MAT 210, Survey Calculus

1. Demonstrate mastery of algebraic computations including factoring, rational expressions, exponents, and radicals.
2. Solve linear and quadratic equations. Graph equations and understand properties of functions.
3. Understand the relationship between exponential functions and logarithmic functions. Perform computations involving the natural (base e) exponential and logarithmic functions.
4. Find derivative of a function using the basic limit definition.
5. Find derivatives using the following: power rule, product rule, quotient rule, chain rule, implicit differentiation, higher order derivatives, derivatives of exponential and logarithmic functions.
6. Solve problems applying derivatives to marginal analysis in business and economics.
7. Apply differentiation to problems involving graphing of functions.
8. Analyze a function using inflection points, maxima, and minima.
9. Solve problems involving increments and differentials.
10. Solve related rates problems.
11. Evaluate both indefinite and definite integrals. Also, solve differential equations involving growth and decay.
12. Evaluate integrals using substitution and integration by parts.
13. Be familiar with functions of several variables and be able to find partial derivatives.
14. Use second partial derivatives test to find maxima/minima/saddle points for functions of two variables.
15. Use Lagrange Multipliers to maximize/minimize, subject to constraints, a function of two or more variables.
16. Evaluate double integrals over rectangular regions.

Objectives for MAT 210

1. Show mastery of algebraic skills involving expression (factoring, rational, exponential, logarithms, and radical) and solving equations (linear, quadratic, exponential, and logarithmic).
2. Find derivatives using all rules including implicit differentiation for algebraic, exponential, and logarithmic functions.
3. Use derivatives for graphing, marginal analysis, increments and differentials applications, and rated rates problems.
4. Evaluate single integrals, both indefinite and definite, by methods of substitution and integration by parts, use single integrals to solve application problems, and evaluate double integrals over rectangular regions.
5. Find partial derivatives of multiple variable functions and solve optimization problems using the Second Partial Derivatives Test and Lagrange Multipliers.