Analytic Geometry and Calculus I

MTH 161

Course Description

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.

Objectives:

• 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.

Objectives:

• 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.

Objectives:

• 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.

Objectives:

• 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.

Objectives:

• 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.

Objectives:

• 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.