Exploratory and objective data analysis methods applied to the physical, engineering, and biological sciences. Brief review of statistical methods and their computational implementation for studying time series analysis, spectral analysis, filtering methods, principal component analysis, orthogonal mode decomposition, and image processing and compression.
Project-oriented computational approach to solving problems arising in the physical/engineering sciences, finance/economics, medical, social, and biological sciences. Problems requiring use of advanced MATLAB routines and toolboxes. Covers graphical techniques for data presentation and communication of scientific results.
Necessary and sufficient conditions for a weak and strong extremum. Legendre transformation, Hamiltonian systems. Constraints and Lagrange multipliers. Space-time problems with examples from elasticity, electromagnetics, and fluid mechanics. Sturm-Liouville problems. Approximate methods.
Overview methods describing qualitative behavior of solutions on nonlinear differential equations. Phase space analysis of fixed pointed and periodic orbits. Bifurcation methods. Description of strange attractors and chaos. Introductions to maps. Applications: engineering, physics, chemistry, and biology.
The Geometry Tutor is a 9 hour course spread over 2 DVD disks that will aid the student in the core topics of Geometry. Geometry is frequently challenging for students because every problem involves a figure that the student must use to solve the problem. It is very important early on to master the art of reading the geometric figures properly in order to do wellin this subject. The best way to do this is to introduce the definitions early on and solve problems involving diagrams to give the student this much needed practice.
The Algebra Word Problem Tutor is a 6 hour course spread over 2 DVD disks that will aid the student skills needed to master Algebra Word Problems. Word problems are frequently hard for students to master because you have to learn how to extract the information out of the problem and decide how to proceed with finding the solution - and there are usually many ways to do this! This DVD course teaches by examples how to set up algebra word problems and solve them. It is applicable to any Algebra course, SAT, GRE, and other standardized tests.
The Algebra 2 Tutor is a 6 hour course spread over 2 DVD disks that will aid the student in the core topics of Algebra 2. This DVD bridges the gap between Algebra 1 and Trigonometry, and contains essential material to do well in advanced mathematics. Many of the topics in contained in this DVD series are used in other Math courses, such as writing equations of lines, graphing equations, and solving systems of equations. These skills are used time again in more advanced courses such as Physics and Calculus.