Description: The sequence Math 115-116-215 is the standard complete introduction to the concepts and methods of calculus. It is taken by the majority of students intending to major in mathematics, science, or engineering, as well as students headed for many other fields. The emphasis is on concepts and solving problems rather than theory and proof. Math 116 presents the concepts of calculus from four points of view: geometric, numerical, algebraic, and verbal. Students develop their reading, writing, and questioning skills. Topics include techniques of integration, application of these, and an introduction to sequences and series and to differential equations.

Text: Deborah Hughes-Hallett, Andrew Gleason, et al.:
Calculus: Single Variable, 4^th Edition, Wiley, 2005

Calculator: TI-84 Graphing Calculator or equivalent. If you have another model, you will be responsible for knowing how to operate the calculator on your own.

Course Content:
This semester we will cover sections 5.1–5.4, 6.1, 6.2, 6.4, 7.1–7.8, 4.8, 8.1–8.5, 8.7, 8.8, 9.1–9.5, 10.1–10.3, and 11.1–11.6 from the textbook. Please note that sections 6.3, 6.5, 8.6, 10.4–10.5, and 11.7–11.11 are not covered.

• Exam 1 (25% of grade) — 5.1–5.4, 6.1, 6.2, 6.4, 7.1–7.8, 4.8, 8.1–8.2, and 8.3 through p.385
  (Note: sections 7.3, 7.4 and 7.6 are considered only lightly, as noted below.)
• Exam 2 (35% of grade) — 8.3 (starting at p.386), 8.4, 8.5, 8.7, 8.8, 9.1–9.4
• Final Exam–Cumulative! (40% of grade) — 9.5, 10.1–10.3, 11.1–11.6, and all of Exam 1 and Exam 2 material.

Notes on coverage:

• The sections indicated for each exam may change if the schedule requires it. If this occurs it will be announced in class prior to the exam.
• The Final Exam is comprehensive. The distribution of material on the final from exams 1 and 2 and following will be announced in class at the end of the semester (as a preliminary estimate, 1/2 to 2/3rds new material is a reasonable guess).
• In section 7.3, the emphasis is on using substitution and algebra to rewrite integrals in a form that makes them easier to evaluate, or allows use of a table of integrals.
• In section 7.4, trigonometric substitution and partial fractions for quadratic or repeated factors will not appear on the exams.
• In section 7.6, Simpson's rule will not appear on the exams.

On all exams, standard graphing calculators (those without a full alphanumeric keypad) are allowed. Problems will be written with the expectation that these calculators will be used. Other or more powerful calculators must be approved. On all exams students are allowed a notecard consisting of both sides of one 3'' by 5'' card.

Grading Policy: All sections of Math 116 use the same grading guidelines to standardize the evaluation process. The three uniform exams are worth 25%, 35%, and 40% of the "Exam component" of each student's grade. The final course grade will be primarily determined by the exam component grade for each student. However, for some students, the final course grade may be modified by the section component grade or the gateway exams. See the  Student Guide for a complete explanation.

Gateway Exams: There will be two gateways. The first reviews differentiation and the second is on techniques of integration. Students will lose a third of a grade (on their grade for the course) for failing to pass the first gateway and a third of a grade for failing to pass the second. Gateways are administered in the gateway lab (B069 EH) and may be taken many times, but no more than twice per day.

Prerequisites: Math 115

Credit: 4 credits

Student Body: Primarily Freshmen and Sophomores

Frequency: This course is offered Fall (I), Winter (II), Spring (IIIa), and Summer (IIIb)

Alternatives:  Math 186 (Honors Anal. Geom. and Calc. II) is a somewhat more theoretical course which covers much of the same material. Math 156 (Applied Honors Calculus II) also covers much of the same material using MAPLE and emphasizing applications to science and engineering.

Subsequent Courses:  Math 215 (Calculus III) is the natural sequel. A student who has done very well in this course could enter the honors sequence at this point by taking  Math 285 (Honors Analytic Geometry and Calculus III) or the corresponding Applied Honors Course,  Math 255.