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