Course Outline

Limits and Continuity of Functions

A. Find limits graphically from sketches and/or graphing calculators.

B. Estimate limits using tables of data.

C. Evaluate limits analytically.

D. Continuity and one-sided limits

E. Intermediate Value Theorem

F. Infinite limits and vertical asymptotes

Derivatives

A. Definition of a derivative, alternative form of the definition of derivative

B. Basic Rules of differentiation

C. Implicit and logarithmic differentiation

D. Curve Sketching: extrema, inflection points, first and second derivative tests

E. Rolle’s Theorem and Mean Value Theorem

F. Optimization: Related rates and Motion applications

G. Local linearity and tangent line approximations

Integration

A. Riemann Sums and Trapezoid Rule

B. First and Second Fundamental Theorems of Calculus

C. Average value of a function on a closed interval

D. U-Substitution technique for integrating

Functions Defined by an Integral

Differential Equations

A. Separable Differential equations

B. Growth and Decay applications

C. Newton’s Law of Cooling

D. Slope Fields

Applications of Integration

A. Area between two curves

B. Solids of revolution

C. Known cross sections

D. Arc Lengths

Integration Techniques, L’Hopital’s Rule, and Improper Integrals

A. Integration by parts

B. Trigonometric integrals

C. Integration by partial fractions

D. Solving logistic differential equations

E. L’Hopital’s Rule

F. Improper integrals and their convergence and divergence

Plane Curves, Parametric Equations, and Polar Curves

A. Plane curves, parametric equations and vectors

B. Polar coordinates and polar graphs

C. Area of a region bounded by polar curves

Infinite Series

A. Convergence and divergence of sequences

B. Definition and Convergence of a series

C. Geometric series and applications

D. P-series

E. Power series and radius and interval of convergence

F. Taylor and Maclaurin series