Course Description

Math 171 is the first of a three semester beginning calculus sequence, which is taken, for the most part, by math, chemistry, and physics majors. The department expects that students passing Math 171 be able to handle routine computations, e.g., limits, derivatives, max-min problems, and calculation of definite integrals using the fundamental theorem of calculus. We expect students to be able to state (write) and apply basic definitions and major theorems. These include, but are not limited to, definitions of limit, continuous function, derivative, definite and indefinite integrals, the intermediate value theorem for continuous functions, the mean value theorem, and the fundamental theorem of calculus. Students are also expected to be able supply simple proofs, e.g., some of the limit theorems, some of the rules of differentiation, and applications of the intermediate and mean value theorems. The list is of course endless, but keep in

Textbook

The textbook is James Stewart Calculus: Early Transcendentals; 9th Edition

Key Points

Students should be taught and expected to express mathematical ideas in grammatically correct, complete sentences.
Students should be able to explain the reasoning behind their computations and justify each step conceptually.
Students should develop proficiency in working with inequalities, both algebraically and graphically.
Students should demonstrate proficiency with key definitions and be able to reproduce and apply them accurately on exams.
Students should build intuition throughout the semester leading them to being able to make conjectures and predictions (at an appropriate level).
As a foundational calculus course, it should also develop students’ proficiency in standard computations.
Students should begin to distinguish between formal proofs, informal arguments, and heuristic reasoning.

Math 171 Course Description and Weekly Schedule
Week	Sections	Topics	Notes
1	Appendix D; 1.5	Trig/Inverse Review; Intro to Limits	This should an intense review and should challenge students who have already seen calculus
2	2.3-2.5	Epsilon-Delta; continuity	The epsilon/delta definition for limits should be given; the instructor should do examples in class computing limits from the definition; there should be examples of functions that aren’t uniformly continuous and at points at which the epsilon depends on the point; at a minimum, students should prove limits from the epsilon-delta definition for linear functions on the exam; professor should show the sinx /x limit in class (and the corresponding cosine limit).
3	2.6, 2.7, 2.8	Limits at Infinity; Definition of Derivative	Professor should do “epsilon-N” proofs in class
4	3.1, 3.2, 3.3	Derivative Rules
5	3.4, 3.5, 3.6	Finish Derivative Rules	In section 3.4, the formula for derivative for inverse function should be given as well as particular examples like exponential and trig
6	J.1, J.2	Vectors and Dot Product; Test 1	Remember that tests are in the evening. Different instructors cover this material at different paces and emphasize different topics. For Test 2, 3.5-3.10, J, K ideally needs to be covered.
7	Finish J.2, J.3, K.1	Vector Functions; Vector Derivatives
8	Finish K.1; K.2; 3.9	Parametric Slopes; Related Rates
9	Finish 3.9; 3.10; 4.1	Linear Approximation; Extrema	In addition, the professor should add information about quadratic approximation. This should include a "derivation" of the approximation - for example finding the unique second degree polynomial that matches the function to the second derivative.
10	4.2, 4.3	Graphical interpretation of derivatives; Test 2	Make sure MVT is applied in 4.3 to prove connections between the sign of the derivative and increasing/decreasing; use MVT to prove things like if f’=0 then f is constant.
11	4.4, 4.7	L’Hospital’s Rule; Optimization Problems	For L’Hospital, they should see all 3 exponential forms.
12	4.9, 5.1, 5.2	Anti–Derivatives, Definite Integrals	For Riemann sums, sigma notation should be used and students should be expected to manipulate sums like this on exams.
13	Finish 5.2, 5.3	Definite Integrals; Fundamental Theorem of Calculus	FTC should be illustrated - perhaps with graphs; "proofs" should be given.
14	5.4, 5.5	Indefinite Integrals; Substitution; Exam 3
15	Finish 5.5	Substitution; Review for Final