Purpose/Objectives:

 

Quantitative methods are important tools in environmental and earth sciences and many other disciplines. It is my belief that these tools are best learned through applied applications. At the end of this course students will be prepared to apply concepts from trigonometry, linear algebra, calculus, and differential equations to solve problems in earth and environmental sciences. Mathematical topics covered will incude:

 Matrix algebra

 Solving systems of equations

 Trigonometric functions

 Eigenvalues and Eigenvectors

 Derivatives (ordinary and partial)

 Integrals

 Numerical integration

 Ordinary differential equations

 

Environmental and earth science topics covered in this course will be diverse, but will include:

 Pesticide movement through watersheds

 Solving systems of chemical reactions

 Population viability analysis for endangered species

 Predator-prey relationships

 Interannual variability in biogeochemical fluxes

 Measuring climate change and uncertainty

 

 

Toolboxes:

Toolbox 1.1: Intro/Vector Algebra

Toolbox 1.2: Matrix Algebra I

Toolbox 1.3: Matrix Algebra II

Toolbox 2.1: Functions I

Toolbox 2.2: Functions II

Toolbox 2.3: Functions III

Toolbox 3.1: Trig Functions & the Unit Circle

Toolbox 4.1: Matrix Inverses

Toolbox 4.2: Determinants

Toolbox 5.1: Introduction to Coordinate Systems

Toolbox 5.2: The Spherical Coordinate System

Toolbox 6.1: Eigenvalues & Eigenvectors I

Toolbox 6.2: Eigenvalues & Eigenvectors II

Toolbox 7.1: Introduction to Derivatives

Toolbox 7.2: Derivatives II

Toolbox 7.3: Derivatives III

Toolbox 7.4: Chain Rule for Derivatives

Toolbox 8.1: Partial Derivatives I

Toolbox 8.2: Partial Derivatives II

Toolbox 9.1: Antiderivatives & Integrals

Toolbox 9.2: Integrals II

Toolbox 9.3: Numerical Integration

Toolbox 10.1: Ordinary Differential Equations

 

Problem Sets:

Problem Set 1: Basic Linear Algebra & Functions

Problem Set 2: Trigonometry & Functions of matrices

Problem Set 3: Functions, Linear Algebra & Coordinate Systems

Problem Set 4: Eigenvectors & Derivatives