Single Variable Calculus II with Matrix Algebra

Course #MA1114

Start Starts: not available

Clock Est. completion in 5 weeks

Location pin Offered through Distance Learning

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Overview

Topics in calculus include applications of integration, special techniques of integration, infinite series, convergence tests, and Taylor series. Matrix algebra topics covered are: the fundamental algebra of matrices including addition, multiplication of matrices, multiplication of a matrix by a constant and a column (vector) by a matrix; elementary matrices and inverses, together with the properties of these operations; solutions to mxn systems of linear algebraic equations using Gaussian elimination and the LU decomposition (without pivoting); determinants, properties of determinants; and a brief introduction to the arithmetic of complex numbers and DeMoivre's theorem. Taught at the rate of nine hours per week for five weeks.

Prerequisites

  • MA1113

Learning Outcomes

  • Use integration to find the area between curves; find volumes of solids of revolution; find total work done in appropriate problems; find the average value of a function.
  • Evaluate appropriate integrals by using trigonometric identities and trigonometric substitution.
  • Use the method of partial fractions to evaluate integrals of rational functions.
  • Recognize improper integrals, determine whether they converge, and if possible, evaluate them.
  • Determine whether or not a sequence converges and if it does, find its limit.
  • Determine whether or not a series converges by appropriate tests, including the ratio, comparison, p-series, and alternating series tests.
  • Find the interval of convergence for a power series.
  • Apply Taylor’s Theorem to find polynomial approximations to given functions and estimate their accuracy.
  • Perform arithmetic operations on complex numbers (addition, subtraction, multiplication, division, raising to powers), determine the magnitude, argument, real part, imaginary part, complex conjugate, and convert between rectangular and polar coordinates.
  • Apply De Moivre’s Theorem; find nth roots of complex numbers; state Euler’s formula.
  • Use Gauss-Jordan elimination to find the general solution for a linear system with m equations and n unknown variables, determine the type of solution set (inconsistent, unique solution, or infinitely many solutions) by Gauss elimination.
  • Perform algebraic operations on matrices and vectors: addition, subtraction, scalar multiplication, matrix multiplication and transposition.
  • Define and describe the basic properties of the inverse of a matrix and find the inverse of a square matrix using Gauss-Jordan method.
  • Compute the determinant of a square matrix either by elementary row operations (EROs) or by cofactor expansion.
  • Use Cramer’s rule (where applicable) to solve small systems of linear equations. Explain why Cramer’s rule is inappropriate for large systems.
  • Find the eigenvalues and associated eigenvectors of square matrices, including cases of repeated or complex eigenvalues.