MTH 161 - Analytic Geometry and Calculus I

1. The student will develop an understanding of, calculate with, and apply limits in several contexts.
   1. Evaluate limits symbolically, numerically and graphically with and without technology.
   2. Discuss the definition of the limit.
   3. Explain the relationship between limits and other concepts including continuity, derivatives, and integrals.
   4. Use L’Hopital’s Rule to evaluate limits.
2. The student will develop an understanding of, calculate with, and apply derivatives in several contexts.
   1. State the definition of the derivative.
   2. Determine where a function is differentiable and where it is not differentiable.
   3. Compute elementary derivatives using the limit definition.
   4. Compute derivatives symbolically, numerically and graphically without technology. Elementary derivatives include polynomials, powers, exponential and logarithmic functions, and trigonometric and inverse trigonometric functions.
   5. Compute derivatives using the power rule, product rule, quotient rule, chain rule and implicit differentiation without technology.
   6. Explain the relationship between a function and its derivatives in a graphical setting.
   7. Use derivatives to solve applied problems including related rates, optimization, and differentials.
3. The student will develop an understanding of, calculate with, and apply integrals in several contexts.
   1. Define the definite integral using the concept of a limit.
   2. Determine the antiderivative of several elementary functions.
   3. Demonstrate an understanding of the Riemann Sum definition of integrals.
   4. Explain the Fundamental Theorem of Calculus and its importance.
   5. Evaluate definite and indefinite integrals using antiderivatives and substitution.
   6. Use appropriate approximation techniques to estimate integrals.
   7. Use integration techniques to solve applied problems.
4. The student will use technology appropriately to do mathematics.
   1. Evaluate limits.
   2. Numerically estimate the values of derivatives.
   3. Estimate definite integrals.
   4. Use tables.
   5. Graph a variety of functions.
5. The student will communicate effectively about mathematics.
   1. Verbally describe solutions to problems using appropriate terminology.
   2. Provide complete written explanations of concepts using appropriate terminology.
6. The student will develop problem-solving and mathematical modeling skills.
   1. Clarify and analyze the meanings of words, phrases and statements.
   2. Learn the meanings of relevant symbols used in mathematics and use them appropriately.
   3. Organize and present information or data in tables, charts, and graphs.
   4. Use mathematics to model and solve problems.
   5. Identify, analyze and evaluate assumptions.
   6. Using mathematical symbolism, identify, state and clarify arguments or reasoning.
   7. Generate and assess solutions to problems.