MATH& 148

Elements of Calculus

LEARNING OUTCOMES

Upon successful completion of Math& 148, the student should be able to:

1. Use the product, quotient and chain rules to differentiate simple algebraic, exponential and logarithmic functions.

2. Construct equations for tangent lines and find average and instantaneous rates of change from symbolic, graphical and numerical information.

3. 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.

4. Use simple substitutions and tables to determine anti-derivatives of simple algebraic and exponential functions.

5. Determine the values (exact or approximate, as appropriate) of definite integrals using the Fundamental Theorem of Calculus and areas.

6. 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.

7. Determine appropriate units for definite integrals and derivatives.

8. Calculate partial derivatives of simple functions of two variables, and apply them to solve optimization problems, compute marginal productivity, and interpret three-dimensional graphics.