Topics typically covered in Math 1310, Calculus I
1. FUNCTIONS AND MODELS (Review)
Four Ways to Represent a Function. Mathematical Models: A Catalog of
Essential Functions. New Functions from Old Functions. Exponential
Functions. Inverse Functions and Logarithms.
2. LIMITS AND DERIVATIVES.
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.
3. DIFFERENTIATION RULES.
Derivatives of Polynomials and Exponential Functions. The Product
and Quotient Rules. Derivatives of Trigonometric Functions. The
Chain Rule. Implicit Differentiation. Derivatives of
Logarithmic Functions. Related Rates. Linear Approximations
4. APPLICATIONS OF DIFFERENTIATION.
Maximum and Minimum Values. The Mean Value Theorem. How
Derivatives Affect the Shape of a Graph. Indeterminate Forms and
l’Hospital’s Rule. Summary of Curve Sketching. Optimization
Areas and Distances. The Definite Integral. The Fundamental
Theorem of Calculus. Indefinite Integrals and the Net Change
Theorem. The Substitution Rule.
6. APPLICATIONS OF INTEGRATION.
Areas Between Curves. Volume by Slicing and/or Shells.
Average Value of a Function.