ChE Tulsa University

 
           

MATH 2014 Calculus I
Required course for ChE program

Catalog Description:  Theory and application of differential calculus of polynomial, exponential, logarithmic, and trigonometric functions. Graphical, numerical, and analytical solutions to applied problems involving derivatives.  Introduction to the integral. 

Prerequisites:  Math 1163 or equivalent, and passing score on the university placement examination.

Corequisites:  none

Prerequisites by Topic:  Solid algebra foundation.

Textbook:  Calculus – Early Transcendentals, 5th Edition , James Stewart

Other Required Material:  None

Course Objectives: Differential calculus and introduction to integral calculus.

Topics Covered:  

  1. Functions and models
    Four Ways to Represent a Function. Mathematical Models: A Catalog of Essential Functions. New Functions from Old Functions. Exponential Functions. Inverse Functions and Logarithms.
  1. Limits and derivatives
    The Tangent and Velocity Problems. The Limit of a Function. Calculating Limits Using the Limit Laws. Continuity. Limits at Infinity; Horizontal Asymptotes. Tangents, Velocities, and Other Rates of Change. Derivatives. The Derivative as a Function.
  1. Differentiation rules
    Derivatives of Polynomials and Exponential Functions. The Product and Quotient Rules. Rates of Change in the Natural and Social Sciences. Derivatives of Trigonometric Functions. The Chain Rule. Implicit Differentiation. Higher Derivatives. Derivatives of Logarithmic Functions. Related Rates. Linear Approximations and Differentials.
  1. Applications of differentiation
    Maximum and Minimum Values. How Derivatives Affect the Shape of a Graph. Indeterminate Forms and L’Hospital’s Rule. Summary of Curve Sketching. Optimization Problems. Antiderivatives.
  • 5. Integrals
    Areas and Distances. The Definite Integral. The Fundamental Theorem of Calculus. Indefinite Integrals and the Net Change Theorem.

Class/Laboratory Schedule: 

Professional Component Contribution: 

Learning mathematical tools to assist in solving real-world science and engineering problems

 Relationship to Program Outcomes: 

  • Outcome a: This course requires the students to apply their knowledge of mathematics.
  • Outcome b: At least one team project is assigned.

Prepared by:  Shirley Pomeranz