MATH 2253
CREDIT: 4 hours. No student may receive credit for both MATH 2253 and MATH 2240.
PREREQUISITE: A grade of C or higher in MATH 1113 or placement by the Mathematics Assessment Test.
COURSE DESCRIPTION: A first course in calculus. Topics include limits, derivatives and integrals of algebraic and trigonometric functions; also, tangent lines, instantaneous rates of change, related rates, maxima, minima, the area between curves, volumes, centers of mass and moments of inertia, and the work done by varying forces. Other topics may be included at the discretion of the lecturer.
TEXT: Thomas’ Calculus, 11th ed.; CALCULATOR: TI-89;
SUGGESTED LECTURE SCHEDULE
This schedule and the choice of exercises is to be taken as a starting point. Individual lecturers should use it as a guide to develop their own courses.
In assignments "NC" means no calculator used, or do without a calculator, "C" means the TI-89 is allowed or required. If neither "NC" or "C" is given, then follow the directions in the book.
CLASS PREPARATION
1 2.1 Rates of Change and Limits (through example 6)
Ex.: pp. 81-3 NC: 1, 5, 9, 21, 23; C: 38, 41, 43, 45
2 Finish 2.1 Ex.: pp. 81-3 NC: 25-33 odd
Begin 2.2 Calculating Limits (through ex. 4)
Ex.: pp. 89-91 NC: 37, 41, 43, 47, 49, 51; C: 51(b), 59, 60
3 Finish 2.2 Ex.: pp. 89-91 NC: 5, 7, 19, 21, 24.
Begin 2.4 One-Sided Limits (through ex. 4)
Omit Precise Definitions of One-Sided Limits and ex. 3
Ex.: pp. 111-3 NC: 1, 5, 11, 15.
4 2.4 Limits Involving sin(θ)/θ only.
Ex.: pp. 111-3 NC: 21, 23, 25, 29, 33,
Begin 2.6 Continuity (through ex. 7)
Ex.: pp. 132-4 NC: 1, 5, 13, 15, 23; C: 41, 43.
5 Finish 2.6 Ex.: pp. 132-4 NC: 17, 29, 33, 35, 37, 45, 47.
6 2.7 Tangents and Derivatives
Ex.: pp. 140-1 NC: 5, 7, 13, 15, 21-31 odd.
7 3.1 The Derivative of a Function (through ex. 3. Optional: ex. 4)
Ex.: pp. 155-8 NC: 1, 3, 7, 13, 15, 19, 23.
8 Finish 3.1 Ex.: pp. 155-8
NC: 25, 27-30, 35, 37, 45, 51, 52; C: 61
9 3.2 Differentiation Rules (to Products and Quotients)
Ex.: p. 169 NC: 1-9 odd; C: 47, 48
10 Finish 3.2 Ex.: pp.169-70
NC: 13, 17, 21, 31, 33, 41, 43, 55; C: 47, 48
11 3.3 The Derivative as a Rate of Change
(Omit Economics and its examples)
Ex.: pp. 179-83 NC: 1, 5-15 odd, 21, 29; C: 27, 31, 33
12 3.4 Derivatives of Trigonometric Functions
Ex.: pp. 188-90 NC: 1, 5, 7, 11, 13, 19, 27, 35, 39, 43, 49; C: 51
13 REVIEW
14 TEST 1
15 3.5 The Chain Rule and Parametric Equations (through ex. 5)
Ex.: pp. 201-2 NC: 9-17 odd, 39, 43, 47, 49; C: 105
16 Continue 3.5 (through ex. 8, only)
Ex.: pp. 201-2 NC: 19, 21, 25, 29, 35, 41, 51, 53, 65.
17 3.6 Implicit Differentiation
Ex.: pp. 211-2 NC: 3, 13, 19, 21, 27, 33, 41, 47, 49, 63.
18 3.6 Exercise Day (Optional)
19 3.7 Related Rates
Ex.: pp. 218-21 NC: 1, 3, 7, 13, 17, 19, 21, 23, 27, 31, 35.
20 3.7 Exercise Day (Optional)
21 4.1 Extreme Values of Functions (Omit the proof of Theorem 2.)
Ex.: pp. 252-3 NC: 1, 3, 5, 37, 43, 47, 53; C: 75, 77, 79
22 Finish 4.1 (Prove Theorem 2)
Ex.: pp. 252-3 NC: 15, 17, 23, 25, 29, 55, 61, 63.
