C-ID Descriptor
Single Variable Calculus I Late Transcendentals

Descriptor Details

  • Single Variable Calculus I Late Transcendentals
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  • Uploaded: 10/12/2017 04:43:56 PM PDT

A first course in differential and integral calculus of a single variable: functions; limits and continuity; techniques and applications of differentiation and integration; Fundamental Theorem of Calculus. Primarily for Science, Technology, Engineering & Math Majors.

Precalculus, or college algebra and trigonometry, or equivalent.

  1. Definition and computation of limits using numerical, graphical, and algebraic approaches
  2. Continuity and differentiability of functions
  3. Derivative as a limit
  4. Interpretation of the derivative as: slope of tangent line, a rate of change
  5. Differentiation formulas: constants, power rule, product rule, quotient rule and chain rule
  6. Derivatives of trigonometric functions
  7. Implicit differentiation with applications, and differentiation of inverse functions
  8. Higher-order derivatives
  9. Graphing functions using first and second derivatives, concavity and asymptotes
  10. Maximum and minimum values, and optimization
  11. Mean Value Theorem
  12. Antiderivatives and indefinite integrals
  13. Applications of integration to areas and volumes
  14. Definite integral; Riemann sum
  15. Properties of the integral
  16. Fundamental Theorem of Calculus
  17. Integration by substitution

At the conclusion of this course, the student should be able to:

  1. Compute the limit of a function at a real number;
  2. Determine if a function is continuous at a real number;
  3. Find the derivative of a function as a limit;
  4. Find the equation of a tangent line to a function;
  5. Compute derivatives using differentiation formulas;
  6. Use differentiation to solve applications such as related rate problems and optimization problems;
  7. Use implicit differentiation;
  8. Graph functions using methods of calculus;
  9. Evaluate a definite integral as a limit;
  10. Evaluate integrals using the Fundamental Theorem of Calculus; and
  11. Use the definite integral to find areas and volumes

Tests, examinations, homework or projects where students demonstrate their mastery of the learning objectives and their ability to devise, organize and present complete solutions to problems.

A college level textbook designed for science, technology, engineering and math majors, and supporting the learning objectives of this course.

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