MTH 253 Series: Calculus and Linear Algebra

Lecture Hours: 5
Credits: 5

Combines topics from linear algebra and infinite series. Includes geometric, Taylor and Fourier Series work with applications; and systems applications using matrices and determinants.

Prerequisite: Placement into WR 115 (or higher), or completion of WR 090 (or higher); and completion of MTH 252 (or higher) or equivalent course as determined by instructor; or consent of instructor. (All prerequisite courses must be completed with a grade of C or better.)
Student Learning Outcomes:

Create mathematical models of abstract and real-world situations using geometric, power, Taylor and Fourier series, and situations involving linear systems using matrices and determinants.
Use inductive reasoning to develop mathematical conjectures involving infinite series models and linear systems modeled with matrices. Use deductive reasoning to verify and apply mathematical arguments involving these models.
Use mathematical problem-solving techniques involving infinite series and linear systems using matrices.
Make mathematical connections and solve problems from other disciplines involving infinite series and linear systems using matrices.
Use oral and written skills to individually and collaboratively communicate about infinite series and their behavior, and about linear systems using matrices and determinants.
Use appropriate technology to enhance mathematical thinking and understanding, to solve mathematical problems involving infinite series models and to solve problems involving linear systems using matrices and determinants.
Demonstrate independent, nontrivial exploration of infinite series and linear systems applications and models.

Statewide General Education Outcomes:

Use appropriate mathematics to solve problems.
Recognize which mathematical concepts are applicable to a scenario, apply appropriate mathematics and technology in its analysis, and then accurately interpret, validate, and communicate the results.

Content Outline

Infinite Series
- Sequence and series patterns
- Geometric series
- Tests for convergence (including root, ratio, comparison, and integral)
- Binomial series
- Taylor series
- Fourier series, other polynomial series
- Applications of infinite series
- Accuracy in polynomial approximations
Systems of Linear Equations/Linear Algebra
- Row reduction and Echelon forms
- Vector equations and matrix equations
- Vector space
- Span and basis
- Solution sets
- Linear Independence
- Linear transformations
Matrix Algebra
- Matrix operations
- Inverses and their characteristics
- Determinants
Eigenvalues and Eigenvectors
- Characteristic equation
- Linear transformations
- Orthogonal projections