## Knowledge Expectations for METR 3113 Atmospheric Dynamics I: Introduction to Atmospheric Kinematics and Dynamics

Purpose: This document describes the principal concepts, technical skills, and fundamental
understanding that all students are expected to possess upon completing METR 3113, Introduction to
Atmospheric Dynamics and Kinematics. Individual instructors may deviate somewhat from the specific
topics and order listed here.

Pre-requisites: Grade of C or better in MATH 2443, PHYS 2524, and METR 2024 (or 2413).
Co-Requisite: MATH 3113.

Students should have a working knowledge of integration, total and partial differentiation,
vectors, analytic geometry, force, velocity, acceleration, Newton’s laws of motion, and basic
thermodynamics. They also should understand the basic structure and physics of the atmosphere and
the principal forces acting upon it prior to starting this course.

Goal of the Course: This course lays the foundation for characterizing the atmosphere
mathematically, for identifying and expressing analytically the forces acting upon it, and for
using various approximations to understand its behavior.

I. Basic Concepts of Calculus and Physics
• Understand the concept of a vector (especially how it differs from a scalar), unit vectors, and
be able to take derivatives of vectors. Be able to operate on vectors and on appropriate products
of vectors and scalars, using the scalar, vector, and inner products, as well as divergence,
gradient, curl, and Laplace operators. Understand the mathematical and physical concepts of
divergence, gradient, curl, and Laplacian and know and be able to apply the vector integral
theorems of Stokes and Gauss.
• Be able to write down from memory and apply the Taylor series expansion and understand its
meaning and practical use.
• Understand and be able to apply absolute and relative motion concepts, work with and convert
between units (SI, Imperial), and understand notions of dimension, precision, accuracy and error.

II. Newton’s Laws of Motion; Energy, Equilibrium and Stability
• Know from memory, both in equation form and from a physical understanding point of view, all
three of Newton’s laws of motion as well as the law of gravitation.
• Understand the concept of balanced and unbalanced forces as related to acceleration and be able
to apply Newton’s Second Law of Motion to one-dimensional problems of variable force and mass.
• Understand the basic physical and mathematical principles of linear versus nonlinear systems
(e.g., the notion of feedback), and be able to apply in quantitative problems the concepts of work,
potential and kinetic energy, energy equilibrium, energy conservation, and energy conversion.
• Understand the physical and mathematical concepts of one-dimensional simple harmonic motion,
particularly as applied to parcel stability theory in the atmosphere, and be able to work
associated problems in which the forcing is either constant or variable.
• Understand, both mathematically and physically, the concept of an eigenvalue in simple
physical
systems.