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Section 6 Learning outcomes for Math 1560

This page outlines the list of competencies each student is expected to achieve in Math 1560. There are five “big themes,” corresponding to the five chapters of the textbook. (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:

  • Chapter 1: Limits and continuity

    1. Explain the concept of a limit using graphical and numerical information. (1.1)
    2. Apply limit laws in an abstract setting (explicit functions not given). (1.3)
    3. Use algebraic (or trigonometric) manipulation to evaluate limits. (1.3)
    4. Algebraically and graphically determine one-sided limits of piecewise-defined functions. (1.4)
    5. Understand the meaning of continuity, both precisely and intuitively. (1.6)
    6. Understand and apply the Intermediate Value Theorem. (1.6)
    7. Evaluate limits involving infinity and determine asymptotic behaviour of a function. (1.5)

  • Chapter 2: Derivatives

    1. Understand and apply the limit definition of the derivative. (2.1)
    2. Understand the practical meaning of the derivative in terms of rates of change. (2.2)
    3. Understand and apply derivative rules (sum, constant, power, product, quotient). (2.3, 2.4)
    4. Calculate derivatives using the chain rule. (2.5)
    5. Understand and apply implicit and logarithmic differentiation. (2.6)
    6. Understand inverse functions and their derivatives. (2.7)

  • Chapter 3: Graphical behaviour of functions

    1. Determine maximum and minimum values of a continuous function on a closed interval. (3.1)
    2. Understand the significance of the Mean Value Theorem. (3.2)
    3. Understand the relationship between the first derivative and the shape of a graph. (3.3)
    4. Use the second derivative to determine concavity, and understand its significance. (3.4)
    5. Produce an accurate sketch of the graph of a function without the use of technology. (3.5)

  • Chapter 4: Applications of the derivative

    1. Solve word problems involving related rates of change. (4.2)
    2. Solve word problems involving optimization. (4.3)
    3. Use linear approximations to estimate function values. (4.4)
    4. Compute the Taylor polynomial of a function to a specified degree. (4.5)
    5. Understand the practical significance of differential calculus.

  • Chapter 5: Integration

    1. Compute antiderivatives and solve initial value problems. (5.1)
    2. Understand and apply properties of definite integrals. (5.2)
    3. Understand the Riemann sum definition of the integral, and use it to approximate an integral. (5.3)
    4. Use Part I of the FTC to compute derivatives of functions defined as integrals. (5.4)
    5. Use Part II of the FTC to evaluate simple definite integrals. (5.4)
    6. Use the method of substitution to evaluate definite and indefinite integrals. (5.5)
    7. Set up and evaluate a definite integral to compute area between curves. (5.6)