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 Motion diagrams, motion with constant acceleration Simple differentiation rules, tangent lines, models and curve fitting. Motion in two or more dimensions 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 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 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 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 Conservation of momentum, impulse, elastic and inelastic collisions, the center of mass, rocket propulsion Mean Value Theorem, optimization and Newton's method. Rotational motion Rotational kinematics, torque, angular momentum, rigid-body motion Vector product, trigonometric functions and polar coordinates. Oscillatory motion 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 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.