If you're looking for online courses this summer to complement your degree or get ahead in your studies, consider one of our selections of online courses currently offered this summer.

Systems of linear equations; real vectors spaces and subspaces; linear combinations and linear spans; linear dependence and linear independence; applications to systems of linear equations and their solution via Gaussian elimination; bases and the dimension of real vector spaces; linear transformations, range, kernel, and Rank-Nullity theorem; matrix representation of a linear transformation; composition of linear transformations and matrix multiplication; invertible matrices and determinants; eigenvalues and eigenvectors of square matrices. Applications of the course material to engineering systems are illustrated.

**Credits:** 3.3

**Course learning outcomes:**

By the end of this course, learners should be able to:

- Solve parametrized or unparametrized systems of linear equations using Gaussian elimination and back substitution; they will be able to write the augmented matrix of a given system of linear equations, transform it into reduced or row-reduced echelon form using a sequence of elementary row operations, and finally solve the system using back substitution. They will be able to determine the number of solutions as a function of the parameter in case the system of linear equations is parametrized.
- Perform basic matrix algebraic operations (addition, scaling, multiplication).
- Understand the notions of eigenvalue, eigenspace, and eigenvector for a given vector space endomorphism; in particular, given a real n √ó n matrix, they will be able to compute the set of all eigenvalues of that matrix, as well as eigenvectors or bases for the eigenspaces corresponding to those eigenvalues.
- Compute the determinant of a real n √ó n matrix and know its main properties; in particular, they will be able to use the determinant in assessing whether or not a given n √ó n matrix is invertible.
- Prove linear algebraic results for general vector spaces; these proofs will require mathematical reasoning, will be expressed in precise mathematical language with full mathematical rigor, and will combine various notions seen in different parts of the course, such as vector subspace, linear span, linear independence, linear mapping, and eigenvalue/eigenspace/eigenvector.
- Understand the mathematical notion of a real vector space, and will be able to determine whether or not a given subset of a real vector space is a vector subspace; in particular, students will be able to work with vector spaces other than the usual Euclidean space Rn.
- Understand the notions of linear combination and linear span of a family of vectors, and will be able to determine whether or not a given vector is in the linear span of a given family of vectors.
- Understand the notions of linear dependence and independence of a family of vectors, and will be able to determine whether or not a given family of vectors in a vector space is linearly independent.
- Understand the notions of basis and dimension of a vector space; they will be able to compute a basis for a given vector space and use it to compute the dimension of the vector space.
- Understand the notion of a linear mapping between vector spaces; in particular, they will be able to determine whether or not a given mapping between vector spaces is linear.
- Understand the notions of kernel and image of a linear mapping; in particular, they will be able to compute the kernel and image of a given real matrix, and they will understand the precise relation between the kernel/image of a real matrix and its column vectors.

This course develops skills that are necessary to organize and present technical information in a professional context. At the end of the course, students will demonstrate English proficiency in listening comprehension and written expression.

**Credits:** K0.2** **

**Course learning outcomes:** TBA

This course will provide the student in the Engineering program with the ability to appropriately incorporate selected economic and business practices into the practice of engineering. The practices covered include business planning for the enterprise, enterprise economic analysis, project management process, project economic analysis, risk analysis and management, quality management, and change management. Assignments and examples are based on situations from engineering-based industries.

**Credits:** 3.0

**Course learning outcomes:**

By the end of this course, learners should be able to solve economic analysis problems:

- Cost concepts and use a variety of cost estimation techniques.
- Time value of money and solve cash flow analysis problems.
- Compare a variety of projects using multiple economic approaches.
- The effect of taxes on project viability and apply to appropriate cash flow analysis.
- Replacement analysis concepts and apply appropriate cash flow analysis to correctly determine minimum equivalent annual costs.
- The effect of inflation on project viability and apply to appropriate cash flow analysis.
- Apply a variety of approaches for dealing with uncertainty and risk associated with projects.
- Risk management approaches associated with project management.
- Change management from an organizational behaviour perspective.
- Recognizing new business opportunities and techniques for generating ideas.
- Feasibility Analysis.
- Assessing a new venture’s financial strength and viability.
- Writing a business plan.
- Basic management processes and concepts.

This course is an introduction to ordinary differential equations and their applications to the natural and engineering sciences. Specific topics include first-order differential equations, linear differential equations with constant coefficients, Laplace transforms, and systems of linear equations. Note: This course is being offered through the Faculty of Arts and Science.

**Credits:** 3.5

**Course learning outcomes:**

By the end of this course, learners should be able to:

- Solving basic initial value problems.
- Solving linear constant coefficient differential equations.
- Computing Laplace and inverse Laplace transforms.
- Using the Laplace transform to solve differential equations.
- Modeling a mass-spring-damper system or RLC circuit using differential equations.
- Modeling interconnected fluid reservoirs using differential equations.

