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Syllabus for Math 2575, Accelerated Calculus III

Sean Fitzpatrick

Section 9 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.
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By the end of the course, you should be able to:
  1. Chapter 13: Vector-Valued Functions
    1. Apply the algebra of vectors to vector-valued functions (13.1)
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    2. Apply concepts of calculus (limit, derivative, antiderivative) to vector-valued functions (13.2)
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    3. Use the derivative of a vector-valued function to find tangent lines (13.2)
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    4. Use vector-valued functions to describe motion (velocity, acceleration, etc.) (13.3)
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    5. Compute the unit tangent and normal vectors and apply them to acceleration (13.4)
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    6. Compute the curvature of a vector-valued function (13.5)
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  2. Chapter 14: Differential Calculus in Several Variables
    1. Determine the differentiability of a function of several variables (14.1)
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    2. Compute and apply the total differential of a function of several variables (14.1)
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    3. Use the chain rule for functions of several variables (14.2)
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    4. Use the gradient vector to compute normal vectors and directional derivatives (14.3)
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    5. Determine the equation of the tangent plane to a surface in three dimensions (14.4)
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    6. Find and classify critical points for functions of two variables (14.5)
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    7. Determine the absolute maximum and minimum values of a function subject to a constraint (14.5, 14.7)
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  3. Chapter 15: Integral Calculus in Several Variables
    1. Understand the definition and properties of a double integral (15.1, 15.2)
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    2. Evaluate double and triple integrals as iterated integrals (15.1,15.6)
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    3. Change the order of integration in a double or triple integral (15.1, 15.2,15.6)
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    4. Use polar, cylindrical and spherical coordinates to evaluate an integral (15.3, 15.7)
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    5. Use a general change of variables to evaluate a double or triple integral (15.8)
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  4. Chapter 16: Vector Calculus
    1. Set up and evaluate line integrals of scalar and vector fields (15.1, 15.3)
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    2. Compute the divergence and curl of a vector field, and interpret their meaning (15.2)
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    3. Apply the Fundamental Theorem of Calculus for line integrals (15.3)
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    4. Use Green’s Theorem to evaluate double integrals and line integrals in the plane (15.4)
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    5. Describe a surface in space using parametric equations (15.5)
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    6. Set up and evaluate the integral of a vector field over a surface (15.6)
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    7. Understand and apply Stokes’ Theorem and the Divergence Theorem (15.7)
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