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 2nd and 3rd law, mass and weight, free-body diagrams Limits, continuity and infinite limits. Using the definition of derivative.
Applications of Newton's laws

Derivatives III

Uniform and non-uniform 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 non-conservative 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, rigid-body 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.