory and practice of how to work, lead, and thrive in organizations. Topics include theories of personality, learning, power, decision making, ethics, culture, leadership, teamwork, and motivation. These topics are taught in three ways:

1. Case studies, role play & simulation exercises followed by class discussion
2. Surveys of Personality & Skills
3. Lectures, discussions, and readings based on the current research on the topic

Topics include: include: linear systems, matrix algebra, Rn as a vector space, a normed space and an inner-product space, linear transformations on Rn, eigenvalues, applications to circuits, mechanics and an introduction to computer methods.

Topics include: limits and continuity; differentiation; applications of the derivative - related rates problems, curve sketching, optimization problems, L'Hopital's rule; definite and indefinite integrals; the Fundamental Theorem of Calculus; applications of integration in geometry, mechanics and other engineering problems.

Topics include: techniques of integration, an introduction to mathematical modeling with differential equations, infinite sequences and series, Taylor series, parametric and polar curves, and application to mechanics and other engineering problems.

This course covers systems of linear equations and Gaussian elimination, applications; vectors in Rn, independent sets and spanning sets; linear transformations, matrices, inverses; subspaces in Rn, basis and dimension; determinants; eigenvalues and diagonalization; systems of differential equations; dot products and orthogonal sets in Rn; projections and the Gram-Schmidt process; diagonalizing symmetric matrices; least squares approximation. Includes an introduction to numeric computation in a weekly laboratory.

Topics include: limits and continuity, differentiation, maximum and minimum problems, definite and indefinite integrals, application of integration to geometry, mechanics and other engineering problems as well as an introduction to first order differential equations.

Ordinary differential equations. Classification. Equations of first order and first degree. Linear equations of order n. Equations of second order. Bessel's equation. Legendre's equation. Series solutions. Systems of simultaneous equations. Partial differential equations. Classification of types. The diffusion equation. Laplace's equation. The wave equation. Solution by separation of variables.

Ordinary differential equations. Equations of first order and first degree. Linear equations of order n. Systems of simultaneous equations. Difference equations. Forecasting. Business dynamics. Basic Set Theory. Counting, Cartesian Product, Combinations, Permutations. Basic Propositional Logic and Proofs. Throughout the course: formulating and analysing differential equation, difference equation, and discrete mathematical models for real-world problems.

An introduction to complex variables and ordinary differential equations. Topics include: Laplace transforms, ordinary higher-order linear differential equations with constant coefficients; transform methods; complex numbers and the complex plane; complex functions; limits and continuity; derivatives and integrals; analytic functions and the Cauchy-Riemann equations; power series as analytic functions; the logarithmic and exponential functions; Cauchy's integral theorem, Laurent series, residues, Cauchy's integral formula, the Laplace transform as an analytic function. Examples are drawn from electrical systems.

The chain rule for functions of several variables; the gradient, directional derivative, tangent plane and small signal modeling and Jacobians. Multiple integrals; change of variables and Jacobians, line integrals: parametric and explicit representations, the divergence and curl of a vector field, surface integrals; parametric and explicit representations, multi-variable Dirac Delta distribution, superposition of vector fields, Helmholtz decomposition theorem, Divergence theorem and Stokes' theorem and application from electromagnetic fields.

Existence and uniqueness of solution for first-order differential equations, general second-order linear ODEs, homogeneous equations, nonhomogeneous equations, variable coefficients, variation of parameters, Systems of ODEs, Fourier series, Laplace transform, interpretation of problems in mathematical terms, single-step numerical methods for ODEs. Introduction to Partial Differential Equations.

Partial differentiation, grad, div, curl, multiple integrals, line integrals, surface integrals, differential equations, first order differential equations, homogeneous linear differential equations, boundary conditions. Formulation of various problems relevant to materials and mining engineering - the concepts above are used.

This course provides the foundations of analysis and rigorous calculus for students who will take subsequent courses where these mathematical concepts are central of applications, but who have only taken courses with limited proofs. Topics include topology of Rn, implicit and inverse function theorems and rigorous integration theory.

Construction of Real Numbers. Metric spaces; compactness and connectedness. Sequences and series of functions, power series; modes of convergence. Interchange of limiting processes; differentiation of integrals. Function spaces; Weierstrass approximation; Fourier series. Contraction mappings; existence and uniqueness of solutions of ordinary differential equations. Countability; Cantor set; Hausdorff dimension.

Function spaces; Arzela-Ascoli theorem, Weierstrass approximation theorem, Fourier series. Introduction to Banach and Hilbert spaces; contraction mapping principle, fundamental existence and uniqueness theorem for ordinary differential equations. Lebesgue integral; convergence theorems, comparison with Riemann integral, L^p spaces. Applications to probability.

Course examines the following: analytic functions, Cauchy-Reimann equations, contour integration, Cauchy's theorem, Taylor and Laurent series, singularities, residue calculus, conformal mapping, harmonic functions, Dirichlet and Neumann problems and Poisson integral formulas. Course includes studies of linear differential equations in the complex plane, including Bessel and Legendre functions.

This course on Newtonian mechanics considers the interactions which influence 2-D, curvilinear motion. These interactions are described in terms of the concepts of force, work, momentum and energy. Initially the focus is on the kinematics and kinetics of particles. Then, the kinematics and kinetics of systems of particles and solid bodies are examined. Finally, simple harmonic motion is discussed. The occurrence of dynamic motion in natural systems, such as planetary motion, is emphasized. Applications to engineered systems are also introduced.

