Course

Course Summary
Credit Type:
Course
ACE ID:
OTLR-0002
Organization:
Outlier.org
Location:
Online
Length:
7 weeks (140-210 hours) or 14 weeks (140-210 hours)
Dates Offered:
Credit Recommendation & Competencies
Level Credits (SH) Subject
Lower-Division Baccalaureate 4 calculus I
Description

Objective:

The course objective is to provide an introduction to calculus with a focus on limits; derivatives; the differentiation of algebraic functions; the examination and uses of the maxima, minima, and convexity of functions; the definite integral; the fundamental theorem of integral calculus; and applications of integration.
The traditional calculus course prepares students for upper level math courses.

Learning Outcomes:

  • find limits of functions presented as graphs, tables, or algebraic expressions
  • use the concept of limit to define the derivative of functions
  • differentiate functions involving polynomials, exponentials, logarithms and trigonometric terms
  • apply the concepts of differentiation to solve optimization problems
  • apply the concepts of differentiation to solve related rates problems
  • use the derivative to draw the graphs of functions involving polynomials, exponentials, logarithms and trigonometric terms
  • find indefinite integrals involving polynomials, exponentials, logarithms, and trigonometric functions
  • find definite integrals involving polynomials, exponentials, logarithms and trigonometric functions
  • apply the definite integral to compute work, distance, and volumes
  • find net area, area under a curve, and area between curves

General Topics:

  • Representing functions
  • Modeling with functions
  • Transforming functions
  • Exponential functions
  • Inverse and logarithmic functions
  • Tangents and instantaneous velocity
  • Limits of function
  • Limit laws
  • Continuity of functions
  • Limits at infinity
  • Derivatives
  • Derivatives as functions
  • Differentiating polynomials and exponential functions
  • The product and quotient rules
  • Differentiating trigonometric functions
  • The chain rule
  • Implicit differentiation
  • Differentiating logarithmic functions
  • Differentiating in the sciences
  • Differentiating exponential functions
  • Related rates
  • Linearization and differentials
  • Hyperbolic functions
  • Finding maximums and minimums
  • The mean value theorem
  • Derivative tests
  • Indeterminates and l'Hospital's rule
  • Sketching curves
  • Optimization
  • Antiderivatives
  • Approximating area and distance
  • Antiderivatives and distance
Instruction & Assessment

Instructional Strategies:

  • Audio Visual Materials
  • Computer Based Training
  • Discussion
  • Lectures
  • Practical Exercises

Methods of Assessment:

  • Examinations
  • Other
  • Quizzes
  • Discussion

Minimum Passing Score:

70%
Supplemental Materials