MATH1B: CALC/ANAL GEOM II
Course Description
This course is a standard second semester Calculus course covering methods of integration, applications of the integral, differential equations, parametric and polar equations, and sequences and series. (C-ID: MATH 220) (C-ID: MATH 900S: Math 1A + Math 1B) PREREQUISITE: Mathematics 1A with a grade of 'C' or better.
Learning Outcomes
- Identify and use the techniques and applications of differentiation and integration learned in Math 1A.
- Evaluate definite and indefinite integrals using the substitution method, integration by parts, trigonometric substitution, and partial fraction expansion.
- Choose an appropriate strategy for integrating a function and perform the integration
- Formulate and evaluate an integral to find area, volume, work, arc length, and surface area, and to solve problems found in business, economics, physics, science, statistics, and other disciplines
- Use technology to approximate definite integrals of functions that cannot be integrated using the above mentioned techniques.
- Evaluate improper integrals and use them to solve applied problems
- Set up and solve differential equations to model applications in business, science, physics, engineering and other disciplines.
- Set up, compute and analyze derivatives and integrals of parametric and polar equations to find local extrema, points of inflection, intervals of increasing/decreasing, concavity, equations of tangent lines, area and arc length, both with and without the use of technology.
- Explain the concepts of convergence, absolute convergence, conditional convergence and divergence of a series and convergence and divergence of a sequence. Use the Integral Test, Comparison Test, Limit Comparison Test, Alternating Series Test, Ratio Test and Root Test to determine convergence or divergence of a series.
- Find the Taylor and MacClauren Series expansion of a function centered about a give point.