SAINT LOUIS UNIVERSITY

1818 Advanced College Credit Program

Analytic Geometry/Calculus 1

Course #MT X-142

Columbia High School, Columbia Community Unit 4

Calculus1

Course Syllabus: Fall/Spring 2014/2015

Instructor: Mrs. Wendy Stevens B.S., M.S.

Contact Information: Columbia High School, 77 Veterans Parkway, Columbia, IL 62236

Phone: 618-281-5001 from 8:00 to 8:45 a.m. or after 3:05 p.m.

e-mail:

Text: Calculus: Graphical, Numerical, Algebraic, Finney, Demana, Waits, Kennedy, 2003

ISBN 0-13-063131-0 Pearson, Prentice Hall

Course Objectives: For the student to be able to:

Find the Limit of a function by several methods

Use the slope of the tangent line, concavity, points of inflection, and other information to sketch the graph of a function.

Find the derivative of a function using several methods.

Use the derivative of a function in a variety of applications.

Find the antiderivative, indefinite and definite integral of various types of functions.

Course Outline:

  1. Real numbers, Functions, and Graphs
  2. Lines
  3. Functions and Graphs
  4. Exponential Functions
  5. Functions and Logarithms
  6. Trigonometric Functions
  1. Limits and Their Properties
  2. Rates of Change and limits
  3. Limits involving infinity
  4. Continuity
  5. Rates of change and tangent lines
  1. Derivatives.
  2. Derivative of a Function
  3. Differentiability
  4. Rules for Differentiation.
  5. Velocity and Other Rates of Change.
  6. Derivatives of Trigonometric Functions.
  7. Chain Rule.
  8. Implicit Differentiation
  9. Derivatives of Inverse Trigonometric Functions
  10. Derivatives of Exponential and Logarithmic Functions
  1. Applications of Derivatives.
  2. Extreme Values of Functions.
  3. Mean Value Theorem.
  4. Increasing and decreasing functions and the first derivative test.
  5. Concavity and the second derivative test.
  6. Modeling and Optimization.
  7. Linearization and Newton’s Method.
  8. Related Rates
  1. The Definite Integral
  2. Estimating with Finite Sums
  3. Definite Integrals
  4. Definite Integrals and Antiderivatives
  5. The Fundamental Theorems of Calculus.
  6. Trapezoidal Rule
  1. Differential Equations and Mathematical Modeling
  2. Antiderivatives and Slope Fields
  3. Integration by Substitution
  4. Integration by Parts
  5. Exponential Growth and Decay
  6. Population Growth
  7. Numerical Methods
  1. Applications of Definite Integrals
  2. Integral as Net Change
  3. Area in the Plane
  4. Volumes
  5. Lengths of Curves
  6. Applications from Science and Statistics
  1. L’Hopital’s Rule, Improper Integrals, and Partial Fractions
  2. L’Hopital’s Rule
  3. Relative Rates of Growth

Chapters 1 through 4 will be covered in the 1st semester and chapters 5 through 7 will be covered in the 2nd semester. With 1st semester exams occurring approximately December 20th and 2nd semester exams occurring approximately May 15th.

Evaluative Criteria: Tests will be given at the end of every chapter and will be worth 200 points. Quizzes will be given when appropriate and may be announced or unannounced with varying point values. Homework will be checked regularly for completeness. Projects and Labs will be calculated as homework.

Grading: Quarter grades will be determined from homework, quizzes, and tests. Homework will make up no more than 30% of each quarter grade. The Semester grade will be determined on the basis: 40% for each quarter grade, 20% final exam. Exams will be given at the end of each semester and are cumulative. The Final grade for St. Louis University will be the average of the two semester’s grades.

Grades will be assigned according to the following scale:

Grading Scale
Letter Grade / Range / Grade Point
A / 93 - 100 / 4.00
A- / 90 - 92 / 3.67
B+ / 87 - 89 / 3.33
B / 83 - 86 / 3.00
B- / 80 – 82 / 2.67
C+ / 77 – 79 / 2.33
C / 73 – 76 / 2.00
C- / 70 – 72 / 1.67
D+ / 69 / 1.33
D / 67 – 68 / 1.00
D- / 66 / 0.67
F / 65 and below / 0.00

Success in the course will be achieved by consistent and diligent working of assigned problems, achieving an understanding of the basic theory behind the methods of problem solving presented, and a thorough knowledge of all high school algebra, geometry, and trigonometry.

Academic Integrity Statement: This class holds the same standards of academic integrity as other classes at Saint Louis University. Complete, specific college guidelines are available at http://www.slu.edu/x12657.xml