# C-ID Descriptor Single Variable Calculus Sequence

## Descriptor Details

• Single Variable Calculus Sequence
• Not Identified
• 900
• Sequence (S)
• 8.0
• Not Identified
• Uploaded: 10/12/2017 04:43:58 PM PDT

## General Description

Differential and integral calculus of a single variable: functions; limits and continuity;
techniques and applications of differentiation and integration; Fundamental Theorem of Calculus; integration; techniques of integration; infinite sequences and series; polar and parametric equations; applications of integration.
Primarily for Science, Technology, Engineering & Math Majors.

## Prerequisites

Precalculus, or college algebra and trigonometry, or equivalent.

## Content

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. Derivatives and integrals of inverse functions and transcendental functions such as trigonometric, exponential or logarithmic;
19. Indeterminate forms and L'Hopital's Rule;
20. Additional techniques of integration including integration by parts and trigonometric substitution;
21. Numerical integration; trapezoidal and Simpson's rule;
22. Improper integrals;
23. Applications of integration to areas and volumes;
24. Additional applications such as work, arc length, area of a surface of revolution, moments and centers of mass, separable differential equations, growth and decay;
25. Introduction to sequences and series;
26. Multiple tests for convergence of sequences and series;
27. Power series, radius of convergence, interval of convergence; and
28. Differentiation and integration of power series.

## Objectives

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;
11. Apply integration to find area;
12. Evaluate definite and indefinite integrals using a variety of integration formulas and techniques;
13. Apply integration to areas and volumes, and other applications such as work or length of a curve;
14. Evaluate improper integrals;
15. Apply convergence tests to sequences and series;
16. Represent functions as power series; and
17. Graph, differentiate and integrate functions in polar and parametric form.

## Evaluation Methods

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.

## Textbooks

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

• No
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