MAC2234 – Survey of Calculus II

Topical Outline with Specific Course Objectives 

  1. The Integral
    1. Find the indefinite integral of a function using antidifferentiation rules.
    2. Apply the Fundamental Theorem of Calculus.
    3. Use definite integrals to find the area between two curves.
    4. Apply a variety of numerical methods for approximating definite integrals such as the Trapezoidal Rule and Simpson's Rule
    5. Apply antidifferentiation techniques, such as integration by substitution and integration by parts, to find indefinite and definite integrals.
    6. Use definite integrals to model applied problems such as producer surplus, consumer surplus, present value and future value.
    7. Recognize an improper integral and determine whether it is convergent or divergent.
  2. Functions of Several Variables
    1. Graph functions of several variables.
    2. Use functions of several variables to model applied problems, including Cobb-Douglas production functions.
    3. Find partial derivatives numerically and symbolically.
    4. Give graphical interpretations of partial derivatives.
    5. Find maxima and minima of functions of several variables.
    6. Use the method of Least Squares to find the line of best fit.
    7. Use the Method of Lagrange Multipliers to solve constrained optimization problems.
    8. Find the total differential of a function of several variables and use it to approximate incremental change in the function.
    9. Evaluate double integrals and use them to model applied problems such as areas of regions, volumes of solids, population density and average values of real-life models.
  3. Differential Equations
    1. Verify general solutions of differential equations and find particular solutions, given the general solution.
    2. Use differential equations to model applied problems such as population and mixture problems.
    3. Use separation of variables to solve differential equations.
    4. Use separable differential equations to model applied problems.
    5. Use Euler’s method to approximate solutions to initial value problems.
  4. Probability Distributions of Random Variables
    1. Verify that a function is a continuous probability density function and use continuous probability density functions to find probabilities.
    2. Find the cumulative distribution function for a random variable with a given probability density function.
    3. Find the expected value and standard deviation of continuous probability density functions.
    4. Model applied problems using special probability density functions such as the uniform probability density function, the exponential probability density function, and the normal probability density function.
  5. Sequences and Series
    1. Find Taylor polynomials for functions.
    2. Use Taylor polynomials to determine the maximum errors of approximations and to approximate definite integrals.
    3. Determine the convergence or divergence of sequences and find the limits of convergent sequences.
    4. Define the sequence of partial sums and determine the convergence or divergence of infinite series (focus on telescoping series and geometric series).
    5. Model applied problems using geometric series.
  6. Systems of Linear Equations and Matrices
    1. Model applied problems using systems of linear equations.
    2. Use Gauss-Jordan elimination to solve systems of linear equations.
    3. Multiply matrices and find the inverse of a square matrix.
    4. Model applied problems using matrices, including Leontief Input-Output Models.
  7. Linear Inequalities and Linear Programming Problems
    1. Graph systems of linear inequalities in two variables.
    2. Model applied problems using linear programming.
    3. Find graphical solutions for linear programming problems.
    4. Use the Simplex Method to solve linear programming problems.

Department policies:

  • Graphing Calculator Required
  • Comprehensive Final
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