Describing motion 
Vectors, functions and
limits 

Displacement, average and instantaneous velocity, average and instantaneous
acceleration. 

Coordinate systems, scalars and vectors, components of vectors, vector addition, the
scalar product, functions, introduction to limits. 
Motion
in one dimension 
Derivatives I
and curve fitting 

Motion diagrams, motion with constant acceleration 

Simple differentiation rules, tangent lines, models and curve fitting. 
Motion
in two or more dimensions 
Derivatives
II and parametric curves 

Motion in a plane, tangential and radial acceleration, projectile motion, circular
motion 

Derivatives and shape of curves, maximum and minimum values, parametric curves. 
The
laws of motion 
Limits and
continuity 

The concept of force, inertial frames, Newton's 2^{nd} and 3^{rd} law,
mass and weight, freebody diagrams 

Limits, continuity and infinite limits. Using the definition of derivative. 
Applications
of Newton's laws 
Derivatives
III 

Uniform and nonuniform circular motion, friction, numerical modeling, the fundamental
forces 

Exponential Functions. Derivative rules, product and quotient rules, chain rule. 
Work
and energy 
Antiderivatives


Work done by varying forces, kinetic energy, conservative and nonconservative forces,
potential energy, conservation of energy 

Antiderivatives, slope fields and simple integration. Rates of Change. Related rates. 
Momentum 
Mean Value
Theorem, Optimization and Newton's Method 

Conservation of momentum, impulse, elastic and inelastic collisions, the center of
mass, rocket propulsion 

Mean Value Theorem, optimization and Newton's method. 
Rotational
motion 
Trigonometric
functions 

Rotational kinematics, torque, angular momentum, rigidbody motion 

Vector product, trigonometric functions and polar coordinates. 
Oscillatory
motion 
Calculus and
trigonometric functions 

Simple harmonic motion, a mass on a spring, a physical pendulum, forced and damped
oscillations 

Derivatives of trigonometric functions. L'Hospital's rule. 
Wave
motion 
Implicit and
inverse functions 

Sinusoidal travelling waves, reflection and transmission, the Doppler effect,
superposition and interference, standing waves 

Implicit functions, inverse functions, logs, derivatives of logs and inverse trig
functions. 