## 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.