The2015 Summer Academy Syllabus

Math 3 – PrecalculusInstructor: Nandini Bhattacharya

Room--TBDOffice: McHenry Library 4165

Monday-Thursday 3:30-4:45 pmPhone: 9-1265

Fax: 459-4511

email:

web site: people.ucsc.edu/~nandini

TextCohen, Lee, and Sklar, Precalculus. A Problem-Oriented
Approach (custom 7th edition for UCSC).

Students will learn concepts in an interactive learning environment during lecture. Sections will be organized in collaborative learning setting. The homework for the class will be done on line.

The course lectures will be built on the following topics:

1)Foundational Chapter on Functions: Definitions, Domain/Range, Combination of Functions: Composite Functions, Graphs (basic), Transformation of Graphs, Inverse Functions.

Topic (1) will be the conceptual Umbrella for topics (2) through (4). Each family of functions discussed in topic (2) through (4) will be connected with the theoretical premise developed in topic (1).

2)Polynomial Functions: Linear, Quadratic, Polynomial of degree 3 or above, Rational Functions.

Graphs and applications of each of the variety of functions will be fully developed. The concept of optimization will be explored in the Quadratic function discussion and it’s relevance to the optimization application problems will be discussed. The application section of this module will be robust with emphasis on maximizing and minimizing quadratic or quadratic like expressions.

3)Exponential and Logarithmic Functions. Revisiting the relationship of a function and it’s inverse with emphasis on graphing and it’s domain and range. Exponential and Log properties and demonstrating their inner connectivity. Solving logarithmic and exponential equations. Applications in relation to growth/ decay/ compounding interest.

4)Trigonometry:

a) Define angle and introduce Right Triangle Trigonometry, Special Triangles and it’s connection to Unit Circle, Reference Angle Principles, Proving Identity. Applications problems related to the area of the polygons and related topics.

The discussion of this sub-unit will be restricted to the degree measurement of angle.

b)Define angular velocity, arc length, linear velocity. Define radian measure and discuss many of the same topics as (a) but the discussion will be restricted to the radian measurement of the angle.

c)Graphs of the six trigonometric functions.

Discussion of basic trigonometric graphs along with the Transformations of Graphs from topic (1) will be the conceptual foundation to deliver this portion of the module.

d)Analytical Trigonometry. Inverse Trigonometric Functions tying the discussion to topic (1). Solving Trigonometric and Inverse Trigonometric Equations.

e)Applications of Trigonometry: Law of sine and cosine. Angle of Elevation and Depression.

Office HoursMonday-Thursday 5-6 pm and also by appointment

Discussion Sections

& Quizzes

You will be able to get help with your homework questions, worksheets and any other questions related to the course during these sessions. You will take your weekly tests in section, reflective of the homework assigned and the worksheet from the previous week. Sections are mandatory and you must enroll in one.

Grading Policy Online Homework (10%)

Worksheet (10%)

Lecture Participation (5%)

4Quizzes (20%)

1 Midterm (20%)

Cumulative Final (35%)

On-line

HomeworkHomework in this class is assigned weekly and submitted on-line

at WebAssign.net . All instructions regarding which sections are due and

their corresponding due dates and time will be administered through the Webassign website. The ISBN for this course is 9781133639480.

Tentative Lecture Schedule

Wed
July 29
Introduction
3.1-3.2 / Thurs
July 30
3.3-3.4 / Mon
August 3
3.5-3.6 / Tue
August 4
3.6, 4.1 / Wed
August 5
4.2, 4.4 / Thurs
August 6
4.4-4.5
Mon
August 10
4.6-4.7 / Tue
August 11
4.7-5.1 / Wed
August 12
5.2-5.3 / Thurs
August 13
5.4-5.5 / Mon
August 17
5.6-5.7 / Tue
August 18
6.1-6.2
Wed
August 19
6.3-6.4 / Thurs
August 20
6.4 / Mon
August 24
Midterm / Tue
August 25
7.1-7.2 / Wed
August 26
7.3-7.4 / Thurs
August 27
7.4-7.5
Mon
August 31
8.1-8.2 / Tue
Sept 1
8.3-8.4 / Wed
Sept 2
8.5-9.1 / Thurs
Sept 3
9.1-9.2 / Mon
Sept 7
Holiday / Tue
Sept 8
9.4-9.5
Wed
Sept 9
10.1-10.2 / Thurs
Sept 10
Final Exam
2-5 pm