Analytic Geometry and Calculus IMTH 161
Prerequisite: MTH 151 with a grade of "C" or better or four years of high school college-preparatory mathematics including trigonometry. Includes functions, graphs, limits, continuity, derivatives and their applications, integrals, as well as differentiation and integration of exponential and logarithmic functions. A GRAPHING CALCULATOR IS REQUIRED. (60-0)
Outcomes and Objectives
The student will develop an understanding of, calculate with, and apply limits in several contexts.
- Evaluate limits symbolically, numerically and graphically with and without technology.
- Discuss the definition of the limit.
- Explain the relationship between limits and other concepts including continuity, derivatives, and integrals.
- Use L'Hopital's Rule to evaluate limits.
The student will develop an understanding of, calculate with, and apply derivatives in several contexts.
- State the definition of the derivative.
- Determine where a function is differentiable and where it is not differentiable.
- Compute elementary derivatives using the limit definition.
- Compute derivatives symbolically, numerically and graphically without technology. Elementary derivatives include polynomials, powers, exponential and logarithmic functions, and trigonometric and inverse trigonometric functions.
- Compute derivatives using the power rule, product rule, quotient rule, chain rule and implicit differentiation without technology.
- Explain the relationship between a function and its derivatives in a graphical setting.
- Use derivatives to solve applied problems including related rates, optimization, and differentials.
The student will develop an understanding of, calculate with, and apply integrals in several contexts.
- Define the definite integral using the concept of a limit.
- Determine the antiderivative of several elementary functions.
- Demonstrate an understanding of the Riemann Sum definition of integrals.
- Explain the Fundamental Theorem of Calculus and its importance.
- Evaluate definite and indefinite integrals using antiderivatives and substitution.
- Use appropriate approximation techniques to estimate integrals.
- Use integration techniques to solve applied problems.
The student will use technology appropriately to do mathematics.
- Evaluate limits.
- Numerically estimate the values of derivatives.
- Estimate definite integrals.
- Use tables.
- Graph a variety of functions.
The student will communicate effectively about mathematics.
- Verbally describe solutions to problems using appropriate terminology.
- Provide complete written explanations of concepts using appropriate terminology.
The student will develop problem-solving and mathematical modeling skills.
- Clarify and analyze the meanings of words, phrases and statements.
- Learn the meanings of relevant symbols used in mathematics and use them appropriately.
- Organize and present information or data in tables, charts, and graphs.
- Use mathematics to model and solve problems.
- Identify, analyze and evaluate assumptions.
- Using mathematical symbolism, identify, state and clarify arguments or reasoning.
- Generate and assess solutions to problems.