23 4.2 The Mean Value Theorem (through ex. 3)
Ex.: pp. 260-2 NC: 1-7 odd, 25, 27; C: 53
24 Finish 4.2 Ex.: pp. 260-2 NC: 29, 33, 37, 47.
25 4.3 Monotonic Functions and the First Derivative Test
Ex.: pp. 266-7 NC: 1-11 odd, 21, 25, 31, 33.
26 4.4 Concavity and Curve Sketching (to ex. 6, only)
Ex.: pp. 274-5 NC: 1, 3, 5 and (just finding the local extrema)
9, 13, 17, 19, 23, 27, 33, 35; C: 85, 87
27 4.5 Applied Optimization Problems (to Economics, only)
Ex.: pp. 285-8 NC: 1-15 odd, 19, 23, 27, 31, 33, 37; C: 38
28 4.5 Exercise Day
29 REVIEW
30 TEST 2
31 4.8 Antiderivatives (through ex. 4. Also, Indefinite Integrals)
Ex.: pp. 314-8 NC: 1, 5, 17, 21, 27, 33, 35, 55, 61, 63.
32 Finish 4.8 Ex.: pp. 314-8
NC: 65, 67, 71, 77, 79, 81, 87, 89, 93, 97, 99.
33 5.1 Estimating with Finite Sums (to Average Value)
Ex.: p. 333 NC: 1, 5, 9.
34 Finish 5.1 Ex.: pp. 334-5 NC: 11, 15, 21.
35 5.2 Sigma Notation and Limits of Finite Sums (through ex. 4)
Ex.: pp. 342-3 NC: 1-11 odd; C: 19, 23
36 Finish 5.2 Ex. pp. 342-3 NC: 15, 17, 29, 33, 37.
37 5.3 The Definite Integral (to Properties) Ex.: p. 352 NC: 1-8 all.
38 Continue 5.3 (to Average Value)
Ex.: p. 353 NC: 9, 11-19 odd, 29, 33.
39 Finish 5.3 Ex.: pp. 353-4 NC: 47, 49, 51, 55, 59.
40 5.4 The Fundamental Theorem of Calculus
(through proof of Theorem 4) Ex.: p. 365 NC: 27-33 odd.
41 Finish 5.4 Ex.: pp. 365-7 NC: 3-11 odd, 19, 23, 37, 41, 43, 63.
42 REVIEW
43 TEST 3
44 3.8 Linearization and Differentials
(Only Differentials and ex. 4(a) and 5.)
Ex.: p. 232 NC: 19-25 odd.
Also 5.5 Indefinite Integrals (through ex. 6)
Ex.: pp. 374-6 NC: 1-11 odd. 19, 23, 29, 43, 45, 49.
45 Finish 5.5 Ex.: pp. 374-6 NC: 19, 23, 29, 43, 45, 49.
Also 5.6 Substitution and Area Between Curves (through ex. 4)
Ex.: pp. 383-7 NC: 3, 5, 15, 17, 21; C: 91, 93
46 Finish 5.6 Ex.: pp. 383-7 NC: 27, 31, 33, 43, 45.
47 6.1 Volumes by Slicing and Rotation About an Axis
(through ex. 5)
Ex.: pp. 405-9 NC: 1, 3, 5, 13-21 odd.
48 Finish 6.1 (Omit ex. 6 and 8)
Ex.: pp. 405-9 NC: 25, 29, 31, 35-41 odd.
49 6.2 Volumes by Cylindrical Shells
Ex.: pp. 414-6 NC: 1, 3, 5, 9, 11, 15-21 odd, 25, 31.
50 6.4 Moments and Centers of Mass (through ex. 2)
Ex.: pp. 434-5 NC: 1, 5, 7, 9.
51 Finish 6.4 Ex.: pp. 434-5 NC: 13-21 odd, 25, 40.
52 6.6 Work (to Pumping) Ex.: pp. 452-5 NC: 1, 5, 13, 25-29 odd.
53 Finish 6.6 Ex.: pp. 452-5 NC: 19, 23, 35.
54 REVIEW
55 TEST 4
56 2.4 One Sided Limits and Limits at Infinity (p. 107 to end)
Ex.: p. 113 NC: 37-51 odd.
57 2.5 Infinite Limits and Vertical Asymptotes
Ex.: p. 122 NC: 3, 5, 11, 19, 23.
58-60 Review for Final Examination