Course Modules:

Module 1: Functions and Derivatives

Section 1: Relations and functions; Graphing techniques; Absolute value; Point-slope form of a line

Section 2: Tangent and sectant lines; Position and velocity; Rates of change; Definition of a derivative

Section 3: Limit of a function; One-sided limits; Continuity; Limit properties; Indeterminate forms

Section 4: Rules for differentiation: polynomials, product, quotient, and power rules; Composition of functions

Module 1 Test covers the work of Module 1.

Module 2: Properties and Derivatives

Section 1: Implicit differentiation; Velocity and acceleration

Section 2: Tangent line approximation; Newton’s method

Section 3: Related rates; Maximum and minimum values; Optimization problems

Section 4: Relative extreme; Vertical asymptotes; Horizontal asymptotes

Section 5: Graphing overview; Concavity; Miscellaneous graphing techniques; Other graphing problems

Module 2 Test covers the work of Modules 1 and 2.

Module 3: Trigonometric Derivatives

Section 1: Trigonometry review; Trigonometric limits; Derivatives of sine and cosine

Section 2: Derivatives of other trig functions; Applications; Inverse functions, arcsine and arctangent; Derivatives of arcsine and arctangent

Section 3: Exponential and logarithmic functions review; The fundamental exponential limit, and the natural logarithmic and exponential functions; Derivatives of logarithmic functions

Section 4: Derivatives of exponential functions; Applications; Logarithmic differentiation

Section 5: Another look at limits; L’Hôpital’s Rule; Mean Value theorem

Module 3 Test covers the work of Modules 1, 2 and 3.

Module 4: Integral Calculus

Section 1: Calculating antiderivatives; Position, velocity, and acceleration—a new look; Differential equations

Section 2: Approximating area; Riemann sums; The fundamental theorem of calculus; The definite integral

Section 3: Properties of the definite integral; Area between curves; Mean value of a function

Section 4: Integration by substitution; Integration by parts; Volumes of revolution-disk/washer method and shell method of volumes with known cross sections

Module 4 Test covers the WHOLE COURSE.