|General Course Description
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.
|Any rationale or comments
Pre-calculus, or college algebra and trigonometry, or equivalent.
- Definition and computation of limits using numerical, graphical, and algebraic approaches;
- Continuity and differentiability of functions;
- Derivative as a limit;
- Interpretation of the derivative as: slope of tangent line, a rate of change;
- Differentiation formulas: constants, power rule, product rule, quotient rule and chain rule;
- Derivatives of transcendental functions such as trigonometric, exponential or logarithmic;
- Implicit differentiation with applications, and differentiation of inverse functions;
- Higher-order derivatives;
- Graphing functions using first and second derivatives, concavity and asymptotes;
- Maximum and minimum values, and optimization;
- Mean Value Theorem;
- Antiderivatives and indefinite integrals;
- Area under a curve;
- Definite integral; Riemann sum;
- Properties of the integral;
- Fundamental Theorem of Calculus;
- Integration by substitution;
- Indeterminate forms and L'Hopital's Rule;
Upon successful completion of the course, students will be able to:
- Compute the limit of a function at a real number;
- Determine if a function is continuous at a real number;
- Find the derivative of a function as a limit;
- Find the equation of a tangent line to a function;
- Compute derivatives using differentiation formulas;
- Use differentiation to solve applications such as related rate problems and optimization problems;
- Use implicit differentiation;
- Graph functions using methods of calculus;
- Evaluate a definite integral as a limit;
- Evaluate integrals using the Fundamental Theorem of Calculus; and
- Apply integration to find area.
|Methods of Evaluation
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.