Single Variable Calculus I Early Transcendentals
  • Final
  • Mathematics
  • Single Variable Calculus I Early Transcendentals
  • Single Variable Calculus I Late Transcendentals MATH 211
  • 4.0
  • 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.

  • 210
  • Pre-calculus, 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 transcendental functions such as trigonometric, exponential or logarithmic;
    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. Area under a curve;
    14. Definite integral; Riemann sum;
    15. Properties of the integral;
    16. Fundamental Theorem of Calculus;
    17. Integration by substitution;
    18. Indeterminate forms and L'Hopital's Rule;

  • Upon successful completion of the course, students will 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. Apply integration to find area.

  • 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.

  • March 31, 2011