Course

Course Summary
Credit Type:
Course
ACE ID:
SOPH-0060
Organization's ID:
MATH1040
Organization:
Location:
Online
Length:
Self-paced (60-90 days)
Dates Offered:
Credit Recommendation & Competencies
Level Credits (SH) Subject
Lower-Division Baccalaureate 4 calculus I
Description

Objective:

In this course, learners will review key precalculus concepts and cover many fundamental topics in calculus. Calculus topics include: limits, graphical interpretation of derivatives, techniques of differentiation, applications of derivatives, graphical interpretation of integrals, an introduction to techniques of integration, and an introduction to applications of indefinite and definite integrals. Applications of derivatives include velocity and acceleration, related rates, curve sketching, optimization, and L’Hopital’s rule. Applications of integration include acceleration and velocity, and the area between two curves.

Learning Outcomes:

  • Write equations of lines and circles
  • Identify, evaluate, and utilize function notation in various situations including the difference quotient
  • Analyze and graph combinations of functions by using basic functions
  • Express average and instantaneous rates of change by using the difference quotient
  • Use graphs, tables, and properties of limits to evaluate limit values or determine if a limit does not exist
  • Determine where a function is continuous using the limit concept, and demonstrate the formal definition of a limit
  • Evaluate the derivative of a function using graphs, limits, and basic derivative rules
  • Calculate first and higher order derivatives using rules and properties of differentiation, and differentiate composite, exponential, and logarithmic functions using the chain rule
  • Approximate function values and errors in calculations by using differentials, and use implicit differentiation to calculate the derivative
  • Locate extreme values of functions using derivatives and critical values
  • Apply Rolle's Theorem and the Mean Value Theorem where appropriate
  • Apply the first and second derivatives to graph a function and apply them to optimization problems
  • Evaluate limits involving infinity and connect these limits with asymptotes, and apply L'Hopital's Rule to evaluate limits of indeterminate forms
  • Compute definite integrals using Riemann Sums, areas, and properties, and calculate indefinite integrals of various functions, and approximate area using geometric formulas and Riemann Sums
  • Apply the Fundamental Theorem of Calculus to evaluate definite integrals in various application settings

General Topics:

  • Lines in the plane
  • Functions and their graphs
  • Combinations of functions
  • Tangent lines, velocities, and growth
  • The limit of a function
  • Continuous functions
  • Definition of a limit
  • Introduction to derivatives
  • Derivatives: properties and formulas
  • The Chain Rule
  • Linear approximation and differential
  • Implicit and logarithmic differentiation
  • Introduction to maximums and minimums
  • Mean Value Theorem
  • The relationship between the shape of f and the first and second derivative
  • Asymptotic behavior and functions
  • L'Hopital's Rule
  • Introduction to integrals
  • The Definitie Integral
  • Antiderivatives
  • Fundamental theorem of calculus and applications
Instruction & Assessment

Instructional Strategies:

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

Methods of Assessment:

  • Examinations
  • Quizzes

Minimum Passing Score:

70%
Supplemental Materials

Other offerings from SOPHIA Learning, LLC

(SOPH-0006)
(SOPH-0029)
(SOPH-0032)
(SOPH-0001)
(SOPH-0031)
(SOPH-0034)