Course for Biology and Information Systems students

Syllabus

• Four Ways to Represent a Function
• Mathematical Models: A Catalog of Essential Functions
• New Functions from Old Functions
• Exponential Function
• Inverse Functions and Logarithms
• The Tangent and Velocity Problems
• The Limit of a Function
• Calculating Limits Using the Limit Laws
• The Precise Definition of a Limit
• Continuity
• Limits at Infinity; Horizontal Asymptotes
• Derivatives and Rates of Change
• The Derivative as a Function
• Derivatives of Polynomials and Exponential Functions
• The Product and Quotient Rules
• Derivatives of Trigonometric Functions
• The Chain Rule
• Implicit Differentiation
• Derivatives of Logarithmic Functions
• Rates of Change in the Natural and Social Sciences
• Exponential Growth and Decay
• Related Rates
• Linear Approximations and Differentials
• Maximum and Minimum Values
• The Mean Value Theorem
• How Derivatives Affect the Shape of a Graph
• Indeterminate Forms and l’Hospitals Rule
• Summary of Curve Sketching
• Graphing with Calculus and Calculators
• Optimization Problems
• Newtons Method
• Antiderivatives
• Areas and Distances
• The Definite Integral
• Fundamental Theorem of Calculus
• Indefinite Integrals and the Net Change Theorem
• The Substitution Rule
• Areas Between Curves
• Volumes
• Volumes by Cylindrical Shells
• Work
• Average Value of a Function
• Integration by Parts