This is a seminar series that will preview the core fields in Mechanical and Industrial Engineering. Each seminar will be given by a professional in one of the major areas in MIE. The format will vary and may include application examples, challenges, case studies, career opportunities, etc. The purpose of the seminar series is to provide first year students with some understanding of the various options within the Department to enable them to make educated choices for second year. This course will be offered on a credit/no credit basis. Students who receive no credit for this course must re-take it in their 2S session. Students who have not received credit for this course at the end of their 2S session will not be permitted to register in session 3F.

Humanities and Social Science elective

This course explores the relationship between changing technologies and cultural representations and teaches a methodology that bridges the world of the artist and the world of the engineer. It enables engineers to explore how the analysis of art has been used in the discussion of the social impacts of technological innovation and to use these methods as they develop new skills in essayistic argument and increase critical vocabulary.

This is a basic course in engineering thermodynamics. Topics covered include: properties and behaviour of pure substances; equation of states for ideal and real gases; compressibility factor; first and second laws of thermodynamics; control mass and control volume analyses; applications of first and second laws of thermodynamics to closed systems, open systems and simple thermal cycles.

Production Fundamentals: Metal casting; metal forming - rolling, forging, extrusion and drawing, and sheet-metal forming; plastic/ceramic/glass forming; metal removal - turning, drilling/ boring/reaming, milling, and grinding; non-traditional machining - ECM, EDM and laser cutting; welding; surface treatment; metrology. Environmental issues in manufacturing processes, recycling of materials. Automation Fundamentals: Automation in material processing and handling - NC, robotics and automatically-guided vehicles; flexible manufacturing - group technology, cellular manufacturing and FMS; and computer-aided design - geometric modelling, computer graphics, concurrent engineering and rapid prototyping.

Instruction and assessment of communication centered around course deliverables that will form part of an ongoing design portfolio.

Design of mechanical joints. Elasto-plastic torsion of circular sections. Elasto-plastic bending of beams. Residual stresses. Shearing stresses in beams. Analysis of plane stress and plane strain problems. Pressure vessels. Design of members using strength criteria. Deflection of beams. Statistically indeterminate structures.

Introduction to the methods of Data Science. Exploratory data analysis and visualization; tools for reproducible analysis. Principles and tools for data collection; awareness of bias in collection methods. Data cleaning. Descriptive statistics and feature analysis. Assessment of data with respect to scientific theories. Data interpretation fallacies. Geographical data representation and manipulation. Text processing, the natural language processing pipeline, and sentiment analysis. Fundamentals of social network analysis and centrality measures. Cloud-based data processing.

Multivariable calculus and its application to engineering analysis. Partial differentiation, double and triple integration, including calculation of volumes, centroids and moments. Differential calculus of curves and surfaces, including calculation of tangents, normals, gradients, divergence and curl. Line/work integrals and surface/flux integrals, and theorems relating them. Emphasis is also on the understanding and visualization of objects, scalar fields and vector fields in 2D and 3D, and their connections to engineering phenomena.

Use of data in engineering decision processes. Elements of probability theory. Discrete and continuous random variables. Standard distributions: binomial, Poisson, hypergeometric, exponential, normal etc. Expectation and variance. Random sampling and parameter estimation. Confidence intervals. Hypothesis testing. Goodness-of-fit tests. Regression and correlation. Statistical Process Control and quality assurance. Engineering applications in manufacturing, instrumentation and process control.

Introduction to numerical analysis techniques including the following topics: root-finding, polynomial interpolation, numerical integration, solution of linear systems of equations, least squares fitting, solution of nonlinear equations, numerical differentiation, solution of ordinary differential equations, and solution of partial differential equations. Lectures as well as tutorial assignments using computational software will emphasize algorithmic thinking and effective programming of computational methods for engineering applications.

Introduction to probability (the role of probability and data in engineering; concepts of population vs. sample). Sample space and events. Definitions of probability. Conditional probability and Bayes' rule. Concept of random variables. Discrete, continuous, and joint distributions. Statistical independence. Expectation, variance, covariance, and correlation. Important discrete and continuous distributions that explain engineering-related phenomena. Brief introduction to the homogeneous Poisson process and related distributions. How to derive distributions. Transformation of random variables. Fundamental sampling distributions, Chi-square, t, and F distributions. Central limit theorem, laws of large numbers. One sample estimation (methods of maximum likelihood, bootstrapping, and jackknife) and hypothesis testing.

Data gathering motivation and methods (observational vs. experimental). Modeling for inference vs. prediction. Data visualizations. Two sample estimation and hypothesis testing. Choice of sample size. Fitting distributions to data. Goodness of fit tests. Simple linear regression and correlation. Multiple linear regression. Model building and model assessment. Design and analysis of single and multi-factor experiments. Analysis of variance. Fixed and random effects models. Multiple comparisons.

Introduction to principles, methods, and tools for the analysis, design, and evaluation of human-centred systems. Consideration of impacts of human physical, physiological, perceptual, and cognitive factors on the design and use of engineered systems. Basic concepts of anthropometrics, work-related hazards, shiftwork, workload, human error and reliability, system complexity, and human factors standards. The human-centred systems design process, including task analysis, user requirements generation, prototyping, and usability evaluation. Design of work/rest schedules, procedures, displays and controls, and information and training systems; design for error prevention and human-computer interaction; design for accessibility and aging populations.