**Prerequisites:** APSC 171, APSC 172, APSC 174

This course enables students to deepen their understanding of chemistry through the study of the structure and properties of matter, energy changes and rates of reaction, basic organic chemistry, equilibrium in chemical systems, and electrochemistry. Students will further develop their problem-solving and investigation skills as they investigate chemical processes, and this course will refine their ability to communicate scientific information.

**Credits:** 3.0

**Course learning outcomes: **

By the end of this course, learners should be able to:

- Describe the atomic structure and chemical bonding, and how they relate to the physical properties of ionic, molecular, covalent networks, and metallic substances.
- Perform calculations to an adequate level of precision.
- Solve problems relating to the physical properties of gases.
- Apply standard chemistry nomenclature (IUPAC) in the context of describing chemicals (including organic compounds) and chemical reactions.
- Use stoichiometry to solve common chemistry problems.
- Use reduction and oxidation chemistry to describe a galvanic cell and other practical applications.
- Calculate reagent concentrations in solutions.
- Use the concept of chemical equilibrium to predict the direction of reactions.
- Solve simplified acid and base problems.

This course presents a basic introduction to the use of classical and geostatistical estimation techniques for mineral resource estimation. Students will learn to recognize the geological influences to ore body modelling, apply various estimation methods, produce mineralization reports, and classify the mineral resources and reserves according to accepted internationally recognized methods. The course also includes basic ore exploration and sampling concepts.

**Credits:** 3.0

**Course learning outcomes:**

By the end of this course, learners should be able to:

- Describe the basic principles of rock failures.
- Recognize appropriate field and laboratory investigation programs to define rock failure criteria.
- Analyze data from field and laboratory investigations to define the failure criteria
- Recognize numerical stress analysis models for excavation design
- Use various empirical/analytical design methods for excavations such as open stopes, pillars, and open pit slopes
- Evaluate appropriate support systems for specified ground conditions

**Prerequisites:** MNTC 302, APSC 182

**Exclusions:** MINE 325

Mining companies develop projects and operate mines as part of a global minerals industry. This course first sets the global context, reviewing the history of mineral economics, the nature, and components of mineral supply and demand, pricing and markets, and aspects of their role in the global economy. The impact of government policies and international treaties on mining companies and projects is discussed. Building blocks of relevant economic concepts and financial tools are reviewed and applied to structured problems. The estimation of mineral resources and mineral reserves, the feasibility assessment process, and the disclosure of the results of work in these areas under National Instrument 43-101, are reviewed. The valuation of companies and evaluation of projects is covered, as are approaches to addressing risk and uncertainty. Sources and types of funding for companies and projects are introduced. Throughout the course, ways in which sustainability is increasingly being reflected in activities studied in this course are highlighted.

**Credits:** 3.5

**Course learning outcomes: **

By the end of this course, learners should be able to:

- Describe the nature and components of global minerals supply, demand, trade, and price.
- Identify national and international policies, regulations, and treaties relevant to the minerals industry.
- Solve structured problems using economic analysis concepts (e.g. time value of money, discounting) and financial analysis tools (e.g. Net Present Value (NPV), Internal Rate of Return (IRR), payback period).
- Describe the estimation of mineral resources and mineral reserves, the feasibility assessment process and different types of reports, and the disclosure of the results of work in these areas under National Instrument 43-101.
- Apply economic and financial tools to valuation of companies, evaluation of projects, and strategic planning.
- Discover how risk and uncertainty are addressed in the techniques and processes of mineral economics.
- Discover sources and types of equity and debt financing for mining companies and projects.
- Examine the impact of sustainability initiatives and frameworks on mining companies and projects, and ways in which sustainability is increasingly being reflected in activities studied in this course.

**Prerequisites:** APSC 221 and MNTC 305, or permission of the Mining Department

**Exclusions:** MINE 330

This course represents an introduction to reliability and maintenance of mining-related equipment, encompassing both mobile fleets and static equipment, including processing plants. It introduces the primary types of maintenance policies and key performance indicators for reliability and maintenance. Analytical tools for resource allocation and prioritization, as well as an integrated methodology for developing maintenance strategies are covered.

**Credits:** 3.0

**Course learning outcomes:**

By the end of this course, learners should be able to:

- Explain qualitative and quantitative reliability and maintenance concepts including risk.
- Justify the selection of maintenance policies and their appropriate applications in mining.
- Explain the relationship between maintenance organizational structures and processes with respect to mining operations taking into account practical realities in the mining context.
- Design maintenance organizational structures including workflow processes.
- Apply relevant analytical techniques for the prioritization of maintenance activities and resources; including Pareto analysis, Failure Mode Analysis, and Failure Rate curves.
- Select appropriate maintenance policies through a structured methodology (RCM), based on application of analytical techniques and incorporating costs.

**Prerequisites:** MNTC 302 and MNTC 304 or APSC 171, APSC 172, and APSC 182

Current Queen’s students, including those from other faculties, can enroll through SOLUS.

Last day to add a course: **May 5**

Non-Queen’s students can apply through Queen’s Online Application Portal.

Application deadline is **April 8**

You can find more information about the registration process here.