Syllabus: M 305G

Preparation for Calculus - CNS

Text: Stewart, Redlin, Watson, Precalculus , sixth edition, ISBN 978-0840068071

Responsible Parties : Amanda Hager, July 2014

Prerequisite and degree relevance: the minimum required score on the mathematics placement exam. Credit for M305G may NOT be earned after a student receives credit for any calculus course (e.g. M408C, M408K, M408N, M408R, or equivalent) with a grade of at least C-.  Only one of M305G and any college-level trigonometry course may be counted. M301, M305G and equivalent courses may not be counted toward the major requirement for the Bachelor of Arts, Plan I, degree with a major in mathematics or toward the Bachelor of Science in Mathematics degree.

Course description: The purpose of this course is to prepare students for calculus courses. Some students are taking this course as a review, many because they did not scored high enough on the mathematics placement exam to enter calculus directly.  The course emphasis is on techniques needed in calculus, with an emphasis on rigorous algebraic practice and on recognizing and interpreting graphs. It is assumed that the students have had at least three and a half years of high school mathematics.

Timing and optional sections: The following table contains suggestions as of timing of topics and includes 36 class hours of content.  Allowing for in-class exams, there remains 3-5 class hours for review or optional topics.

 

Topic

Stewart-Redlin-Watson section

Number of class hours

Unit 1:  Algebra and function basics, 9 hours

Exponents

1.2

0.5

Quadratic Formula

1.5

0.5

Absolute Value Eq

1.5

0.5

Absolute Value Ineq

1.7

0.5

Quadratic, Rat’l Ineq

1.7

1

Functions, Notation, D/R

2.1

0.5

Graph Types (Toolbox Functions)

2.2

0.5

Increasing/Decreasing/Pos/Neg

2.3

0.5

Average Rate of Change

2.4

0.5

Transformations

2.5

1

Algebra and Composition of Fcns

2.6

1

Domains of Compositions, Sums, etc.

2.6

1

Rational functions, asymptotes

3.7

1

Unit 2:  Exponential and logarithmic functions, 8 hours

One-to-one, invertible fcns

2.7

1

Exponential functions, graphing

4.1, 4.2

1

Log functions, graphing

4.3

2

Properties of logs and exp fcns

4.4

1

Solving exp/log equations

4.5

2

Modeling with exp/log

4.6

1

Unit 3:  Trigonometry, 12 hours

Angles/triangles/radians

5.1, 6.1

1

Unit circle

5.2

1

Graphing sine/cosine, amp/period

5.3

1

Graphing tan

5.4

1

Transformations of trig graphs

5.3, 5.4

1

Solving trig equations

7.4, 7.5

2

Solving right triangles, ang of elevation

6.2

2

Identities/trig identities

7.1, 7.2

2

Inverse trig functions

5.5, 6.4

1

Unit 4:  Limits, 7 hours

 

 

PW defined functions

2.1, 2.2

1

Limits via graphs, tables

13.1

2

Limits formally

13.2

2

Limits at infinity, infinite limits, cont.

13.4

2