Multivariable Calculus
Curves, partial derivatives, optimization, multiple integrals and vector calculus, applied to fluid mechanics and electromagnetism.
MATH-209 Year 2 3 credits 12 lessons · 7 h 17 min
Offered by HSM University · Engineering Core
This is the Canadian version of this course. See the American version.
What you'll learn
- Describe functions of several variables with surfaces, contour maps and level surfaces, and decide whether limits exist
- Compute partial derivatives, gradients and directional derivatives, and use differentials to estimate measurement error
- Find and classify critical points and solve constrained optimization problems with Lagrange multipliers
- Evaluate double and triple integrals in Cartesian, polar, cylindrical and spherical coordinates for areas, volumes, mass, centroids and second moments
- Compute line and surface integrals, work and flux, and apply Green's, Stokes' and the divergence theorems
- Describe curves and motion with vector functions, and compute velocity, acceleration, arc length and curvature
- Classify critical points with the Hessian, fit data by least squares, interpret Lagrange multipliers and apply numerical optimization
- Change variables in multiple integrals with the Jacobian, and compute hydrostatic forces, mass moments of inertia and probabilities
- Use gradient, divergence, curl and the Laplacian in cylindrical and spherical coordinates, including vector identities and potentials
- Derive and apply the continuity, Euler and Bernoulli equations, stream functions and potential flows in fluid mechanics
- Convert Maxwell's equations between integral and differential form and solve electrostatic and induction problems
- Formulate, solve, verify and interpret multivariable models of engineering systems
Course content
12 lessons · 7 h 17 min total · final exam
- 1 Functions of several variables 40 min · quiz
- 2 Vector functions, curves and motion 33 min · quiz
- 3 Partial derivatives and gradients 47 min · quiz
- 4 Optimization in several variables 37 min · quiz
- 5 Double and triple integrals 44 min · quiz
- 6 Change of variables and applications of multiple integrals 34 min · quiz
- 7 Line and surface integrals 42 min · quiz
- 8 Divergence and Stokes' theorems 41 min · quiz
- 9 Vector operators in curvilinear coordinates 31 min · quiz
- 10 Vector calculus in fluid mechanics 32 min · quiz
- 11 Vector calculus in electromagnetism 27 min · quiz
- 12 Case studies and course project 29 min · quiz
- E Final exam 20 questions
Requirements
Recommended background. You can start any course at any time.
Description
Curves, partial derivatives, optimization, multiple integrals and vector calculus, applied to fluid mechanics and electromagnetism.
Part of the Engineering stream, typically taken in year 2.