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Section 5 Learning outcomes for Math 2575

This page outlines the list of competencies each student is expected to achieve in Math 2575. The number following each outcome below indicates the corresponding textbook section. The online homework, tutorial assignments, and tests are all designed to help you achieve these outcomes.

By the end of the course, you should be able to:

  1. General skills

    1. Communicate mathematical results clearly and effectively

    2. Use software to assist with computational aspects of the course

  2. Chapter 12: Vectors

    1. Use dot and cross products to compare vectors and construct vectors such as projections and normal vectors

    2. Use vectors to describe equations of lines and planes

  3. Chapter 13: Vector-Valued Functions

    1. Understand the relationship between the formula for a vector-valued function and its graph (13.1)

    2. Apply the algebra of vectors to vector-valued functions (13.1)

    3. Apply concepts of calculus (limit, derivative, antiderivative) to vector-valued functions (13.2)

    4. Understand the significance of the derivative of a vector-valued function in terms of tangents (13.2)

    5. Use vector-valued functions to describe motion (velocity, acceleration, etc.) (13.3)

    6. Compute the unit tangent and normal vectors and understand their significance (13.4)

    7. Compute the curvature of a vector-valued function (13.5)

  4. Chapter 14: Differential Calculus in Several Variables

    1. Explain what it means for a function of several variables to be differentiable (14.1)

    2. Compute and apply the total differential of a function of several variables (14.1)

    3. Understand and apply the chain rule for functions of several variables (14.2)

    4. Describe the chain rule in terms of matrix multiplication (14.6)

    5. Understand the significance of the gradient vector (14.3)

    6. Compute the directional derivative of a function of several variables (14.3)

    7. Determine the equation of the tangent plane to a surface in three dimensions (14.4)

    8. Find and classify critical points for functions of two variables (14.5)

    9. Determine the absolute maximum and minimum values of a function subject to a constraint (14.5, 14.7)

  5. Chapter 15: Integral Calculus in Several Variables

    1. Understand the definition and properties of a double integral (15.1, 15.2)

    2. Evaluate a double integral by writing it as an iterated integral (15.1)

    3. Change the order of integration in a double integral (15.1, 15.2)

    4. Evaluate a double integral using polar coordinates (15.3)

    5. Use double integrals to compute centre of mass and moments of inertia (15.4)

    6. Set up and evaluate a triple integral in rectangular coordinates (15.6)

    7. Use cylindrical and spherical coordinates to evaluate a triple integral (15.7)

    8. Use a general change of variables to evaluate a double or triple integral (15.8)

    9. Determine the best method (or coordinate system) to solve a double or triple integral

  6. Chapter 16: Vector Calculus

    1. Set up and evaluate line integrals of scalar and vector fields (15.1, 15.3)

    2. Compute the divergence and curl of a vector field, and interpret their meaning (15.2)

    3. Determine if a vector field is conservative, and if so, find a potential function (15.3)

    4. Understand and apply the Fundamental Theorem of Calculus for line integrals (15.3)

    5. Understand and apply Green's Theorem (15.4)

    6. Describe a surface in space using parametric equations (15.5)

    7. Compute the surface area of a parametric surface (15.5)

    8. Set up and evaluate the integral of a vector field over a surface (15.6)

    9. Understand and apply Stokes' Theorem (15.7)

    10. Understand and apply the Divergence Theorem (15.7)

    11. Compare and contrast the different integral theorems, and the relationships between them