Outcomes:

After completing this class, students should be able to:

• Use the product, quotient and chain rules to differentiate simple algebraic, exponential and logarithmic functions.
• Construct equations for tangent lines and find average and instantaneous rates of change from symbolic, graphical and numerical information.
• Apply the concepts, techniques and vocabulary of limits, continuity and first and second derivatives to solve problems in contexts such as marginal analysis, product elasticity, related rates, exponential growth/decay and optimization.
• Use simple substitutions, integration by parts and tables to determine antiderivatives of simple algebraic and exponential functions.
• Determine the values (exact or approximate, as appropriate) of definite integrals using the Fundamental Theorem of Calculus and areas.
• Apply the ideas of definite and indefinite integrals to solve problems in contexts such as total change/accumulation, consumer and producer surplus, exponential growth and decay, etc.
• Determine appropriate units for definite integrals and derivatives.
• Calculate partial derivatives of simple functions of two variables, and apply them to solve optimization problems, compute marginal productivity, and interpret three-dimensional graphics.