Multivariable and Vector Calculus MATH 4620

Upon successful completion of this course, the student will be able to:

• Outline the fundamental mathematical principles of single and multiple integrals and partial derivatives necessary for engineering analysis. [1]
• Apply principles of calculus to solve optimization and constrained optimization problems using the methods of Lagrange multipliers. [1,2]
• Perform vector calculus operations, both differential and integral, in suitable curvilinear coordinate systems. [1]
• Supply physical interpretations of the gradient of a scalar and a vector field, the normal vector, the directional derivative and Laplace's equation. [1,2]
• Identify conservative and non-conservative vector fields and simplify calculations using this knowledge. [1]
• Interpret the divergence and curl of a vector field using physical examples such as electromagnetic fields and the motion of a fluid. [1,2]
• Evaluate line and surface integrals for general surfaces and curves. [1]
• Use vector theorems - Gauss' Divergence, Green's and Stokes' theorems - to transform between different vector integral calculations in order to solve most efficiently. [1]

Engineering accreditation

The Canadian Engineering Accreditation Board (CEAB) oversees the accreditation of engineering programs across Canada. To measure the effectiveness of an engineering program the CEAB has identified twelve specific attributes that the graduate is expected to possess and use as the foundation to developing and advancing an engineering career. To ensure that the overall curriculum of the Bachelor of Engineering in Electrical program covers these attributes sufficiently, the learning outcomes for each course have been mapped to applicable CEAB graduate attributes.

1. A knowledge base for engineering: Demonstrated competence in university level mathematics, natural sciences, engineering fundamentals, and specialized engineering knowledge appropriate to the program.

2. Problem analysis: An ability to use appropriate knowledge and skills to identify, formulate, analyze, and solve complex engineering problems in order to reach substantiated conclusions.

3. Investigation: An ability to conduct investigations of complex problems by methods that include appropriate experiments, analysis and interpretation of data, and synthesis of information in order to reach valid conclusions.

4. Design: An ability to design solutions for complex, open-ended engineering problems and to design systems, components or processes that meet specified needs with appropriate attention to health and safety risks, applicable standards, and economic, environmental, cultural and societal considerations.

5. Use of engineering tools: An ability to create, select, apply, adapt, and extend appropriate techniques, resources, and modern engineering tools to a range of engineering activities, from simple to complex, with an understanding of the associated limitations.

6. Individual and team work: An ability to work effectively as a member and leader in teams, preferably in a multi-disciplinary setting.

7. Communication skills: An ability to communicate complex engineering concepts within the profession and with society at large. Such ability includes reading, writing, speaking and listening, and the ability to comprehend and write effective reports and design documentation, and to give and effectively respond to clear instructions.

8. Professionalism: An understanding of the roles and responsibilities of the professional engineer in society, especially the primary role of protection of the public and the public interest.

9. Impact of engineering on society and the environment: An ability to analyze social and environmental aspects of engineering activities. Such ability includes an understanding of the interactions that engineering has with the economic, social, health, safety, legal, and cultural aspects of society, the uncertainties in the prediction of such interactions; and the concepts of sustainable design and development and environmental stewardship.

10. Ethics and equity: An ability to apply professional ethics, accountability, and equity.

11. Economics and project management: An ability to appropriately incorporate economics and business practices including project, risk, and change management into the practice of engineering and to understand their limitations.

12. Life-long learning: An ability to identify and to address their own educational needs in a changing world in ways sufficient to maintain their competence and to allow them to contribute to the advancement of knowledge.

Effective as of Fall 2017