# MATH 118 Precalculus

**JOHN FELICE ROME CENTER, LOYOLA UNIVERSITY CHICAGO**

**COURSE CODE:** "MATH 118"

**COURSE NAME:** "PRECALCULUS"

**SEMESTER & YEAR:** Spring Semester 2013

**SYLLABUS**

**INSTRUCTOR:** Gatto Renato, rgatto1@luc.edu

**HOURS:** TTH 17:00-18:15

**UNITS:** 3.00

**PREREQUISITES: **Math 117 (College Algebra) with a grade of “C-” or

better, or Math Placement Test.

**OFFICE HOURS:** TTH 18:15-19:15 by appointment

**COURSE AIMS:**

The main objective of the course is to provide an understanding of selected topics

in calculus of one variable and their applications. Conceptual and computational

skills will be developed, with emphasis on understanding concepts.

**SUMMARY OF COURSE CONTENT:**

Functions and change with an emphasis on linear, quadratic, exponential, and

logarithmic functions and their graphs. Specific geometry topic include concavity

and how transformations affect graphs. Topics in trigonometry include radians,

sinusoidal functions, identities, sum/difference formulas, double/half angle formulas,

and trigonometric equations. Other topics include polar coordinates.

**LEARNING OUTCOMES:**

The student will have built a strong foundation to studying Calculus.

**TEXTBOOK:**

“Algebra and Trigonometry”, Sheldon Axler, 1^{th} Edition, Wiley, ISBN 978-1118-08841-8.

**REQUIRED RESERVED READING:**

NONE

**RECOMMENDED RESERVED READING:**

NONE

**GRADING POLICY**

**-ASSESSMENT METHODS:**

There will be 2 exams each carrying 20% of the final grade, a final examination (comprehensive) worth 40%, and homework worth 10%. The remaining 10% is associated with attendance and class participation:

2 Exams..................................................40%

Final Exam .............................................40%

Homework .............................................10%

Attendance and Class Participation .......10%

**-ASSESSMENT CRITERIA:**

The grade scale is as follows:

A: 90%-100% (The student demonstrates complete, accurate, and critical knowledge of all the topics, is able to make

appropriate connections among different parts of the subject matter, uses the appropriate language and terminology

correctly and rigorously and is autonomous in his study)

B: 80%-89% (The student has a somewhat accurate knowledge of the subject matter and uses clear logic in his/her

arguments)

C: 70%-79% (The student has the essential knowledge of the subject matter, understands the topics, and can express

it in a simple language)

D: 60%-69% (The student has a superficial, mnemonic knowledge of the subject matter, is uncertain and makes errors

in the presentations)

F: below 60% (At best, the students has a superficial knowledge of some of the topics discussed in the course. He

makes serious errors in the presentations).

Numerically, the final grade is computed as follows: G=0.20 E1 + 0.20 E2 + 0.4 F + 0.1 H + 0.1 A,

where G is the final grade, E1 the score in the first exam, E2 the score in the second exam, F the score in the final,

H the average score in the homework, and A is the score associated with attendance and class

participation. The conversion between numerical grade and letter grade is described by the following table:

A 100 - 93

A- 92 - 89

B+ 88 - 86

B 85 - 81

B- 80 - 78

C+ 77 - 75

C 74 - 71

C- 70 - 68

D+ 67 - 63

D 62 - 60

F 59 - 0

**-ADDITIONAL CLASS POLICIES:**

Cheating is not tolerated (please see the University Catalog for the policy regarding

academic dishonesty).

Coming late to class or leaving early will be possible only with permission of the instructor.

No make-up exams will be given.

**-ATTENDANCE REQUIREMENTS:**

Attendance will contribute to the final grade. Full credit for attendance will be given to people

with two or fewer unexcused absences. Three or more absences will result with a proportional

reduction of the grade.

** **

** **

**SCHEDULE**

Week 1. REVIEW OF INTERMEDIATE ALGEBRA: Real line, algebra of the real

numbers, inequalities, intervals, and absolute value, coordinate plane.

Week 2. FUNCTIONS AND THEIR GRAPHS: Functions, function transformations and

graphs, composition of functions.

Week 3. FUNCTIONS AND THEIR GRAPHS: Inverse functions,

a graphical approach to inverse functions.

Week 4. COMBINING ALGEBRA AND GEOMETRY: Lines, quadratic expressions and

conic sections. POLYNOMIAL AND RATIONAL FUNCTIONS: Integer exponents.

Week 5. EXPONENTS AND LOGARITHMS: Exponents and exponential functions.

**EXAM 1**. POLYNOMIAL AND RATIONAL FUNCTIONS: Polynomials, rational

functions.

Week 6. EXPONENTS AND LOGARITHMS: Exponents and exponential functions,

logarithms as inverses of exponential functions.

Week 7. EXPONENTS AND LOGARITHMS: Applications of logarithms, exponential

growth.

Week 8. "e" AND THE NATURAL LOGARITHM: Defining "e" and "ln", approximations

and area with "e" and "ln", exponential growth revisited.

Week 9. TRIGONOMETRIC FUNCTIONS: The unit circle, radiants, cosine and sine.

**EXAM 2**.

Week 10. TRIGONOMETRIC FUNCTIONS: More trigonometric functions, trigonometry

in right triangles, trigonometric identities.

Week 11. TRIGONOMETRIC ALGEBRA AND GEOMETRY: Inverse trigonometric

functions, inverse trigonometric identities, using trigonometry to compute

areas.

Week 12. TRIGONOMETRIC ALGEBRA AND GEOMETRY: The law of sines and the law

of cosines, double-angle and half-angle formulas, addition and subtraction

formulas. APPLICATION OF TRIGONOMETRY: Transformations of

trigonometric functions, polar coordinates. **FINAL EXAM**.