Course Overview
This course provides an introduction to multivariable calculus - differentiation and integration - and differential equations. Calculus will be used in a variety of Civil engineering applications including: calculating moments and centroids for three dimensional objects, solving non-uniform distributed loading problems, axial loading of non-uniform members, optimizing a solution to a problem involving multiple variables, using calculus and physical constraints, and application of simple differential equations to engineering problems. In all areas, the use of the computer to find a numerical solution to a physical problem will be emphasized using a mathematics computer software package and/or a spreadsheet program.
Prerequisite(s)
Credits
4.0
- Not offered this term
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Learning Outcomes
Upon successful completion of this course, the student will be able to:
- Apply differential and integral calculus to calculating:
- Center of gravity and centroid of a solid.
- Force resultants due to distributed loads.
- Internal shear and internal moment through a differential relationship with external load.
- Bending moments and internal stress.
- Fluid pressure.
- Fluid drainage rate/mixing problems.
- Optimal solution to a physical problem.
- Model physical processes (e.g. population growth, mass under gravity, air-resistance, storage equations and traffic following) with first-order differential equations.
- Solve separable first-order differential equations analytically and symbolically using Maple.
- Use complex numbers and relate to physical properties such as vibrational frequencies.
- Use Taylor's Series and Fourier Series expansions of functions.
- Use spreadsheets and other software to numerically analyze:
- Integrals and derivatives using finite differences. Applied to problems such as estimating volume of a cut for road construction, calculation of displacements on non-uniform members.
- Solutions to first order differential equations.
- Choose and apply appropriate numerical methods to solving calculus based problems and understand the limitations of such methods.
- Solve problems in the appropriate coordinate system for the problem, Cartesian; cylindrical or spherical.
Effective as of Fall 2012
Related Programs
Calculus for Civil Engineering 2 (MATH 3422) is offered as a part of the following programs:
- Indicates programs accepting international students.
- Indicates programs eligible for students to apply for Post-graduation Work Permit (PGWP).
School of Construction and the Environment
- Civil Engineering
Diploma Full-time
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