Indiana-Purdue University at Fort Wayne

Honors Calculus - Course Contents



Calculus I - MA 163H

  1. REAL NUMBERS

  2. INEQUALITIES AND ABSOLUTE VALUE

  3. NUMBER SETS

  4. SEQUENCES AND LIMITS OF SEQUENCES
    1. Limits of Number Sequences
    2. Divergent Sequences
    3. Computing with the Limits of Sequences
    4. Monotone Sequences
    5. Non-Monotone Sequences
    6. Sequences with a Variable
    7. Sequences
    		                      Class of 1999-2000

  5. FUNCTIONS
    1. Definition of Functions and Their Graphs
    2. Limits of Functions. Asymptotes
    3. Continuos Functions
    4. Properties of Continuous Functions
    5. Intermediate Value Theorem for Continuos Functions
    6. Monotone Functions and Inverse Functions
    7. Parametric Curves
    8. Project 3
    		                FM Radio signal

  6. DERIVATIVES
    1. Definition of the Velocity. The Slope of the Tangent Line
    2. Rules of Differentiation
    3. The Differentiation of Parametric Equations
    4. Differentiation of Trigonometric Functions
    5. Differentiation of Exponential and Logarithm Functions
    6. Taylor's Formula and the Binomial Theorem
    7. Mean Value Theorem for Derivatives. Rolle's Theorem
    8. Taylor's Polynomial with Lagranges Remainder
    9. Project 4
    		                Class of 1998-1999 with Matt Kubik, Director of the Honors Program

  7. ANALYSIS OF FUNCTIONS
    1. Increasing and Decreasing Functions
    2. First and Second Derivative Test
    3. Extrema Problems
    4. Related Rates

  8. L'HOSPITAL'S RULE

  9. INTEGRALS
    1. The Area Problem. Definite Integrals
    2. The Fundamental Theorem of Calculus
    3. Antiderivatives. Indefinite Integrals
    4. Techniques of Integration
    5. Integration by Substitution
    6. Computation of Areas with Definite Integrals

  10. INTERDISCIPLINARY PROJECTS
    1. Biology
    2. Chemistry
    3. Computer Science
    4. Engineering
    5. Geosciences
    6. Music
    7. Physics

Calculus II - MA 164H

  1. INTEGRALS I
    1. The Area Problem. Definite Integrals
    2. The Fundamental Theorem of Calculus
    3. Antiderivatives. Indefinite Integrals
    4. Techniques of Integration
    5. Integration by Substitution
    6. Computation of Areas with Definite Integrals
    7. Exercises
    8. Project 1

  2. INTEGRALS II
    1. Integration by Parts
    2. Exercises
    3. Improper Integrals
    4. Exercises
    5. Project 2

  3. SERIES
    1. Absolutely Convergent Series
    2. Series with Positive Terms
    3. Stirling's Formula
    4. Series of Functions
    5. Power Series
    6. MacLaurin and Taylor Series
    7. Binomial Series
    8. Integration with Series
    9. Exercises
    10. Project 3

  4. FOURIER SERIES
    1. Riemann's Lemma
    2. Dirichlet's Integral Formula
    3. Convergence Criterion for Fourier Series
    4. Project 4

  5. INTERDISCIPLINARY PROJECTS
    1. Biology
    2. Chemistry
    3. Computer Science
    4. Engineering
    5. Geosciences
    6. Music
    7. Physics