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Precalculus, or college algebra and trigonometry, or equivalent.

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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

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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.