# MATH 160 Survey of Calculus*

### Credits

### General Education Competency

Mathematical Ways of Knowing## MATH 160Survey of Calculus*

Please note: This is not a course syllabus. A course syllabus is unique to a particular section of a course by instructor. This curriculum guide provides general information about a course.

## I. General Information

### Department

Mathematics & Engineering

## II. Course Specification

### Course Type

### General Education Competency

### Credit Hours Narrative

### Prerequisite Narrative

### Grading Method

### Repeatable

## III. Catalog Course Description

This course is designed for students with business, social science and life science majors. It covers functions, limits, continuity, derivative, maxima-minima, applications of the derivative, exponential and logarithmic functions, functions of several variables, maxima and minima of functions of several variables, integration, and applications of the integral.

## IV. Student Learning Outcomes

Upon completion of this course, a student will be able to:

## V. Topical Outline (Course Content)

a. Functions: real numbers, inequalities, sets, intervals, Cartesian plane, lines, slopes, exponents, domain, range, quadratic, polynomial, rational, exponential, piecewise and composite functions, shifting, difference quotient, applications b. Derivatives: limits, continuity, average and instantaneous rate of change, secant and tangent lines, definition of derivative, power rule, product rule, quotient rule, chain rule, higher-order derivatives, velocity, acceleration, nondifferentiable functions, business applications c. Applications of Derivative: relative extreme points, critical numbers, graphing, first- derivative test, concavity, inflections points, second-derivative test, absolute extreme values, applications of optimization, implicit differentiation, related rates d. Exponential & Logarithmic Functions: graphing, compound interest, the number e, exponential growth, natural logarithms, applications of logarithms, derivatives of logarithmic and exponential functions, applications of derivatives e. Integration: antiderivatives, indefinite integrals, integration rules, area under a curve, definite integral, Fundamental Theorem of Integral Calculus, applications of integrals, average value of a function, area between curves, applications of area, integration by substitution, differentials f. Integration Techniques and Differential Equations: integration by parts, integral tables, improper integrals, numerical integration, trapezoidal approximation and error, Simpson's Rule and error, differential equations, general and particular solutions, separation of variables, applications of differential equations g. Calculus of Several Variables: functions of two variables, graphing, relative extreme points and saddle points, partial derivatives, functions of three or more variables, higher-order partial derivatives, optimizing functions of several variables, critical points, second-derivative test, applications, least squares, fitting exponential curves with least squares, Lagrange Multipliers, total differentials and approximate changes, multiple integrals.