**Course** Description: | Limits, derivatives, differentiation of algebraic and
transcendental functions; linear approximation, curve sketching,
optimization, indeterminate forms. The integral, Fundamental
Theorem of Calculus, areas. Emphasis on science and engineering
applications. |

**Course Objectives:** | The student will understand the limit and the derivative both
conceptually and operationally. The student will learn how to use
calculus concepts to model and solve various typical problems in
science and engineering, with particular emphasis on graphs,
optimization problems, and basic integration problems.
The student will learn to set up word problems clearly and
concisely and to provide clear solutions. |

**Topical Outline:** | 1. Functions, rates of change, limits.
2. Differentiation rules: polynomials and transcendental
functions, sum, product and quotient rules, chain rule, implicit
differentiation; inverse functions.
3. Applications of differentiation: linear approximation,
Newton's method, curve sketching and convexity, optimization
problems, related rate problems, L'Hospital's rule.
4. The integral and summation notation, anti-differentiation,
Fundamental Theorem of calculus. Areas between curves and some
techniques of integration. |