MATH&151-152-153 Course Outline
| DIVISION | Science and Mathematics |
| CURRICULUM | College Transfer |
| TITLE | Calculus w/Analytic Geometry |
| NUMBER | MATH&151, MAT&152, MAT&153 (fromerly 124,125,&126) |
| TYPE | Mathematics |
| CREDITS | Five |
| LENGTH | One quarter of five lecture hours per week. |
| CLASS SIZE | 35 |
| PREREQUISITE | MATH&142 with 2.2 or better to get into MATH&151. |
| COURSE DESCRIPTIONS: MATH&151 Study of global and local behavior of functions including: limits, continuity, and rates of change. Derivatives of all classes of elementary functions are considered together with their applications. MATH&152 The definite integral and its applications; antiderivatives and the fundamental theorem; basic techniques of integration; numerical integration methods and differential equations. MATH&152 Polar forms; vectors in space; derivatives and integrals of functions of two and three variables. COURSE OBJECTIVES: To introduce students to the use of calculus in context by emphasizing the modeling approach throughout. Students are expected to understand the derivative and definite integral beyond the purely symbolic level. Concepts are presented using the rule of three (numerical, graphical and algebraic representations). The appropriate use of technology (graphing calculators and a symbolic algebra system) is required. COURSE CONTENT: MATH&151 A library of functions: graphs, numerical analysis, operations, local and global behavior. The derivative: velocity, general rate of change, interpretations, higher derivatives, local linearality, limits, differentiability. Using the derivative: critical points, concavity, families of curves, newton's method, optimization, antiderivatives. MATH&152 The definite integral: Riemann sums, as total change, as area, as an average, properties, improper. Techniques: The fundamental theorem, substitution, parts, tables, approximation methods. Applications: area, volume, probability, arc length, work. Differential equations: slope fields, Euler's method, separation of variables, applications. MATH&153 Parametric and polar representation of curves: differentiation and integration of these forms. Vectors in space: dot products, lines and planes, surfaces, cylindrical and spherical coordinates. Vector-valued functions: derivatives and integrals, modeling motion, curvature. Functions of two or three variables: partial derivatives, directional derivatives and gradient vectors, tangent planes and normal lines, linearalization, optimization, Lagrange multipliers, double and triple integrals with applications. |
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