Semester 1

1. FUNCTION & GRAPHS
Functions & function notation 
Absolute Value & Piecewise Defined Functions 
Inequalities 
Composition & Combination of Functions 
Exponential & logarithmic functions 
Transformation of Functions 
Trigonometric Functions 
Polynomial & Rational Functions 

2. LIMITS & CONTINUITY
Intuitive Definition of a Limit 
Algebraic Techniques for Finding Limits 
One-Sided Limits 
Infinite Limits 
Limits at Infinity 
Limits of Special Trigonometric Functions 
Continuity 

3. DERIVATIVES
Definition of the Derivative 
Differentiation Rules 
The Chain Rule 
Derivatives of Exponential Functions 
Derivative of Logarithmic Functions 
Derivatives of Inverse Functions 
Differentiability & Continuity 
Implicit Differentiation 
Logarithmic Differentiation 
Limits & Continuity of Vector-Valued Functions 

4. APPLICATION OF THE DERIVATIVE
Tangent & Normal Lines 
Position, Velocity, & Acceleration (PVA) 
Related rates 
Relative Extrema & the First Derivative Test 
Concavity & the Second Derivative Test 
Absolute Extrema & Optimization 
Rolle's Rule & the Mean Value Theorem 
Differentials 

Semester 2

1. ANTI-DERIVITIVES
Differential Equations and Slope Fields 
Antiderivatives 
The Chain Rule for Antiderivatives 
Antiderivatives of Logarrithms 
Antiderivatives of Inverse Trig Functions 
Trigonometric Substitutions 
The Definite Integral 
Fundamental Theorem of Calculus 

2. APPLICATION
Net Change and Displacement 
Volume 
Separable Differential Equations 
Work 
Other Applications of Definite Integrals