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CALCULUS - MATH 1501 (4 Credit Hours)
Description: Topics to include functions, limits, continuity, the derivative, antidifferentiation, the definite integral, and applications.
Prerequisites: Math 1113 - Pre-calculus or its equivalent
Course Structure:
- Unit 1: Review of Functions and their Properties
- Unit 2: Limits and Continuity
- Unit 3: Derivatives and Differentiation
- Unit 4: Applications of the Derivative
- Unit 5: Integration
- Unit 6: Applications of the Integral
Course Objectives:
- Unit 1: Review of Functions and their Properties
- Describe the domain, range, and action of a one variable function.
- Understand various ways of describing functions and various properties that a function can have such as odd, even, or monotone.
- Compute sums, differences, products, quotients, and compositions of functions.
- Compute translations, reflections, and scalings of curves and graphs of functions.
- Compute trigonometric functions and understand their definitions.
- Solve triangles.
- Unit 2: Limits and Continuity
- 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.
- Unit 3: Derivatives and Differentiation
- Explain the definition of derivative and how it is related to tangent lines and rates of change, and to compute derivatives from the limit definition.
- Compute derivatives using all of 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 problems.
- Unit 4: Applications of the Derivative
- 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.
- Unit 5: Integration
- 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 integral.
- Unit 6: Applications of the Integral
- Define and compute the arc length
- Compute the area of surfaces of revolutions
- Compute volumes of revolution
- Compute consumer's surplus
- Compute work and center of mass problems