Courses

Calculus I - MATH 1501

Summer 2024

Description

This course includes material on functions, limits, continuity, the derivative, anti-differentiation, the definite integral, and techniques of integration.

Learning Objectives

After completing this course, students will be able to:

• Calculate and evaluate limits and represent these concepts graphically, algebraically, numerically and in words. Apply knowledge of limits and continuity to analyze and solve real-world problems. Determine when the use of technology is appropriate in solving problems related to limits and continuity and how to apply the technology.
• Explain the definition of the derivative and how it is related to tangent lines and rates of change, and to compute derivatives from limit definitions. Compute derivatives using all the standard rules, displaying in particular a strong mastery of the Chain Rule. Compute derivatives of trigonometric functions and compute closely related trigonometric limits. Explain the concept of an implicitly defined function, and use the technique of implicit differentiation to differentiate functions that are defined implicitly. Model and solve related rates word problems.
• Solve problems related to rates of change. Identify and describe properties of functions and their graphs. Apply the properties of functions and their graphs to real life problem situations.
• Calculate anti-derivatives by using some basic rules. Evaluate anti-derivatives using the substitution technique. Define the definite integral. Evaluate a few definite integrals using the definition as a limit of Riemann sums. State the Fundamental Theorem of Calculus. Apply the Fundamental Theorem of Calculus to evaluate definite integrals.

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