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