BRONX COMMUNITY COLLEGE
of the City University of New York
DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE
SYLLABUS: MTH 31 - Analytic Geometry and Calculus I
(4 credits/6 hours per week)
PREREQUISITE: MTH 30 or equivalent and, if required,
ENG 2 and RDL 2
TEXT:
Calculus (8th Edition) by James Stewart, Cengage
Learning. ISBN 978-1285740621
Students who do not need MTH 33 may use
Single Variable Calculus (8th Edition) by James Stewart, Cengage Learning ISBN 978-1305266636
This course is
a Pathways Core B (Mathematical and
Quantitative Reasoning) Course:
A course in this area must meet all of the following learning outcomes. A
student will:
a) Interpret and draw
appropriate inferences from quantitative representations, such as formulas,
graphs, or tables.
b) Use algebraic,
numerical, graphical, or statistical methods to draw accurate conclusions and
solve mathematical problems.
c) Represent quantitative
problems expressed in natural language in a suitable mathematical format.
d) Effectively communicate
quantitative analysis or solutions to mathematical problems in written or oral
form.
e) Evaluate solutions to
problems for reasonableness using a variety of means, including informed
estimation.
f) Apply mathematical
methods to problems in other fields of study.
Course
Learning Outcomes (Pathways
Learning Outcomes contributed to)
On successful completion of this course a student
will be able to:
1. Evaluate limits at a value and at infinity by
using limit laws and the Squeeze Theorem (a, b, c, e)
2.
Differentiate
algebraic and trigonometric functions including by use the limit definition; Product,
Quotient, and Chain Rules; and implicit differentiation (a, b)
3.
Use
differentiation to compute instantaneous rates of change and tangent lines (c,
d, e, f)
4.
Compute maxima and minima of functions using calculus to solve
optimization problems
arising in applications and other fields of study
(b,
c, d, e, f)
5.
Model
and solve related rates problems (b, c, d, f)
6.
Apply
methods of calculus to curve sketching (a, b, e)
7.
Anti-differentiate
algebraic and trigonometric functions (a, b)
8.
Approximate
integrals by Riemann sums (b, d, e)
9.
Evaluate
elementary integrals, including by use of substitution and the Fundamental
Theorem of Calculus (b, d, e)
10. Compute definite integrals geometrically or
using calculus to determine areas enclosed by curves (a, b, c, d, f)
SECTION TOPIC
SUGGESTED
EXERCISES
Chapter 1: Functions and Limits
1.4 The Tangent
and Velocity Problems 49/
1, 3, 5, 7
1.5 The Limit
of a Function 59/
1-5, 12-14, 17, 23-28
1.6 Calculating
Limits Using Limit Laws 70/
1, 3-23 odd
1.8 Continuity 91/
3, 7, 9, 15-21 odd, 25, 33, 37, 39, 41, 44, 45,
47,
49, 53, 55, 57
Review 96/
1-11 odd, 17, 23, 27, 29
Chapter 2: Derivatives
2.1 Derivatives 113/
1, 3, 7, 21-31 odd, 39-47 odd, 53, 57, 59
2.2 The
Derivative as a Function 125/
1, 3, 4, 7, 19, 20, 21, 25-33 odd, 39-51 odd
2.3 Differentiation
Formulas 140/
1-43 odd, 51, 53, 69, 77
2.4 Derivatives
of Trigonometric Functions 150/
1-17 odd, 25, 29, 39-49 odd
2.5 The
Chain Rule 158/
1-45 odd, 47, 51, 55, 69, 71
2.6 Implicit
Differentiation 166/
1-19 odd, 25, 27, 31, 35, 43, 45
2.7 Rates
of Change in the Natural and 178/
1-9 odd, 15, 18
Social
Sciences
2.8 Related
Rates 185/
1, 3, 9, 10, 11, 13-33 odd
2.9 Linear
Approximations and Differentials 192/
1, 3, 5, 7-25 odd, 31
Review 196/
3, 5, 11, 13-37, 45, 51, 59, 61, 75, 77, 79, 82
Chapter 3: Applications of
Differentiation
3.1 Maximum
and Minimum Values 211/
3, 5, 15-27 odd, 29-55 odd
3.2 The
Mean Value Theorem 219/
1, 11, 13, 17, 21
3.3 How
Derivatives Affect the Shape of a Graph 227/
1, 5, 7, 8, 9-17 odd, 33-41 odd
3.4 Limits
at Infinity; Horizontal Asymptotes 241/
3, 9-29 odd, 37, 41
3.5 Summary
of Curve Sketching 250/
1-35 odd
3.7 Optimization
Problems 256/
3, 5, 7, 11, 17, 21, 27, 31
3.8 NewtonÕs
Method 276/
5, 7, 13-19 odd, 29
3.9 Antiderivatives 282/
1-41 odd, 43, 45, 47
Review 286/
1-27 odd, 38, 41, 46, 49, 55, 57
Chapter 4: Integrals
4.1 Areas and
Distance 303/
1, 3, 5, 13, 15, 21, 25
4.2 The
Definite Integral 316/
3, 5, 9, 17, 21-25 odd, 31, 33, 37
4.3 The
Fundamental Theorem of Calculus 327/
3, 7-35 odd, 45, 51, 53
4.4 Indefinite
Integrals and the Net Change Theorem 336/
1-11 odd, 19-41 odd, 55, 57
4.5 The
Substitution Rule 346/
1-29 odd, 35-51 odd
Review 349/
2, 5, 11-29 odd, 35, 37, 39
8/03
C.OÕS.
8/07 MM
7/11 MM, 9/11 AM
6/12 EA new ed
1/16 EA new ed
10/17 EA for
Pathways compliance