Develop essential mathematics skills with expert instruction and practical examples.
Linear Algebra and Geometry 1Systems of equations, matrices, vectors, and geometryChapter 1: Systems of linear equationsS1. Introduction to the courseS2. Some basic conceptsYou will learn: some basic concepts that will be used in this course.
Most of them are known from high-school courses in mathematics, some of them are new; the latter will appear later in the course and will be treated more in depth then. S3. Systems of linear equations; building up your geometrical intuitionYou will learn: some basic concepts about linear equations and systems of linear equations; geometry behind systems of linear equations.
S4. Solving systems of linear equations; Gaussian eliminationYou will learn: solve systems of linear equations using Gaussian elimination (and back-substitution) and Gauss-Jordan elimination in cases of systems with unique solutions, inconsistent systems, and systems with infinitely many solutions (parameter solutions). S5.
Some applications in mathematics and natural sciencesYou will learn: how systems of linear equations are used in other branches of mathematics and in natural sciences. Chapter 2: Matrices and determinantsS6. Matrices and matrix operationsYou will learn: the definition of matrices and their arithmetic operations (matrix addition, matrix subtraction, scalar multiplication, matrix multiplication).
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