# MATH 170 Calculus 1*

This is the first course in the calculus sequence. It covers algebraic and transcendental functions, rate of change, limits, continuity, differentiation of algebraic, trig, exponential, logarithmic and hyperbolic functions, differentials, applications of differentiation, definite and indefinite integrals, area between curves, volumes and other applications of integration, indeterminate forms and L’Hopital’s Rule.

### Credits

### Semester Contact Hours Lecture

75

### Prerequisite

MATH 147### General Education Competency

GEM Mathematical Ways of Knowing## MATH 170Calculus 1*

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

### Semester Contact Hours Lecture

### Prerequisite Narrative

### Grading Method

### Repeatable

## III. Catalog Course Description

This is the first course in the calculus sequence. It covers algebraic and transcendental functions, rate of change, limits, continuity, differentiation of algebraic, trig, exponential, logarithmic and hyperbolic functions, differentials, applications of differentiation, definite and indefinite integrals, area between curves, volumes and other applications of integration, indeterminate forms and L’Hopital’s Rule.

## IV. Student Learning Outcomes

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

- Demonstrate an understanding of the limiting process as it applies to functions, continuity, derivatives and integrals.
- Demonstrate an understanding of the concept of the derivative including its geometric and physical interpretations, apply it to calculate derivatives of functions using rules of differentiation, and solve applied problems.
- Demonstrate an understanding of the concept of the integral including its geometric and physical interpretations, apply it to calculate indefinite and definite integrals, and solve applied problems.
- The student will be able to demonstrate an understanding of the limiting process as it applies to functions, continuity, derivatives and integrals.
- The student will be able to demonstrate an understanding of the concept of the derivative including its geometric and physical interpretations, apply it to calculate derivatives of functions using rules of differentiation, and solve applied problems.
- The student will be able to demonstrate an understanding of the concept of the integral including its geometric and physical interpretations, apply it to calculate indefinite and definite integrals, and solve applied problems.

## V. Topical Outline (Course Content)

Represent functions verbally, numerically, graphically, algebraically Graph, evaluate and use common functions (linear, polynomial, power, rational, trigonometric, algebraic, exponential, logarithmic) Perform operations on functions (transformations, algebraic combinations, composition) Use graphing calculators to graph functions Exponential functions (evaluate, graph, applications) Inverse functions (inverses in general and inverse trig functions) Logarithms (properties, natural logs, solve equations, evaluate) Trigonometric functions (properties, graphs, identities) Tangent and velocity problems Limit of a function Calculate limits using the Limit Laws, also one-sided limits The precise (? and ?) definition of a limit Continuity Limits at Infinity : Horizontal Asymptotes Tangents, Velocities, and Other Rates of Change Derivatives (definition as a limit, interpretation as the slope of a tangent, interpretation as a rate of change, derivation as a function, when differentiation fails) Derivatives of polynomials and exponential functions Product Rule for differentiation Quotient Rule for differentiation Applications of rates of change in natural and social sciences Derivatives of trig functions The Chain Rule Implicit Differentiation. Higher derivatives Derivatives of logarithmic functions Logarithmic differentiation Hyperbolic functions (definitions, identities, derivatives) Related Rates Linear approximations and differentials Maximum and Minimum values Mean Value Theorem How derivatives (f ’ and f ’’ ) relate to the shape of a graph Indeterminate forms and L’Hospital’s Rule Curve sketching using intercepts, domain, symmetry, asymptotes, f ’, f ’’, etc. Graphing with calculus and calculators Optimization problems Applications of the derivative to business and economics Newton’s Method Antiderivatives Area under a curve and distance Definite integrals The Fundamental Theorem of Calculus Indefinite integrals Integration by substitution The natural logarithm defined as an integral Areas between curves Volumes of solids of revolution using disks, washers, shells Volumes of solids with known cross-sections Work Average value of a function