1. The learner will demonstrate the ability to work with logarithmic and exponential functions by:

• Manipulating logarithmic and exponential equations;
• Solving logarithmic and exponential equations;
• Recognizing and graphing logarithmic and exponential functions;
• Differentiating exponential and logarithmic functions.

2. The learner will demonstrate a knowledge of inverse functions by:

• Determining if a function is one-to-one;
• Finding the inverse of one-to-one functions;
• Differentiating the inverse of trigonometric functions (including using trigonometric substitution).

3. The learner will put to use the idea of integration of a function by:

• Approximating the area under a curve as the sum of several rectangles;
• Evaluating simple indefinite integrals;
• Evaluating indefinite integrals by substitution;
• Evaluating finite sums (using sigma notation);
• Evaluating definite integrals;
• Evaluating definite integrals by substitution;
• Stating and explaining the fundamental theorem of calculus;
• Solving definite integrals using logarithms;
• Applying integration to linear motion problems.

4. The learner will apply the techniques of integration to various problems by:

• Determining the area between two functions;
• Determining the volumes of solids of revolution around an axis;
• Determining the volumes of cylindrical shells of revolution around an axis;
• Using integration techniques to determine the length of a curve in a plane;
• Calculating surface areas of revolution;
• Solving work problems using integration;
• Solving pressure and force problems using integration.

5. The learner will demonstrate the ability to use a variety of integration techniques by:

• Interpreting and using a table of integrals;
• Performing integration by parts;
• Integrating powers of trigonometric functions;
• Applying trigonometric substitutions to integration problems;
• Integrating rational functions by partial fractions;
• Approximating definite integrals using Simpson's Rule.

6. The learner will apply both an analytical and qualitative approach to find a solution to an ordinary differential equation by:

• Analyzing directional fields and phase portraits;
• Approximating the solutions of differential equations using Euler's Method;
• Performing the method of separation of variable in order to access exact solution representation;
• Modeling with differential equations.

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