NORTHALLEGHENYSCHOOL DISTRICT

MATHEMATICS DEPARTMENT

HONORS CALCULUS SYLLABUS

COURSE NUMBER: 3422

Instructors:

Units of Credit: 1.0J.

Course Length: Full YearS.

Honors Calculus Syllabus

Course Overview

Honors Calculus is a course designated for students who have completed four years of honors math with a high level of achievement. The topics covered in Honors Calculus make it the standard first course in a basic calculus sequence required for all mathematics, science, engineering, and statistics students at the college level. Therefore, students may obtain four college credits through the University of PittsburghCollege in High School program. The course emphasizes a multi-representational approach to calculus, with concepts, results, and problems being expressed in multiple ways: geometrically, numerically, analytically, and graphically.

Textbook

Finney, Demana, Waits, Kennedy, Calculus: Graphical, Numerical, Algebraic, Boston: Pearson Prentice Hall, 2007.

Course Outline:

The following topics are covered in Honors Calculus:

Chapter 1: Prerequisites for Calculus

  • Algebraic Methods Review (lines, absolute value, inequalities)
  • Functions andGraphs (definitions, properties, notation)
  • Polynomial and Rational Functions
  • Exponential and Logarithmic Functions
  • Trigonometric Functions
  • Parametrically defined Functions

Chapter 2: Limits and Continuity

  • Rates of Change and Limits
  • Limits Involving Infinity
  • Continuity
  • Rates of Change and Tangent Lines

Chapter 3: Derivatives

  • Derivative of a Function
  • Differentiability
  • Rules of Differentiation
  • Motion along a line: position, velocity, acceleration
  • Derivatives of Trigonometric Functions
  • Chain Rule
  • Derivatives of Parametric equations
  • Implicit Differentiation
  • Derivatives of Inverse Trigonometric Functions
  • Derivatives of Exponential and Logarithmic Functions
  • Logarithmic Differentiation

Chapter 4: Applications of Derivatives

  • Extreme Values of Functions
  • Mean Value Theorem
  • Graphing using the first and second derivative
  • Modeling and Optimization
  • Differentials and linear approximation
  • Newton’s Method
  • Related Rates

Chapter 5: The Definite Integral

  • Estimating with Finite Sums
  • Definite Integrals
  • Definite Integrals and Antiderivatives
  • Indefinite integrals: Recover a function from its growth rate (derivative)
  • Fundamental Theorem of Calculus
  • Trapezoidal Rule

Chapter 6: Differential Equations and Mathematical Modeling

  • Area under a curve
  • Antidifferentiation by Substitution
  • Antidifferentiation by Parts
  • Integration of powers of sines and cosines
  • Exponential Growth and Decay
  • Logistic Growth
  • Partial Fraction Decomposition

Chapter 8: L’Hopital’s Rule

  • L’Hopital’s Rule

Expected levels of student achievement

Course grades will be determined by the collective point totals from assessments, homework, classroom projects/participation and standardized test preparation assignments. It is expected that all students will participate in daily classroom activities and maintain a notebook. Students must complete all assigned work and participate in class discussion.

Technology description

Students are expected to continue to grow in their use of technology. Students are expected to obtain a graphics calculator. We recommend purchasing from the Texas Instruments TI-84 family of calculators. Students are expected to access online resources and grades.

Standardized Test Preparation

The North Allegheny Mathematics Curriculum is designed to prepare students for standardized tests while meeting Pennsylvania State Mathematics Standards and Eligible Content. The focus will be on numbers and operations, algebraic concepts, geometry, data analysis and probability, and measurement. Students will be expected to complete Open Ended tasks throughout the course.