Calculus

The first semester of a multi-semester sequence of differential and integral calculus generally taken for college credit (4 hours). Topics include limits; derivatives considered algebraically, symbolically and graphically; differentials and their use as approximations; the indefinite and definite integrals; inverse functions; logarithmic and exponential functions; and symbolic and numeric methods of integration. Appropriate for math majors and students in partner disciplines requiring understanding of fundamental principles of calculus, with emphasis on deductive reasoning and proof.

Required Text

“Calculus: Graphical, Numerical, Algebraic 4th Edition” by Ross L. Finney, Franklin D. Demana, Bert K. Waits and Daniel Kennedy.

Required Supplies

  • TI-84+ (or higher) graphing calculator
  • 1- or 2-inch binder
  • Loose leaf paper or equivalent

Course Format and Procedures

There will be a test on each chapter that is covered. There will be announced and unannounced quizzes
on homework and various sections covered. Homework problems will be assigned daily and corrected
daily. Late assignments may be made up in a reasonable time frame. There will be a cumulative midterm
and final exam for all students. Any student with a grade of 93% or above for all four quarters may be
exempt from the final. There will be no exemptions from the midterm exam. (Prerequisite: Grade of C or above in pre-calculus, placement by academic adviser or permission of instructor.)

Grading Procedures

In keeping with BP Board of Education policies:

  • Grades reported on progress reports and report cards shall be derived from work that measures mastery of knowledge, skills and student learning objectives.
  • When calculating student grades, more weight shall be given to assignments/assessments designed to evaluate student learning than to assignments/assessments provided to practice and guide next-step instruction.
  • Quarterly grades are broken down as follows:
    • Tests will constitute 50% of a student’s grade per quarter.
    • Quizzes will constitute 30% of student’s grade per quarter.
    • Homework will constitute 20% of your quarter grade.
    • The midterm will be cumulative and constitute 10% of a student’s overall grade.
    • The final exam will also be cumulative and constitute 10% of a student’s overall grade.

Student and Parent Resources

Course Outline (tentative)

Preparation for Calculus

  • Graphs and Models
  • Linear Models and Rates of Change
  • Functions and Their Graphs
  • Fitting Models to Data

Limits and their Properties

  • A Preview of Calculus
  • Finding Limits Graphically and Numerically
  • Evaluating Limits Analytically
  • Continuity and One-Sided Limits
  • Infinite Limits

Differentiation

  • The Derivative and the Tangent Line Problem
  • Basic Differentiation Rules and Rates of Change
  • Product and Quotient Rules and Higher-Order Derivatives
  • The Chain Rule
  • Implicit Differentiation

Applications of Differentiation

  • Extrema on an Interval
  • Rolle’s Theorem and the Mean Value Theorem
  • Increasing and Decreasing Functions and the First Derivative Test
  • Concavity and the Second Derivative Test
  • Limits at Infinity
  • A Summary of Curve Sketching
  • Optimization Problems
  • Newton’s Method
  • Differentials

Integration

  • Anti-derivatives and Indefinite Integration
  • Area
  • Riemann Sums and Definite Integrals
  • The Fundamental Theorem of Calculus
  • Integration by Substitution
  • Numerical Integration

Logarithmic, Exponential and Other Transcendental Functions

  • The Natural Logarithmic Function: Differentiation
  • The Natural Logarithmic Function: Integration
  • Inverse Functions
  • Exponential Functions: Differentiation and Integration
  • Other Bases and Applications
  • Inverse Trigonometric Functions: Differentiation
  • Inverse Trigonometric Functions: Integration
  • Hyperbolic Functions