Differentiation and integration of exponential and logarithmic functions, techniques of integration, applications of the definite integral, the calculus of transcendental functions, parametric equations, polar coordinates, indeterminate forms and LíHopitalís Rule, improper integrals, sequences and series.
Course Learning Outcomes
The student will:
Use the concepts of definite integrals to solve problems involving area, volume, work, and other physical applications.
Use substitution, integration by parts, trigonometric substitution, partial fractions, and tables of anti-derivatives to evaluate definite and indefinite integrals.
Define an improper integral.
Apply the concepts of limits, convergence, and divergence to evaluate some classes of improper integrals.
Determine convergence or divergence of sequences and series.
Use Taylor and MacLaurin series to represent functions.
Use Taylor or MacLaurin series to integrate functions not integrable by conventional methods.
Use the concept of parametric equations and polar coordinates to find areas, lengths of curves, and representations of conic sections.
Apply L'hôpital's Rule to evaluate limits of indeterminate forms.
College level readiness in reading and writing
Willliam Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz; Calculus, Early Transcendentals, 3rd ed.; Pearson
Required: Students must buy an access code to MyMathLab, an online course management system which includes a complete eBook; students will first need a Course ID provided by the instructor in order to register; online purchase of MyMathLab access at www.mymathlab.com;
ISBN for hard copies of access codes: 9780134856926
Hardbound text (optional), ISBN: 9780134995991
Loose Leaf text + free MyMathLab access, ISBN: 9780134996684
Calculators may be required for some assignments/assessments at the discrection of the Instructor. Refer to class syllabus for details.
Neither cell phones nor PDAís can be used as calculators. Calculators may be cleared before tests.
Differentiation and Integration Formulas:
Students are expected to memorize the differentiation formulas on the last page inside the back cover of the text and integration formulas 1- 20 in the attached chart.
Chapter 6. Applications of Integration
6.1 Velocity and Net Change
6.2 Regions Between Curves
6.3 Volume by Slicing
6.4 Volume by Shells
6.5 Lengths of Curves
6.6 Surface Area
6.7 Physical Applications (cover work and density and mass; all other topics optional)
Chapter 7. Logarithmic, Exponential, and Hyperbolic Functions
7.1 Logarithmic and Exponential Functions Revisited