Math 115. Preparation for Calculus

Course Description: Reviews trigonometric, rational, exponential, and logarithmic functions; provides a full treatment of limits, and may include the definition of derivative, and an introduction to finding area under a curve. Intended for students who need preparation for Math 220 (Calculus), either because they lack the content background or because they are not prepared for the rigor of a university calculus course.

The sole purpose of Math 115 is to prepare students to take Math 220: Calculus at the University of Illinois. This is done by reviewing some concepts students should have learned in previous high school mathematics courses but exploring the mathematics more deeply and from an advanced viewpoint. The goals are to introduce students to the underlying logic and reasoning, create a familiarity with mathematical notation and give students the opportunities to improve their critical thinking, problem solving, and study skills.

Textbook: No textbook is required for Math 115. Students are instructed to view their lecture notes and written homework assignments as the text. However, Stewart, Calculus: Early Transcendentals, 8th edition, with Enhanced Webassign, is recommended for the course since the assumption is that students who take this course are intending to take Math 220 which also uses the Stewart book.

Unit 1 (~13 lectures)

Brief Function Review

• Domain and Range
• Graphs of functions
  • Transformations
  • Continuity

Sequences and Series

• Simple sequences
  • Arithmetic, Geometric, etc
• Limits of sequences
• Series
  • Summation notation
  • Finite series
  • Infinite series

Unit 2 (~13 lectures)

Graphs of Polynomial and Rational Functions

• Use of limits to determine end behavior

Exponential Functions

• Use of limits to determine end behavior

Inverse Functions

• Use of limits to determine end behavior

Logarithmic Functions

• Use of limits to determine end behavior

Unit 3 (~13 lectures)

Trigonometric Functions

• Radians and angles
• Relationship between right triangle trig and the unit circle
• Graphs of sine, cosine, and tangent functions and their transformations
• Inverse trig functions
• Solving trig equations

Unit 4 (if time)

Applications of limits

• Derivative
• Area under a curve

 

This syllabus assumes MWF lectures with no discussion sections – 43 lecture hours per semester. It includes 39 lectures, 3 exam lectures, and 3 leeway hours.